Mercurial > dropbear
changeset 142:d29b64170cf0 libtommath-orig
import of libtommath 0.32
line wrap: on
line diff
--- a/bn.ind Tue Jun 15 14:42:57 2004 +0000 +++ b/bn.ind Sun Dec 19 11:33:56 2004 +0000 @@ -1,82 +1,82 @@ \begin{theindex} - \item mp\_add, \hyperpage{25} - \item mp\_add\_d, \hyperpage{48} - \item mp\_and, \hyperpage{25} - \item mp\_clear, \hyperpage{7} - \item mp\_clear\_multi, \hyperpage{8} - \item mp\_cmp, \hyperpage{20} - \item mp\_cmp\_d, \hyperpage{21} - \item mp\_cmp\_mag, \hyperpage{19} - \item mp\_div, \hyperpage{26} - \item mp\_div\_2, \hyperpage{22} - \item mp\_div\_2d, \hyperpage{24} - \item mp\_div\_d, \hyperpage{48} - \item mp\_dr\_reduce, \hyperpage{36} - \item mp\_dr\_setup, \hyperpage{36} - \item MP\_EQ, \hyperpage{18} - \item mp\_error\_to\_string, \hyperpage{6} - \item mp\_expt\_d, \hyperpage{39} - \item mp\_exptmod, \hyperpage{39} - \item mp\_exteuclid, \hyperpage{47} - \item mp\_gcd, \hyperpage{47} - \item mp\_get\_int, \hyperpage{16} - \item mp\_grow, \hyperpage{12} - \item MP\_GT, \hyperpage{18} - \item mp\_init, \hyperpage{7} - \item mp\_init\_copy, \hyperpage{9} - \item mp\_init\_multi, \hyperpage{8} - \item mp\_init\_set, \hyperpage{17} - \item mp\_init\_set\_int, \hyperpage{17} - \item mp\_init\_size, \hyperpage{10} - \item mp\_int, \hyperpage{6} - \item mp\_invmod, \hyperpage{48} - \item mp\_jacobi, \hyperpage{48} - \item mp\_lcm, \hyperpage{47} - \item mp\_lshd, \hyperpage{24} - \item MP\_LT, \hyperpage{18} - \item MP\_MEM, \hyperpage{5} - \item mp\_mod, \hyperpage{31} - \item mp\_mod\_d, \hyperpage{48} - \item mp\_montgomery\_calc\_normalization, \hyperpage{34} - \item mp\_montgomery\_reduce, \hyperpage{33} - \item mp\_montgomery\_setup, \hyperpage{33} - \item mp\_mul, \hyperpage{27} - \item mp\_mul\_2, \hyperpage{22} - \item mp\_mul\_2d, \hyperpage{24} - \item mp\_mul\_d, \hyperpage{48} - \item mp\_n\_root, \hyperpage{40} - \item mp\_neg, \hyperpage{25} - \item MP\_NO, \hyperpage{5} - \item MP\_OKAY, \hyperpage{5} - \item mp\_or, \hyperpage{25} - \item mp\_prime\_fermat, \hyperpage{41} - \item mp\_prime\_is\_divisible, \hyperpage{41} - \item mp\_prime\_is\_prime, \hyperpage{42} - \item mp\_prime\_miller\_rabin, \hyperpage{41} - \item mp\_prime\_next\_prime, \hyperpage{42} - \item mp\_prime\_rabin\_miller\_trials, \hyperpage{42} - \item mp\_prime\_random, \hyperpage{43} - \item mp\_prime\_random\_ex, \hyperpage{43} - \item mp\_radix\_size, \hyperpage{45} - \item mp\_read\_radix, \hyperpage{45} - \item mp\_read\_unsigned\_bin, \hyperpage{46} - \item mp\_reduce, \hyperpage{32} - \item mp\_reduce\_2k, \hyperpage{37} - \item mp\_reduce\_2k\_setup, \hyperpage{37} - \item mp\_reduce\_setup, \hyperpage{32} - \item mp\_rshd, \hyperpage{24} - \item mp\_set, \hyperpage{15} - \item mp\_set\_int, \hyperpage{16} - \item mp\_shrink, \hyperpage{11} - \item mp\_sqr, \hyperpage{29} - \item mp\_sub, \hyperpage{25} - \item mp\_sub\_d, \hyperpage{48} - \item mp\_to\_unsigned\_bin, \hyperpage{46} - \item mp\_toradix, \hyperpage{45} - \item mp\_unsigned\_bin\_size, \hyperpage{46} - \item MP\_VAL, \hyperpage{5} - \item mp\_xor, \hyperpage{25} - \item MP\_YES, \hyperpage{5} + \item mp\_add, \hyperpage{29} + \item mp\_add\_d, \hyperpage{52} + \item mp\_and, \hyperpage{29} + \item mp\_clear, \hyperpage{11} + \item mp\_clear\_multi, \hyperpage{12} + \item mp\_cmp, \hyperpage{24} + \item mp\_cmp\_d, \hyperpage{25} + \item mp\_cmp\_mag, \hyperpage{23} + \item mp\_div, \hyperpage{30} + \item mp\_div\_2, \hyperpage{26} + \item mp\_div\_2d, \hyperpage{28} + \item mp\_div\_d, \hyperpage{52} + \item mp\_dr\_reduce, \hyperpage{40} + \item mp\_dr\_setup, \hyperpage{40} + \item MP\_EQ, \hyperpage{22} + \item mp\_error\_to\_string, \hyperpage{10} + \item mp\_expt\_d, \hyperpage{43} + \item mp\_exptmod, \hyperpage{43} + \item mp\_exteuclid, \hyperpage{51} + \item mp\_gcd, \hyperpage{51} + \item mp\_get\_int, \hyperpage{20} + \item mp\_grow, \hyperpage{16} + \item MP\_GT, \hyperpage{22} + \item mp\_init, \hyperpage{11} + \item mp\_init\_copy, \hyperpage{13} + \item mp\_init\_multi, \hyperpage{12} + \item mp\_init\_set, \hyperpage{21} + \item mp\_init\_set\_int, \hyperpage{21} + \item mp\_init\_size, \hyperpage{14} + \item mp\_int, \hyperpage{10} + \item mp\_invmod, \hyperpage{52} + \item mp\_jacobi, \hyperpage{52} + \item mp\_lcm, \hyperpage{51} + \item mp\_lshd, \hyperpage{28} + \item MP\_LT, \hyperpage{22} + \item MP\_MEM, \hyperpage{9} + \item mp\_mod, \hyperpage{35} + \item mp\_mod\_d, \hyperpage{52} + \item mp\_montgomery\_calc\_normalization, \hyperpage{38} + \item mp\_montgomery\_reduce, \hyperpage{37} + \item mp\_montgomery\_setup, \hyperpage{37} + \item mp\_mul, \hyperpage{31} + \item mp\_mul\_2, \hyperpage{26} + \item mp\_mul\_2d, \hyperpage{28} + \item mp\_mul\_d, \hyperpage{52} + \item mp\_n\_root, \hyperpage{44} + \item mp\_neg, \hyperpage{29} + \item MP\_NO, \hyperpage{9} + \item MP\_OKAY, \hyperpage{9} + \item mp\_or, \hyperpage{29} + \item mp\_prime\_fermat, \hyperpage{45} + \item mp\_prime\_is\_divisible, \hyperpage{45} + \item mp\_prime\_is\_prime, \hyperpage{46} + \item mp\_prime\_miller\_rabin, \hyperpage{45} + \item mp\_prime\_next\_prime, \hyperpage{46} + \item mp\_prime\_rabin\_miller\_trials, \hyperpage{46} + \item mp\_prime\_random, \hyperpage{47} + \item mp\_prime\_random\_ex, \hyperpage{47} + \item mp\_radix\_size, \hyperpage{49} + \item mp\_read\_radix, \hyperpage{49} + \item mp\_read\_unsigned\_bin, \hyperpage{50} + \item mp\_reduce, \hyperpage{36} + \item mp\_reduce\_2k, \hyperpage{41} + \item mp\_reduce\_2k\_setup, \hyperpage{41} + \item mp\_reduce\_setup, \hyperpage{36} + \item mp\_rshd, \hyperpage{28} + \item mp\_set, \hyperpage{19} + \item mp\_set\_int, \hyperpage{20} + \item mp\_shrink, \hyperpage{15} + \item mp\_sqr, \hyperpage{33} + \item mp\_sub, \hyperpage{29} + \item mp\_sub\_d, \hyperpage{52} + \item mp\_to\_unsigned\_bin, \hyperpage{50} + \item mp\_toradix, \hyperpage{49} + \item mp\_unsigned\_bin\_size, \hyperpage{50} + \item MP\_VAL, \hyperpage{9} + \item mp\_xor, \hyperpage{29} + \item MP\_YES, \hyperpage{9} \end{theindex}
--- a/bn.tex Tue Jun 15 14:42:57 2004 +0000 +++ b/bn.tex Sun Dec 19 11:33:56 2004 +0000 @@ -49,7 +49,7 @@ \begin{document} \frontmatter \pagestyle{empty} -\title{LibTomMath User Manual \\ v0.30} +\title{LibTomMath User Manual \\ v0.32} \author{Tom St Denis \\ [email protected]} \maketitle This text, the library and the accompanying textbook are all hereby placed in the public domain. This book has been @@ -96,27 +96,34 @@ also build in MSVC, Borland C out of the box. For any other ISO C compiler a makefile will have to be made by the end developer. -To build the library for GCC simply issue the - +\subsection{Static Libraries} +To build as a static library for GCC issue the following \begin{alltt} make \end{alltt} -command. This will build the library and archive the object files in ``libtommath.a''. Now you simply link against that -and include ``tommath.h'' within your programs. - -Alternatively to build with MSVC type - +command. This will build the library and archive the object files in ``libtommath.a''. Now you link against +that and include ``tommath.h'' within your programs. Alternatively to build with MSVC issue the following \begin{alltt} nmake -f makefile.msvc \end{alltt} -This will build the library and archive the object files in ``tommath.lib''. This has been tested with MSVC version 6.00 -with service pack 5. +This will build the library and archive the object files in ``tommath.lib''. This has been tested with MSVC +version 6.00 with service pack 5. -There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile. It requires Cygwin -to work with since it requires the auto-export/import functionality. The resulting DLL and imprt library ``libtomcrypt.dll.a'' -can be used to link LibTomMath dynamically to any Windows program using Cygwin. +\subsection{Shared Libraries} +To build as a shared library for GCC issue the following +\begin{alltt} +make -f makefile.shared +\end{alltt} +This requires the ``libtool'' package (common on most Linux/BSD systems). It will build LibTomMath as both shared +and static then install (by default) into /usr/lib as well as install the header files in /usr/include. The shared +library (resource) will be called ``libtommath.la'' while the static library called ``libtommath.a''. Generally +you use libtool to link your application against the shared object. + +There is limited support for making a ``DLL'' in windows via the ``makefile.cygwin\_dll'' makefile. It requires +Cygwin to work with since it requires the auto-export/import functionality. The resulting DLL and import library +``libtommath.dll.a'' can be used to link LibTomMath dynamically to any Windows program using Cygwin. \subsection{Testing} To build the library and the test harness type @@ -144,6 +151,96 @@ that is being performed. The numbers represent how many times the test was invoked. If an error is detected the program will exit with a dump of the relevent numbers it was working with. +\section{Build Configuration} +LibTomMath can configured at build time in three phases we shall call ``depends'', ``tweaks'' and ``trims''. +Each phase changes how the library is built and they are applied one after another respectively. + +To make the system more powerful you can tweak the build process. Classes are defined in the file +``tommath\_superclass.h''. By default, the symbol ``LTM\_ALL'' shall be defined which simply +instructs the system to build all of the functions. This is how LibTomMath used to be packaged. This will give you +access to every function LibTomMath offers. + +However, there are cases where such a build is not optional. For instance, you want to perform RSA operations. You +don't need the vast majority of the library to perform these operations. Aside from LTM\_ALL there is +another pre--defined class ``SC\_RSA\_1'' which works in conjunction with the RSA from LibTomCrypt. Additional +classes can be defined base on the need of the user. + +\subsection{Build Depends} +In the file tommath\_class.h you will see a large list of C ``defines'' followed by a series of ``ifdefs'' +which further define symbols. All of the symbols (technically they're macros $\ldots$) represent a given C source +file. For instance, BN\_MP\_ADD\_C represents the file ``bn\_mp\_add.c''. When a define has been enabled the +function in the respective file will be compiled and linked into the library. Accordingly when the define +is absent the file will not be compiled and not contribute any size to the library. + +You will also note that the header tommath\_class.h is actually recursively included (it includes itself twice). +This is to help resolve as many dependencies as possible. In the last pass the symbol LTM\_LAST will be defined. +This is useful for ``trims''. + +\subsection{Build Tweaks} +A tweak is an algorithm ``alternative''. For example, to provide tradeoffs (usually between size and space). +They can be enabled at any pass of the configuration phase. + +\begin{small} +\begin{center} +\begin{tabular}{|l|l|} +\hline \textbf{Define} & \textbf{Purpose} \\ +\hline BN\_MP\_DIV\_SMALL & Enables a slower, smaller and equally \\ + & functional mp\_div() function \\ +\hline +\end{tabular} +\end{center} +\end{small} + +\subsection{Build Trims} +A trim is a manner of removing functionality from a function that is not required. For instance, to perform +RSA cryptography you only require exponentiation with odd moduli so even moduli support can be safely removed. +Build trims are meant to be defined on the last pass of the configuration which means they are to be defined +only if LTM\_LAST has been defined. + +\subsubsection{Moduli Related} +\begin{small} +\begin{center} +\begin{tabular}{|l|l|} +\hline \textbf{Restriction} & \textbf{Undefine} \\ +\hline Exponentiation with odd moduli only & BN\_S\_MP\_EXPTMOD\_C \\ + & BN\_MP\_REDUCE\_C \\ + & BN\_MP\_REDUCE\_SETUP\_C \\ + & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\ + & BN\_FAST\_S\_MP\_MUL\_HIGH\_DIGS\_C \\ +\hline Exponentiation with random odd moduli & (The above plus the following) \\ + & BN\_MP\_REDUCE\_2K\_C \\ + & BN\_MP\_REDUCE\_2K\_SETUP\_C \\ + & BN\_MP\_REDUCE\_IS\_2K\_C \\ + & BN\_MP\_DR\_IS\_MODULUS\_C \\ + & BN\_MP\_DR\_REDUCE\_C \\ + & BN\_MP\_DR\_SETUP\_C \\ +\hline Modular inverse odd moduli only & BN\_MP\_INVMOD\_SLOW\_C \\ +\hline Modular inverse (both, smaller/slower) & BN\_FAST\_MP\_INVMOD\_C \\ +\hline +\end{tabular} +\end{center} +\end{small} + +\subsubsection{Operand Size Related} +\begin{small} +\begin{center} +\begin{tabular}{|l|l|} +\hline \textbf{Restriction} & \textbf{Undefine} \\ +\hline Moduli $\le 2560$ bits & BN\_MP\_MONTGOMERY\_REDUCE\_C \\ + & BN\_S\_MP\_MUL\_DIGS\_C \\ + & BN\_S\_MP\_MUL\_HIGH\_DIGS\_C \\ + & BN\_S\_MP\_SQR\_C \\ +\hline Polynomial Schmolynomial & BN\_MP\_KARATSUBA\_MUL\_C \\ + & BN\_MP\_KARATSUBA\_SQR\_C \\ + & BN\_MP\_TOOM\_MUL\_C \\ + & BN\_MP\_TOOM\_SQR\_C \\ + +\hline +\end{tabular} +\end{center} +\end{small} + + \section{Purpose of LibTomMath} Unlike GNU MP (GMP) Library, LIP, OpenSSL or various other commercial kits (Miracl), LibTomMath was not written with bleeding edge performance in mind. First and foremost LibTomMath was written to be entirely open. Not only is the
--- a/bn_error.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_error.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_ERROR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> static const struct { int code; @@ -39,3 +40,4 @@ return "Invalid error code"; } +#endif
--- a/bn_fast_mp_invmod.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_fast_mp_invmod.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_FAST_MP_INVMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,12 +14,11 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* computes the modular inverse via binary extended euclidean algorithm, * that is c = 1/a mod b * - * Based on mp_invmod except this is optimized for the case where b is + * Based on slow invmod except this is optimized for the case where b is * odd as per HAC Note 14.64 on pp. 610 */ int @@ -141,3 +142,4 @@ __ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); return res; } +#endif
--- a/bn_fast_mp_montgomery_reduce.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_fast_mp_montgomery_reduce.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,11 +14,10 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* computes xR**-1 == x (mod N) via Montgomery Reduction * - * This is an optimized implementation of mp_montgomery_reduce + * This is an optimized implementation of montgomery_reduce * which uses the comba method to quickly calculate the columns of the * reduction. * @@ -165,3 +166,4 @@ } return MP_OKAY; } +#endif
--- a/bn_fast_s_mp_mul_digs.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_fast_s_mp_mul_digs.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_FAST_S_MP_MUL_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* Fast (comba) multiplier * @@ -33,8 +34,9 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { - int olduse, res, pa, ix; - mp_word W[MP_WARRAY]; + int olduse, res, pa, ix, iz; + mp_digit W[MP_WARRAY]; + register mp_word _W; /* grow the destination as required */ if (c->alloc < digs) { @@ -43,82 +45,52 @@ } } - /* clear temp buf (the columns) */ - memset (W, 0, sizeof (mp_word) * digs); + /* number of output digits to produce */ + pa = MIN(digs, a->used + b->used); - /* calculate the columns */ - pa = a->used; - for (ix = 0; ix < pa; ix++) { - /* this multiplier has been modified to allow you to - * control how many digits of output are produced. - * So at most we want to make upto "digs" digits of output. - * - * this adds products to distinct columns (at ix+iy) of W - * note that each step through the loop is not dependent on - * the previous which means the compiler can easily unroll - * the loop without scheduling problems - */ - { - register mp_digit tmpx, *tmpy; - register mp_word *_W; - register int iy, pb; + /* clear the carry */ + _W = 0; + for (ix = 0; ix <= pa; ix++) { + int tx, ty; + int iy; + mp_digit *tmpx, *tmpy; + + /* get offsets into the two bignums */ + ty = MIN(b->used-1, ix); + tx = ix - ty; - /* alias for the the word on the left e.g. A[ix] * A[iy] */ - tmpx = a->dp[ix]; + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = b->dp + ty; - /* alias for the right side */ - tmpy = b->dp; - - /* alias for the columns, each step through the loop adds a new - term to each column + /* this is the number of times the loop will iterrate, essentially its + while (tx++ < a->used && ty-- >= 0) { ... } */ - _W = W + ix; + iy = MIN(a->used-tx, ty+1); - /* the number of digits is limited by their placement. E.g. - we avoid multiplying digits that will end up above the # of - digits of precision requested - */ - pb = MIN (b->used, digs - ix); + /* execute loop */ + for (iz = 0; iz < iy; ++iz) { + _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); + } - for (iy = 0; iy < pb; iy++) { - *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++); - } - } + /* store term */ + W[ix] = ((mp_digit)_W) & MP_MASK; + /* make next carry */ + _W = _W >> ((mp_word)DIGIT_BIT); } /* setup dest */ - olduse = c->used; + olduse = c->used; c->used = digs; { register mp_digit *tmpc; - - /* At this point W[] contains the sums of each column. To get the - * correct result we must take the extra bits from each column and - * carry them down - * - * Note that while this adds extra code to the multiplier it - * saves time since the carry propagation is removed from the - * above nested loop.This has the effect of reducing the work - * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the - * cost of the shifting. On very small numbers this is slower - * but on most cryptographic size numbers it is faster. - * - * In this particular implementation we feed the carries from - * behind which means when the loop terminates we still have one - * last digit to copy - */ tmpc = c->dp; - for (ix = 1; ix < digs; ix++) { - /* forward the carry from the previous temp */ - W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT)); - + for (ix = 0; ix < digs; ix++) { /* now extract the previous digit [below the carry] */ - *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); + *tmpc++ = W[ix]; } - /* fetch the last digit */ - *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK)); /* clear unused digits [that existed in the old copy of c] */ for (; ix < olduse; ix++) { @@ -128,3 +100,4 @@ mp_clamp (c); return MP_OKAY; } +#endif
--- a/bn_fast_s_mp_mul_high_digs.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_fast_s_mp_mul_high_digs.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,10 +14,9 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ - #include <tommath.h> -/* this is a modified version of fast_s_mp_mul_digs that only produces - * output digits *above* digs. See the comments for fast_s_mp_mul_digs +/* this is a modified version of fast_s_mul_digs that only produces + * output digits *above* digs. See the comments for fast_s_mul_digs * to see how it works. * * This is used in the Barrett reduction since for one of the multiplications @@ -26,73 +27,69 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { - int oldused, newused, res, pa, pb, ix; - mp_word W[MP_WARRAY]; + int olduse, res, pa, ix, iz; + mp_digit W[MP_WARRAY]; + mp_word _W; - /* calculate size of product and allocate more space if required */ - newused = a->used + b->used + 1; - if (c->alloc < newused) { - if ((res = mp_grow (c, newused)) != MP_OKAY) { + /* grow the destination as required */ + pa = a->used + b->used; + if (c->alloc < pa) { + if ((res = mp_grow (c, pa)) != MP_OKAY) { return res; } } - /* like the other comba method we compute the columns first */ - pa = a->used; - pb = b->used; - memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word)); - for (ix = 0; ix < pa; ix++) { - { - register mp_digit tmpx, *tmpy; - register int iy; - register mp_word *_W; + /* number of output digits to produce */ + pa = a->used + b->used; + _W = 0; + for (ix = digs; ix <= pa; ix++) { + int tx, ty, iy; + mp_digit *tmpx, *tmpy; - /* work todo, that is we only calculate digits that are at "digs" or above */ - iy = digs - ix; + /* get offsets into the two bignums */ + ty = MIN(b->used-1, ix); + tx = ix - ty; - /* copy of word on the left of A[ix] * B[iy] */ - tmpx = a->dp[ix]; + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = b->dp + ty; - /* alias for right side */ - tmpy = b->dp + iy; - - /* alias for the columns of output. Offset to be equal to or above the - * smallest digit place requested + /* this is the number of times the loop will iterrate, essentially its + while (tx++ < a->used && ty-- >= 0) { ... } */ - _W = W + digs; - - /* skip cases below zero where ix > digs */ - if (iy < 0) { - iy = abs(iy); - tmpy += iy; - _W += iy; - iy = 0; + iy = MIN(a->used-tx, ty+1); + + /* execute loop */ + for (iz = 0; iz < iy; iz++) { + _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); } - /* compute column products for digits above the minimum */ - for (; iy < pb; iy++) { - *_W++ += ((mp_word) tmpx) * ((mp_word)*tmpy++); - } - } + /* store term */ + W[ix] = ((mp_digit)_W) & MP_MASK; + + /* make next carry */ + _W = _W >> ((mp_word)DIGIT_BIT); } /* setup dest */ - oldused = c->used; - c->used = newused; + olduse = c->used; + c->used = pa; + + { + register mp_digit *tmpc; - /* now convert the array W downto what we need - * - * See comments in bn_fast_s_mp_mul_digs.c - */ - for (ix = digs + 1; ix < newused; ix++) { - W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT)); - c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); - } - c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK)); + tmpc = c->dp + digs; + for (ix = digs; ix <= pa; ix++) { + /* now extract the previous digit [below the carry] */ + *tmpc++ = W[ix]; + } - for (; ix < oldused; ix++) { - c->dp[ix] = 0; + /* clear unused digits [that existed in the old copy of c] */ + for (; ix < olduse; ix++) { + *tmpc++ = 0; + } } mp_clamp (c); return MP_OKAY; } +#endif
--- a/bn_fast_s_mp_sqr.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_fast_s_mp_sqr.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_FAST_S_MP_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* fast squaring * @@ -31,109 +32,98 @@ * Based on Algorithm 14.16 on pp.597 of HAC. * */ +/* the jist of squaring... + +you do like mult except the offset of the tmpx [one that starts closer to zero] +can't equal the offset of tmpy. So basically you set up iy like before then you min it with +(ty-tx) so that it never happens. You double all those you add in the inner loop + +After that loop you do the squares and add them in. + +Remove W2 and don't memset W + +*/ + int fast_s_mp_sqr (mp_int * a, mp_int * b) { - int olduse, newused, res, ix, pa; - mp_word W2[MP_WARRAY], W[MP_WARRAY]; + int olduse, res, pa, ix, iz; + mp_digit W[MP_WARRAY], *tmpx; + mp_word W1; - /* calculate size of product and allocate as required */ - pa = a->used; - newused = pa + pa + 1; - if (b->alloc < newused) { - if ((res = mp_grow (b, newused)) != MP_OKAY) { + /* grow the destination as required */ + pa = a->used + a->used; + if (b->alloc < pa) { + if ((res = mp_grow (b, pa)) != MP_OKAY) { return res; } } - /* zero temp buffer (columns) - * Note that there are two buffers. Since squaring requires - * a outer and inner product and the inner product requires - * computing a product and doubling it (a relatively expensive - * op to perform n**2 times if you don't have to) the inner and - * outer products are computed in different buffers. This way - * the inner product can be doubled using n doublings instead of - * n**2 - */ - memset (W, 0, newused * sizeof (mp_word)); - memset (W2, 0, newused * sizeof (mp_word)); + /* number of output digits to produce */ + W1 = 0; + for (ix = 0; ix <= pa; ix++) { + int tx, ty, iy; + mp_word _W; + mp_digit *tmpy; + + /* clear counter */ + _W = 0; + + /* get offsets into the two bignums */ + ty = MIN(a->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = a->dp + ty; + + /* this is the number of times the loop will iterrate, essentially its + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MIN(a->used-tx, ty+1); - /* This computes the inner product. To simplify the inner N**2 loop - * the multiplication by two is done afterwards in the N loop. - */ - for (ix = 0; ix < pa; ix++) { - /* compute the outer product - * - * Note that every outer product is computed - * for a particular column only once which means that - * there is no need todo a double precision addition - * into the W2[] array. - */ - W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]); + /* now for squaring tx can never equal ty + * we halve the distance since they approach at a rate of 2x + * and we have to round because odd cases need to be executed + */ + iy = MIN(iy, (ty-tx+1)>>1); + + /* execute loop */ + for (iz = 0; iz < iy; iz++) { + _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); + } - { - register mp_digit tmpx, *tmpy; - register mp_word *_W; - register int iy; - - /* copy of left side */ - tmpx = a->dp[ix]; + /* double the inner product and add carry */ + _W = _W + _W + W1; - /* alias for right side */ - tmpy = a->dp + (ix + 1); - - /* the column to store the result in */ - _W = W + (ix + ix + 1); + /* even columns have the square term in them */ + if ((ix&1) == 0) { + _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]); + } - /* inner products */ - for (iy = ix + 1; iy < pa; iy++) { - *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++); - } - } + /* store it */ + W[ix] = _W; + + /* make next carry */ + W1 = _W >> ((mp_word)DIGIT_BIT); } /* setup dest */ olduse = b->used; - b->used = newused; + b->used = a->used+a->used; - /* now compute digits - * - * We have to double the inner product sums, add in the - * outer product sums, propagate carries and convert - * to single precision. - */ { - register mp_digit *tmpb; - - /* double first value, since the inner products are - * half of what they should be - */ - W[0] += W[0] + W2[0]; - + mp_digit *tmpb; tmpb = b->dp; - for (ix = 1; ix < newused; ix++) { - /* double/add next digit */ - W[ix] += W[ix] + W2[ix]; - - /* propagate carry forwards [from the previous digit] */ - W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT)); + for (ix = 0; ix < pa; ix++) { + *tmpb++ = W[ix] & MP_MASK; + } - /* store the current digit now that the carry isn't - * needed - */ - *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); - } - /* set the last value. Note even if the carry is zero - * this is required since the next step will not zero - * it if b originally had a value at b->dp[2*a.used] - */ - *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK)); - - /* clear high digits of b if there were any originally */ + /* clear unused digits [that existed in the old copy of c] */ for (; ix < olduse; ix++) { *tmpb++ = 0; } } - mp_clamp (b); return MP_OKAY; } +#endif
--- a/bn_mp_2expt.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_2expt.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_2EXPT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* computes a = 2**b * @@ -36,7 +37,8 @@ a->used = b / DIGIT_BIT + 1; /* put the single bit in its place */ - a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT); + a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); return MP_OKAY; } +#endif
--- a/bn_mp_abs.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_abs.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_ABS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* b = |a| * @@ -35,3 +36,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_add.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_add.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_ADD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* high level addition (handles signs) */ int mp_add (mp_int * a, mp_int * b, mp_int * c) @@ -45,3 +46,4 @@ return res; } +#endif
--- a/bn_mp_add_d.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_add_d.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_ADD_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* single digit addition */ int @@ -101,3 +102,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_addmod.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_addmod.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_ADDMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* d = a + b (mod c) */ int @@ -33,3 +34,4 @@ mp_clear (&t); return res; } +#endif
--- a/bn_mp_and.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_and.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_AND_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* AND two ints together */ int @@ -49,3 +50,4 @@ mp_clear (&t); return MP_OKAY; } +#endif
--- a/bn_mp_clamp.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_clamp.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_CLAMP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* trim unused digits * @@ -36,3 +37,4 @@ a->sign = MP_ZPOS; } } +#endif
--- a/bn_mp_clear.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_clear.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_CLEAR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,16 +14,19 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* clear one (frees) */ void mp_clear (mp_int * a) { + int i; + /* only do anything if a hasn't been freed previously */ if (a->dp != NULL) { /* first zero the digits */ - memset (a->dp, 0, sizeof (mp_digit) * a->used); + for (i = 0; i < a->used; i++) { + a->dp[i] = 0; + } /* free ram */ XFREE(a->dp); @@ -32,3 +37,4 @@ a->sign = MP_ZPOS; } } +#endif
--- a/bn_mp_clear_multi.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_clear_multi.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_CLEAR_MULTI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> #include <stdarg.h> void mp_clear_multi(mp_int *mp, ...) @@ -26,3 +27,4 @@ } va_end(args); } +#endif
--- a/bn_mp_cmp.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_cmp.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_CMP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* compare two ints (signed)*/ int @@ -35,3 +36,4 @@ return mp_cmp_mag(a, b); } } +#endif
--- a/bn_mp_cmp_d.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_cmp_d.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_CMP_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* compare a digit */ int mp_cmp_d(mp_int * a, mp_digit b) @@ -36,3 +37,4 @@ return MP_EQ; } } +#endif
--- a/bn_mp_cmp_mag.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_cmp_mag.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_CMP_MAG_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* compare maginitude of two ints (unsigned) */ int mp_cmp_mag (mp_int * a, mp_int * b) @@ -47,3 +48,4 @@ } return MP_EQ; } +#endif
--- a/bn_mp_cnt_lsb.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_cnt_lsb.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_CNT_LSB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> static const int lnz[16] = { 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 @@ -45,3 +46,4 @@ return x; } +#endif
--- a/bn_mp_copy.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_copy.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_COPY_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* copy, b = a */ int @@ -60,3 +61,4 @@ b->sign = a->sign; return MP_OKAY; } +#endif
--- a/bn_mp_count_bits.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_count_bits.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_COUNT_BITS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* returns the number of bits in an int */ int @@ -37,3 +38,4 @@ } return r; } +#endif
--- a/bn_mp_div.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_div.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_DIV_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,78 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> + +#ifdef BN_MP_DIV_SMALL + +/* slower bit-bang division... also smaller */ +int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d) +{ + mp_int ta, tb, tq, q; + int res, n, n2; + + /* is divisor zero ? */ + if (mp_iszero (b) == 1) { + return MP_VAL; + } + + /* if a < b then q=0, r = a */ + if (mp_cmp_mag (a, b) == MP_LT) { + if (d != NULL) { + res = mp_copy (a, d); + } else { + res = MP_OKAY; + } + if (c != NULL) { + mp_zero (c); + } + return res; + } + + /* init our temps */ + if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) { + return res; + } + + + mp_set(&tq, 1); + n = mp_count_bits(a) - mp_count_bits(b); + if (((res = mp_copy(a, &ta)) != MP_OKAY) || + ((res = mp_copy(b, &tb)) != MP_OKAY) || + ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || + ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) { + goto __ERR; + } + + while (n-- >= 0) { + if (mp_cmp(&tb, &ta) != MP_GT) { + if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || + ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) { + goto __ERR; + } + } + if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) || + ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) { + goto __ERR; + } + } + + /* now q == quotient and ta == remainder */ + n = a->sign; + n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG); + if (c != NULL) { + mp_exch(c, &q); + c->sign = n2; + } + if (d != NULL) { + mp_exch(d, &ta); + d->sign = n; + } +__ERR: + mp_clear_multi(&ta, &tb, &tq, &q, NULL); + return res; +} + +#else /* integer signed division. * c*b + d == a [e.g. a/b, c=quotient, d=remainder] @@ -187,7 +260,7 @@ */ /* get sign before writing to c */ - x.sign = a->sign; + x.sign = x.used == 0 ? MP_ZPOS : a->sign; if (c != NULL) { mp_clamp (&q); @@ -209,3 +282,7 @@ __Q:mp_clear (&q); return res; } + +#endif + +#endif
--- a/bn_mp_div_2.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_div_2.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_DIV_2_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* b = a/2 */ int mp_div_2(mp_int * a, mp_int * b) @@ -60,3 +61,4 @@ mp_clamp (b); return MP_OKAY; } +#endif
--- a/bn_mp_div_2d.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_div_2d.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_DIV_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* shift right by a certain bit count (store quotient in c, optional remainder in d) */ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) @@ -89,3 +90,4 @@ mp_clear (&t); return MP_OKAY; } +#endif
--- a/bn_mp_div_3.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_div_3.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_DIV_3_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* divide by three (based on routine from MPI and the GMP manual) */ int @@ -71,3 +72,4 @@ return res; } +#endif
--- a/bn_mp_div_d.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_div_d.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_DIV_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> static int s_is_power_of_two(mp_digit b, int *p) { @@ -54,7 +55,7 @@ /* power of two ? */ if (s_is_power_of_two(b, &ix) == 1) { if (d != NULL) { - *d = a->dp[0] & ((1<<ix) - 1); + *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1); } if (c != NULL) { return mp_div_2d(a, ix, c, NULL); @@ -62,10 +63,12 @@ return MP_OKAY; } +#ifdef BN_MP_DIV_3_C /* three? */ if (b == 3) { return mp_div_3(a, c, d); } +#endif /* no easy answer [c'est la vie]. Just division */ if ((res = mp_init_size(&q, a->used)) != MP_OKAY) { @@ -100,3 +103,4 @@ return res; } +#endif
--- a/bn_mp_dr_is_modulus.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_dr_is_modulus.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_DR_IS_MODULUS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* determines if a number is a valid DR modulus */ int mp_dr_is_modulus(mp_int *a) @@ -35,3 +36,4 @@ return 1; } +#endif
--- a/bn_mp_dr_reduce.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_dr_reduce.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_DR_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* reduce "x" in place modulo "n" using the Diminished Radix algorithm. * @@ -86,3 +87,4 @@ } return MP_OKAY; } +#endif
--- a/bn_mp_dr_setup.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_dr_setup.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_DR_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* determines the setup value */ void mp_dr_setup(mp_int *a, mp_digit *d) @@ -24,3 +25,4 @@ ((mp_word)a->dp[0])); } +#endif
--- a/bn_mp_exch.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_exch.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_EXCH_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* swap the elements of two integers, for cases where you can't simply swap the * mp_int pointers around @@ -26,3 +27,4 @@ *a = *b; *b = t; } +#endif
--- a/bn_mp_expt_d.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_expt_d.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_EXPT_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* calculate c = a**b using a square-multiply algorithm */ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) @@ -49,3 +50,4 @@ mp_clear (&g); return MP_OKAY; } +#endif
--- a/bn_mp_exptmod.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_exptmod.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_EXPTMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* this is a shell function that calls either the normal or Montgomery @@ -31,6 +32,7 @@ /* if exponent X is negative we have to recurse */ if (X->sign == MP_NEG) { +#ifdef BN_MP_INVMOD_C mp_int tmpG, tmpX; int err; @@ -57,22 +59,42 @@ err = mp_exptmod(&tmpG, &tmpX, P, Y); mp_clear_multi(&tmpG, &tmpX, NULL); return err; +#else + /* no invmod */ + return MP_VAL +#endif } +#ifdef BN_MP_DR_IS_MODULUS_C /* is it a DR modulus? */ dr = mp_dr_is_modulus(P); +#else + dr = 0; +#endif +#ifdef BN_MP_REDUCE_IS_2K_C /* if not, is it a uDR modulus? */ if (dr == 0) { dr = mp_reduce_is_2k(P) << 1; } +#endif /* if the modulus is odd or dr != 0 use the fast method */ +#ifdef BN_MP_EXPTMOD_FAST_C if (mp_isodd (P) == 1 || dr != 0) { return mp_exptmod_fast (G, X, P, Y, dr); } else { +#endif +#ifdef BN_S_MP_EXPTMOD_C /* otherwise use the generic Barrett reduction technique */ return s_mp_exptmod (G, X, P, Y); +#else + /* no exptmod for evens */ + return MP_VAL; +#endif +#ifdef BN_MP_EXPTMOD_FAST_C } +#endif } +#endif
--- a/bn_mp_exptmod_fast.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_exptmod_fast.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_EXPTMOD_FAST_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 * @@ -84,29 +85,52 @@ /* determine and setup reduction code */ if (redmode == 0) { +#ifdef BN_MP_MONTGOMERY_SETUP_C /* now setup montgomery */ if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) { goto __M; } +#else + err = MP_VAL; + goto __M; +#endif /* automatically pick the comba one if available (saves quite a few calls/ifs) */ +#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C if (((P->used * 2 + 1) < MP_WARRAY) && P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { redux = fast_mp_montgomery_reduce; - } else { + } else +#endif + { +#ifdef BN_MP_MONTGOMERY_REDUCE_C /* use slower baseline Montgomery method */ redux = mp_montgomery_reduce; +#else + err = MP_VAL; + goto __M; +#endif } } else if (redmode == 1) { +#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C) /* setup DR reduction for moduli of the form B**k - b */ mp_dr_setup(P, &mp); redux = mp_dr_reduce; +#else + err = MP_VAL; + goto __M; +#endif } else { +#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C) /* setup DR reduction for moduli of the form 2**k - b */ if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) { goto __M; } redux = mp_reduce_2k; +#else + err = MP_VAL; + goto __M; +#endif } /* setup result */ @@ -116,16 +140,21 @@ /* create M table * - * The M table contains powers of the input base, e.g. M[x] = G^x mod P + * * The first half of the table is not computed though accept for M[0] and M[1] */ if (redmode == 0) { +#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C /* now we need R mod m */ if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) { goto __RES; } +#else + err = MP_VAL; + goto __RES; +#endif /* now set M[1] to G * R mod m */ if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) { @@ -269,7 +298,7 @@ * to reduce one more time to cancel out the factor * of R. */ - if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) { + if ((err = redux(&res, P, mp)) != MP_OKAY) { goto __RES; } } @@ -285,3 +314,5 @@ } return err; } +#endif +
--- a/bn_mp_exteuclid.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_exteuclid.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_EXTEUCLID_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* Extended euclidean algorithm of (a, b) produces a*u1 + b*u2 = u3 @@ -67,3 +68,4 @@ _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); return err; } +#endif
--- a/bn_mp_fread.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_fread.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_FREAD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* read a bigint from a file stream in ASCII */ int mp_fread(mp_int *a, int radix, FILE *stream) @@ -59,3 +60,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_fwrite.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_fwrite.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_FWRITE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> int mp_fwrite(mp_int *a, int radix, FILE *stream) { @@ -44,3 +45,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_gcd.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_gcd.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_GCD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* Greatest Common Divisor using the binary method */ int mp_gcd (mp_int * a, mp_int * b, mp_int * c) @@ -105,3 +106,4 @@ __U:mp_clear (&v); return res; } +#endif
--- a/bn_mp_get_int.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_get_int.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_GET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* get the lower 32-bits of an mp_int */ unsigned long mp_get_int(mp_int * a) @@ -37,3 +38,4 @@ /* force result to 32-bits always so it is consistent on non 32-bit platforms */ return res & 0xFFFFFFFFUL; } +#endif
--- a/bn_mp_grow.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_grow.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_GROW_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* grow as required */ int mp_grow (mp_int * a, int size) @@ -49,3 +50,4 @@ } return MP_OKAY; } +#endif
--- a/bn_mp_init.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_init.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_INIT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,17 +14,23 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> -/* init a new bigint */ +/* init a new mp_int */ int mp_init (mp_int * a) { + int i; + /* allocate memory required and clear it */ - a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), MP_PREC); + a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC); if (a->dp == NULL) { return MP_MEM; } + /* set the digits to zero */ + for (i = 0; i < MP_PREC; i++) { + a->dp[i] = 0; + } + /* set the used to zero, allocated digits to the default precision * and sign to positive */ a->used = 0; @@ -31,3 +39,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_init_copy.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_init_copy.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_INIT_COPY_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* creates "a" then copies b into it */ int mp_init_copy (mp_int * a, mp_int * b) @@ -24,3 +25,4 @@ } return mp_copy (b, a); } +#endif
--- a/bn_mp_init_multi.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_init_multi.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_INIT_MULTI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> #include <stdarg.h> int mp_init_multi(mp_int *mp, ...) @@ -51,3 +52,4 @@ return res; /* Assumed ok, if error flagged above. */ } +#endif
--- a/bn_mp_init_set.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_init_set.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_INIT_SET_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* initialize and set a digit */ int mp_init_set (mp_int * a, mp_digit b) @@ -24,3 +25,4 @@ mp_set(a, b); return err; } +#endif
--- a/bn_mp_init_set_int.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_init_set_int.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_INIT_SET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* initialize and set a digit */ int mp_init_set_int (mp_int * a, unsigned long b) @@ -23,3 +24,4 @@ } return mp_set_int(a, b); } +#endif
--- a/bn_mp_init_size.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_init_size.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_INIT_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,22 +14,31 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* init an mp_init for a given size */ int mp_init_size (mp_int * a, int size) { + int x; + /* pad size so there are always extra digits */ size += (MP_PREC * 2) - (size % MP_PREC); /* alloc mem */ - a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), size); + a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size); if (a->dp == NULL) { return MP_MEM; } + + /* set the members */ a->used = 0; a->alloc = size; a->sign = MP_ZPOS; + /* zero the digits */ + for (x = 0; x < size; x++) { + a->dp[x] = 0; + } + return MP_OKAY; } +#endif
--- a/bn_mp_invmod.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_invmod.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_INVMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,163 +14,26 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* hac 14.61, pp608 */ int mp_invmod (mp_int * a, mp_int * b, mp_int * c) { - mp_int x, y, u, v, A, B, C, D; - int res; - /* b cannot be negative */ if (b->sign == MP_NEG || mp_iszero(b) == 1) { return MP_VAL; } +#ifdef BN_FAST_MP_INVMOD_C /* if the modulus is odd we can use a faster routine instead */ if (mp_isodd (b) == 1) { return fast_mp_invmod (a, b, c); } - - /* init temps */ - if ((res = mp_init_multi(&x, &y, &u, &v, - &A, &B, &C, &D, NULL)) != MP_OKAY) { - return res; - } - - /* x = a, y = b */ - if ((res = mp_copy (a, &x)) != MP_OKAY) { - goto __ERR; - } - if ((res = mp_copy (b, &y)) != MP_OKAY) { - goto __ERR; - } - - /* 2. [modified] if x,y are both even then return an error! */ - if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) { - res = MP_VAL; - goto __ERR; - } - - /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ - if ((res = mp_copy (&x, &u)) != MP_OKAY) { - goto __ERR; - } - if ((res = mp_copy (&y, &v)) != MP_OKAY) { - goto __ERR; - } - mp_set (&A, 1); - mp_set (&D, 1); - -top: - /* 4. while u is even do */ - while (mp_iseven (&u) == 1) { - /* 4.1 u = u/2 */ - if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { - goto __ERR; - } - /* 4.2 if A or B is odd then */ - if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) { - /* A = (A+y)/2, B = (B-x)/2 */ - if ((res = mp_add (&A, &y, &A)) != MP_OKAY) { - goto __ERR; - } - if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { - goto __ERR; - } - } - /* A = A/2, B = B/2 */ - if ((res = mp_div_2 (&A, &A)) != MP_OKAY) { - goto __ERR; - } - if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { - goto __ERR; - } - } +#endif - /* 5. while v is even do */ - while (mp_iseven (&v) == 1) { - /* 5.1 v = v/2 */ - if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { - goto __ERR; - } - /* 5.2 if C or D is odd then */ - if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) { - /* C = (C+y)/2, D = (D-x)/2 */ - if ((res = mp_add (&C, &y, &C)) != MP_OKAY) { - goto __ERR; - } - if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { - goto __ERR; - } - } - /* C = C/2, D = D/2 */ - if ((res = mp_div_2 (&C, &C)) != MP_OKAY) { - goto __ERR; - } - if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { - goto __ERR; - } - } - - /* 6. if u >= v then */ - if (mp_cmp (&u, &v) != MP_LT) { - /* u = u - v, A = A - C, B = B - D */ - if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { - goto __ERR; - } - - if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) { - goto __ERR; - } +#ifdef BN_MP_INVMOD_SLOW_C + return mp_invmod_slow(a, b, c); +#endif - if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { - goto __ERR; - } - } else { - /* v - v - u, C = C - A, D = D - B */ - if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { - goto __ERR; - } - - if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) { - goto __ERR; - } - - if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { - goto __ERR; - } - } - - /* if not zero goto step 4 */ - if (mp_iszero (&u) == 0) - goto top; - - /* now a = C, b = D, gcd == g*v */ - - /* if v != 1 then there is no inverse */ - if (mp_cmp_d (&v, 1) != MP_EQ) { - res = MP_VAL; - goto __ERR; - } - - /* if its too low */ - while (mp_cmp_d(&C, 0) == MP_LT) { - if ((res = mp_add(&C, b, &C)) != MP_OKAY) { - goto __ERR; - } - } - - /* too big */ - while (mp_cmp_mag(&C, b) != MP_LT) { - if ((res = mp_sub(&C, b, &C)) != MP_OKAY) { - goto __ERR; - } - } - - /* C is now the inverse */ - mp_exch (&C, c); - res = MP_OKAY; -__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); - return res; + return MP_VAL; } +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/bn_mp_invmod_slow.c Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,171 @@ +#include <tommath.h> +#ifdef BN_MP_INVMOD_SLOW_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* hac 14.61, pp608 */ +int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c) +{ + mp_int x, y, u, v, A, B, C, D; + int res; + + /* b cannot be negative */ + if (b->sign == MP_NEG || mp_iszero(b) == 1) { + return MP_VAL; + } + + /* init temps */ + if ((res = mp_init_multi(&x, &y, &u, &v, + &A, &B, &C, &D, NULL)) != MP_OKAY) { + return res; + } + + /* x = a, y = b */ + if ((res = mp_copy (a, &x)) != MP_OKAY) { + goto __ERR; + } + if ((res = mp_copy (b, &y)) != MP_OKAY) { + goto __ERR; + } + + /* 2. [modified] if x,y are both even then return an error! */ + if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) { + res = MP_VAL; + goto __ERR; + } + + /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ + if ((res = mp_copy (&x, &u)) != MP_OKAY) { + goto __ERR; + } + if ((res = mp_copy (&y, &v)) != MP_OKAY) { + goto __ERR; + } + mp_set (&A, 1); + mp_set (&D, 1); + +top: + /* 4. while u is even do */ + while (mp_iseven (&u) == 1) { + /* 4.1 u = u/2 */ + if ((res = mp_div_2 (&u, &u)) != MP_OKAY) { + goto __ERR; + } + /* 4.2 if A or B is odd then */ + if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) { + /* A = (A+y)/2, B = (B-x)/2 */ + if ((res = mp_add (&A, &y, &A)) != MP_OKAY) { + goto __ERR; + } + if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) { + goto __ERR; + } + } + /* A = A/2, B = B/2 */ + if ((res = mp_div_2 (&A, &A)) != MP_OKAY) { + goto __ERR; + } + if ((res = mp_div_2 (&B, &B)) != MP_OKAY) { + goto __ERR; + } + } + + /* 5. while v is even do */ + while (mp_iseven (&v) == 1) { + /* 5.1 v = v/2 */ + if ((res = mp_div_2 (&v, &v)) != MP_OKAY) { + goto __ERR; + } + /* 5.2 if C or D is odd then */ + if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) { + /* C = (C+y)/2, D = (D-x)/2 */ + if ((res = mp_add (&C, &y, &C)) != MP_OKAY) { + goto __ERR; + } + if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) { + goto __ERR; + } + } + /* C = C/2, D = D/2 */ + if ((res = mp_div_2 (&C, &C)) != MP_OKAY) { + goto __ERR; + } + if ((res = mp_div_2 (&D, &D)) != MP_OKAY) { + goto __ERR; + } + } + + /* 6. if u >= v then */ + if (mp_cmp (&u, &v) != MP_LT) { + /* u = u - v, A = A - C, B = B - D */ + if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) { + goto __ERR; + } + + if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) { + goto __ERR; + } + + if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) { + goto __ERR; + } + } else { + /* v - v - u, C = C - A, D = D - B */ + if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) { + goto __ERR; + } + + if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) { + goto __ERR; + } + + if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) { + goto __ERR; + } + } + + /* if not zero goto step 4 */ + if (mp_iszero (&u) == 0) + goto top; + + /* now a = C, b = D, gcd == g*v */ + + /* if v != 1 then there is no inverse */ + if (mp_cmp_d (&v, 1) != MP_EQ) { + res = MP_VAL; + goto __ERR; + } + + /* if its too low */ + while (mp_cmp_d(&C, 0) == MP_LT) { + if ((res = mp_add(&C, b, &C)) != MP_OKAY) { + goto __ERR; + } + } + + /* too big */ + while (mp_cmp_mag(&C, b) != MP_LT) { + if ((res = mp_sub(&C, b, &C)) != MP_OKAY) { + goto __ERR; + } + } + + /* C is now the inverse */ + mp_exch (&C, c); + res = MP_OKAY; +__ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); + return res; +} +#endif
--- a/bn_mp_is_square.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_is_square.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_IS_SQUARE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* Check if remainders are possible squares - fast exclude non-squares */ static const char rem_128[128] = { @@ -69,7 +70,7 @@ return MP_OKAY; } - /* product of primes less than 2^31 */ + if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) { return res; } @@ -101,3 +102,4 @@ ERR:mp_clear(&t); return res; } +#endif
--- a/bn_mp_jacobi.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_jacobi.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_JACOBI_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* computes the jacobi c = (a | n) (or Legendre if n is prime) * HAC pp. 73 Algorithm 2.149 @@ -97,3 +98,4 @@ __A1:mp_clear (&a1); return res; } +#endif
--- a/bn_mp_karatsuba_mul.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_karatsuba_mul.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_KARATSUBA_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* c = |a| * |b| using Karatsuba Multiplication using * three half size multiplications @@ -76,9 +77,6 @@ goto X0Y0; /* now shift the digits */ - x0.sign = x1.sign = a->sign; - y0.sign = y1.sign = b->sign; - x0.used = y0.used = B; x1.used = a->used - B; y1.used = b->used - B; @@ -162,3 +160,4 @@ ERR: return err; } +#endif
--- a/bn_mp_karatsuba_sqr.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_karatsuba_sqr.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_KARATSUBA_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,12 +14,11 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* Karatsuba squaring, computes b = a*a using three * half size squarings * - * See comments of mp_karatsuba_mul for details. It + * See comments of karatsuba_mul for details. It * is essentially the same algorithm but merely * tuned to perform recursive squarings. */ @@ -113,3 +114,4 @@ ERR: return err; } +#endif
--- a/bn_mp_lcm.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_lcm.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_LCM_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* computes least common multiple as |a*b|/(a, b) */ int mp_lcm (mp_int * a, mp_int * b, mp_int * c) @@ -52,3 +53,4 @@ mp_clear_multi (&t1, &t2, NULL); return res; } +#endif
--- a/bn_mp_lshd.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_lshd.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_LSHD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* shift left a certain amount of digits */ int mp_lshd (mp_int * a, int b) @@ -59,3 +60,4 @@ } return MP_OKAY; } +#endif
--- a/bn_mp_mod.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_mod.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* c = a mod b, 0 <= c < b */ int @@ -40,3 +41,4 @@ mp_clear (&t); return res; } +#endif
--- a/bn_mp_mod_2d.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_mod_2d.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MOD_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* calc a value mod 2**b */ int @@ -47,3 +48,4 @@ mp_clamp (c); return MP_OKAY; } +#endif
--- a/bn_mp_mod_d.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_mod_d.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MOD_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,10 +14,10 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> int mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) { return mp_div_d(a, b, NULL, c); } +#endif
--- a/bn_mp_montgomery_calc_normalization.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_montgomery_calc_normalization.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,31 +14,31 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> -/* calculates a = B^n mod b for Montgomery reduction - * Where B is the base [e.g. 2^DIGIT_BIT]. - * B^n mod b is computed by first computing - * A = B^(n-1) which doesn't require a reduction but a simple OR. - * then C = A * B = B^n is computed by performing upto DIGIT_BIT +/* * shifts with subtractions when the result is greater than b. * * The method is slightly modified to shift B unconditionally upto just under * the leading bit of b. This saves alot of multiple precision shifting. */ -int -mp_montgomery_calc_normalization (mp_int * a, mp_int * b) +int mp_montgomery_calc_normalization (mp_int * a, mp_int * b) { int x, bits, res; /* how many bits of last digit does b use */ bits = mp_count_bits (b) % DIGIT_BIT; - /* compute A = B^(n-1) * 2^(bits-1) */ - if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { - return res; + + if (b->used > 1) { + if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { + return res; + } + } else { + mp_set(a, 1); + bits = 1; } + /* now compute C = A * B mod b */ for (x = bits - 1; x < (int)DIGIT_BIT; x++) { if ((res = mp_mul_2 (a, a)) != MP_OKAY) { @@ -51,3 +53,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_montgomery_reduce.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_montgomery_reduce.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MONTGOMERY_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* computes xR**-1 == x (mod N) via Montgomery Reduction */ int @@ -23,7 +24,7 @@ /* can the fast reduction [comba] method be used? * - * Note that unlike in mp_mul you're safely allowed *less* + * Note that unlike in mul you're safely allowed *less* * than the available columns [255 per default] since carries * are fixed up in the inner loop. */ @@ -46,7 +47,7 @@ /* mu = ai * rho mod b * * The value of rho must be precalculated via - * bn_mp_montgomery_setup() such that + * montgomery_setup() such that * it equals -1/n0 mod b this allows the * following inner loop to reduce the * input one digit at a time @@ -110,3 +111,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_montgomery_setup.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_montgomery_setup.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MONTGOMERY_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* setups the montgomery reduction stuff */ int @@ -47,7 +48,8 @@ #endif /* rho = -1/m mod b */ - *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK; + *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; return MP_OKAY; } +#endif
--- a/bn_mp_mul.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_mul.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* high level multiplication (handles sign) */ int mp_mul (mp_int * a, mp_int * b, mp_int * c) @@ -21,12 +22,18 @@ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; /* use Toom-Cook? */ +#ifdef BN_MP_TOOM_MUL_C if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) { res = mp_toom_mul(a, b, c); + } else +#endif +#ifdef BN_MP_KARATSUBA_MUL_C /* use Karatsuba? */ - } else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) { + if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) { res = mp_karatsuba_mul (a, b, c); - } else { + } else +#endif + { /* can we use the fast multiplier? * * The fast multiplier can be used if the output will @@ -35,14 +42,21 @@ */ int digs = a->used + b->used + 1; +#ifdef BN_FAST_S_MP_MUL_DIGS_C if ((digs < MP_WARRAY) && MIN(a->used, b->used) <= (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { res = fast_s_mp_mul_digs (a, b, c, digs); - } else { - res = s_mp_mul (a, b, c); - } + } else +#endif +#ifdef BN_S_MP_MUL_DIGS_C + res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */ +#else + res = MP_VAL; +#endif + } - c->sign = neg; + c->sign = (c->used > 0) ? neg : MP_ZPOS; return res; } +#endif
--- a/bn_mp_mul_2.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_mul_2.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MUL_2_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* b = a*2 */ int mp_mul_2(mp_int * a, mp_int * b) @@ -74,3 +75,4 @@ b->sign = a->sign; return MP_OKAY; } +#endif
--- a/bn_mp_mul_2d.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_mul_2d.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MUL_2D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* shift left by a certain bit count */ int mp_mul_2d (mp_int * a, int b, mp_int * c) @@ -77,3 +78,4 @@ mp_clamp (c); return MP_OKAY; } +#endif
--- a/bn_mp_mul_d.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_mul_d.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MUL_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* multiply by a digit */ int @@ -70,3 +71,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_mulmod.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_mulmod.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_MULMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* d = a * b (mod c) */ int @@ -33,3 +34,4 @@ mp_clear (&t); return res; } +#endif
--- a/bn_mp_n_root.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_n_root.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_N_ROOT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* find the n'th root of an integer * @@ -124,3 +125,4 @@ __T1:mp_clear (&t1); return res; } +#endif
--- a/bn_mp_neg.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_neg.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_NEG_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* b = -a */ int mp_neg (mp_int * a, mp_int * b) @@ -26,3 +27,4 @@ } return MP_OKAY; } +#endif
--- a/bn_mp_or.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_or.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_OR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* OR two ints together */ int mp_or (mp_int * a, mp_int * b, mp_int * c) @@ -42,3 +43,4 @@ mp_clear (&t); return MP_OKAY; } +#endif
--- a/bn_mp_prime_fermat.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_prime_fermat.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_PRIME_FERMAT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* performs one Fermat test. * @@ -54,3 +55,4 @@ __T:mp_clear (&t); return err; } +#endif
--- a/bn_mp_prime_is_divisible.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_prime_is_divisible.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_PRIME_IS_DIVISIBLE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* determines if an integers is divisible by one * of the first PRIME_SIZE primes or not @@ -42,3 +43,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_prime_is_prime.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_prime_is_prime.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_PRIME_IS_PRIME_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,12 +14,11 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* performs a variable number of rounds of Miller-Rabin * * Probability of error after t rounds is no more than - * (1/4)^t when 1 <= t <= PRIME_SIZE + * * Sets result to 1 if probably prime, 0 otherwise */ @@ -75,3 +76,4 @@ __B:mp_clear (&b); return err; } +#endif
--- a/bn_mp_prime_miller_rabin.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_prime_miller_rabin.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_PRIME_MILLER_RABIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* Miller-Rabin test of "a" to the base of "b" as described in * HAC pp. 139 Algorithm 4.24 @@ -95,3 +96,4 @@ __N1:mp_clear (&n1); return err; } +#endif
--- a/bn_mp_prime_next_prime.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_prime_next_prime.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_PRIME_NEXT_PRIME_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* finds the next prime after the number "a" using "t" trials * of Miller-Rabin. @@ -162,3 +163,4 @@ return err; } +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/bn_mp_prime_rabin_miller_trials.c Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,48 @@ +#include <tommath.h> +#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + + +static const struct { + int k, t; +} sizes[] = { +{ 128, 28 }, +{ 256, 16 }, +{ 384, 10 }, +{ 512, 7 }, +{ 640, 6 }, +{ 768, 5 }, +{ 896, 4 }, +{ 1024, 4 } +}; + +/* returns # of RM trials required for a given bit size */ +int mp_prime_rabin_miller_trials(int size) +{ + int x; + + for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) { + if (sizes[x].k == size) { + return sizes[x].t; + } else if (sizes[x].k > size) { + return (x == 0) ? sizes[0].t : sizes[x - 1].t; + } + } + return sizes[x-1].t + 1; +} + + +#endif
--- a/bn_mp_prime_random_ex.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_prime_random_ex.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_PRIME_RANDOM_EX_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* makes a truly random prime of a given size (bits), * @@ -92,6 +93,9 @@ /* is it prime? */ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; } + if (res == MP_NO) { + continue; + } if (flags & LTM_PRIME_SAFE) { /* see if (a-1)/2 is prime */ @@ -116,3 +120,4 @@ } +#endif
--- a/bn_mp_radix_size.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_radix_size.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_RADIX_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* returns size of ASCII reprensentation */ int mp_radix_size (mp_int * a, int radix, int *size) @@ -63,3 +64,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_radix_smap.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_radix_smap.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_RADIX_SMAP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,7 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* chars used in radix conversions */ const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; +#endif
--- a/bn_mp_rand.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_rand.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_RAND_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* makes a pseudo-random int of a given size */ int @@ -47,3 +48,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_read_radix.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_read_radix.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_READ_RADIX_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* read a string [ASCII] in a given radix */ int mp_read_radix (mp_int * a, char *str, int radix) @@ -74,3 +75,4 @@ } return MP_OKAY; } +#endif
--- a/bn_mp_read_signed_bin.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_read_signed_bin.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_READ_SIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* read signed bin, big endian, first byte is 0==positive or 1==negative */ int @@ -34,3 +35,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_read_unsigned_bin.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_read_unsigned_bin.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_READ_UNSIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* reads a unsigned char array, assumes the msb is stored first [big endian] */ int @@ -48,3 +49,4 @@ mp_clamp (a); return MP_OKAY; } +#endif
--- a/bn_mp_reduce.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_reduce.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_REDUCE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* reduces x mod m, assumes 0 < x < m**2, mu is * precomputed via mp_reduce_setup. @@ -38,9 +39,20 @@ goto CLEANUP; } } else { +#ifdef BN_S_MP_MUL_HIGH_DIGS_C if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { goto CLEANUP; } +#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) + if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { + goto CLEANUP; + } +#else + { + res = MP_VAL; + goto CLEANUP; + } +#endif } /* q3 = q2 / b**(k+1) */ @@ -82,3 +94,4 @@ return res; } +#endif
--- a/bn_mp_reduce_2k.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_reduce_2k.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_REDUCE_2K_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* reduces a modulo n where n is of the form 2**p - d */ int @@ -54,3 +55,4 @@ return res; } +#endif
--- a/bn_mp_reduce_2k_setup.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_reduce_2k_setup.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_REDUCE_2K_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* determines the setup value */ int @@ -40,3 +41,4 @@ mp_clear(&tmp); return MP_OKAY; } +#endif
--- a/bn_mp_reduce_is_2k.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_reduce_is_2k.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_REDUCE_IS_2K_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,12 +14,12 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* determines if mp_reduce_2k can be used */ int mp_reduce_is_2k(mp_int *a) { - int ix, iy, iz, iw; + int ix, iy, iw; + mp_digit iz; if (a->used == 0) { return 0; @@ -34,7 +36,7 @@ return 0; } iz <<= 1; - if (iz > (int)MP_MASK) { + if (iz > (mp_digit)MP_MASK) { ++iw; iz = 1; } @@ -43,3 +45,4 @@ return 1; } +#endif
--- a/bn_mp_reduce_setup.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_reduce_setup.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_REDUCE_SETUP_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,13 +14,11 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* pre-calculate the value required for Barrett reduction * For a given modulus "b" it calulates the value required in "a" */ -int -mp_reduce_setup (mp_int * a, mp_int * b) +int mp_reduce_setup (mp_int * a, mp_int * b) { int res; @@ -27,3 +27,4 @@ } return mp_div (a, b, a, NULL); } +#endif
--- a/bn_mp_rshd.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_rshd.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_RSHD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* shift right a certain amount of digits */ void mp_rshd (mp_int * a, int b) @@ -64,3 +65,4 @@ /* remove excess digits */ a->used -= b; } +#endif
--- a/bn_mp_set.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_set.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_SET_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* set to a digit */ void mp_set (mp_int * a, mp_digit b) @@ -21,3 +22,4 @@ a->dp[0] = b & MP_MASK; a->used = (a->dp[0] != 0) ? 1 : 0; } +#endif
--- a/bn_mp_set_int.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_set_int.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_SET_INT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* set a 32-bit const */ int mp_set_int (mp_int * a, unsigned long b) @@ -40,3 +41,4 @@ mp_clamp (a); return MP_OKAY; } +#endif
--- a/bn_mp_shrink.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_shrink.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_SHRINK_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* shrink a bignum */ int mp_shrink (mp_int * a) @@ -27,3 +28,4 @@ } return MP_OKAY; } +#endif
--- a/bn_mp_signed_bin_size.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_signed_bin_size.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_SIGNED_BIN_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,10 +14,10 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* get the size for an signed equivalent */ int mp_signed_bin_size (mp_int * a) { return 1 + mp_unsigned_bin_size (a); } +#endif
--- a/bn_mp_sqr.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_sqr.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* computes b = a*a */ int @@ -20,22 +21,34 @@ { int res; +#ifdef BN_MP_TOOM_SQR_C /* use Toom-Cook? */ if (a->used >= TOOM_SQR_CUTOFF) { res = mp_toom_sqr(a, b); /* Karatsuba? */ - } else if (a->used >= KARATSUBA_SQR_CUTOFF) { + } else +#endif +#ifdef BN_MP_KARATSUBA_SQR_C +if (a->used >= KARATSUBA_SQR_CUTOFF) { res = mp_karatsuba_sqr (a, b); - } else { + } else +#endif + { +#ifdef BN_FAST_S_MP_SQR_C /* can we use the fast comba multiplier? */ if ((a->used * 2 + 1) < MP_WARRAY && a->used < (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) { res = fast_s_mp_sqr (a, b); - } else { + } else +#endif +#ifdef BN_S_MP_SQR_C res = s_mp_sqr (a, b); - } +#else + res = MP_VAL; +#endif } b->sign = MP_ZPOS; return res; } +#endif
--- a/bn_mp_sqrmod.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_sqrmod.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_SQRMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* c = a * a (mod b) */ int @@ -33,3 +34,4 @@ mp_clear (&t); return res; } +#endif
--- a/bn_mp_sqrt.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_sqrt.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_SQRT_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* this function is less generic than mp_n_root, simpler and faster */ int mp_sqrt(mp_int *arg, mp_int *ret) @@ -73,3 +74,4 @@ return res; } +#endif
--- a/bn_mp_sub.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_sub.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_SUB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* high level subtraction (handles signs) */ int @@ -51,3 +52,4 @@ return res; } +#endif
--- a/bn_mp_sub_d.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_sub_d.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_SUB_D_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* single digit subtraction */ int @@ -81,3 +82,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_submod.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_submod.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_SUBMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* d = a - b (mod c) */ int @@ -34,3 +35,4 @@ mp_clear (&t); return res; } +#endif
--- a/bn_mp_to_signed_bin.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_to_signed_bin.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_TO_SIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* store in signed [big endian] format */ int @@ -26,3 +27,4 @@ b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1); return MP_OKAY; } +#endif
--- a/bn_mp_to_unsigned_bin.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_to_unsigned_bin.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_TO_UNSIGNED_BIN_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* store in unsigned [big endian] format */ int @@ -41,3 +42,4 @@ mp_clear (&t); return MP_OKAY; } +#endif
--- a/bn_mp_toom_mul.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_toom_mul.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_TOOM_MUL_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,9 +14,13 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> -/* multiplication using the Toom-Cook 3-way algorithm */ +/* multiplication using the Toom-Cook 3-way algorithm + * + * Much more complicated than Karatsuba but has a lower asymptotic running time of + * O(N**1.464). This algorithm is only particularly useful on VERY large + * inputs (we're talking 1000s of digits here...). +*/ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) { mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; @@ -270,3 +276,4 @@ return res; } +#endif
--- a/bn_mp_toom_sqr.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_toom_sqr.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_TOOM_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* squaring using Toom-Cook 3-way algorithm */ int @@ -218,3 +219,4 @@ return res; } +#endif
--- a/bn_mp_toradix.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_toradix.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_TORADIX_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* stores a bignum as a ASCII string in a given radix (2..64) */ int mp_toradix (mp_int * a, char *str, int radix) @@ -67,3 +68,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_toradix_n.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_toradix_n.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_TORADIX_N_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* stores a bignum as a ASCII string in a given radix (2..64) * @@ -81,3 +82,4 @@ return MP_OKAY; } +#endif
--- a/bn_mp_unsigned_bin_size.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_unsigned_bin_size.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_UNSIGNED_BIN_SIZE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* get the size for an unsigned equivalent */ int @@ -21,3 +22,4 @@ int size = mp_count_bits (a); return (size / 8 + ((size & 7) != 0 ? 1 : 0)); } +#endif
--- a/bn_mp_xor.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_xor.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_XOR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* XOR two ints together */ int @@ -36,10 +37,11 @@ } for (ix = 0; ix < px; ix++) { - t.dp[ix] ^= x->dp[ix]; + } mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } +#endif
--- a/bn_mp_zero.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_mp_zero.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_MP_ZERO_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* set to zero */ void @@ -22,3 +23,4 @@ a->used = 0; memset (a->dp, 0, sizeof (mp_digit) * a->alloc); } +#endif
--- a/bn_prime_sizes_tab.c Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,51 +0,0 @@ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> - -/* this table gives the # of rabin miller trials for a prob of failure lower than 2^-96 */ -static const struct { - int k, t; -} sizes[] = { -{ 128, 28 }, -{ 256, 16 }, -{ 384, 10 }, -{ 512, 7 }, -{ 640, 6 }, -{ 768, 5 }, -{ 896, 4 }, -{ 1024, 4 }, -{ 1152, 3 }, -{ 1280, 3 }, -{ 1408, 3 }, -{ 1536, 3 }, -{ 1664, 3 }, -{ 1792, 2 } }; - -/* returns # of RM trials required for a given bit size */ -int mp_prime_rabin_miller_trials(int size) -{ - int x; - - for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) { - if (sizes[x].k == size) { - return sizes[x].t; - } else if (sizes[x].k > size) { - return (x == 0) ? sizes[0].t : sizes[x - 1].t; - } - } - return 1; -} - -
--- a/bn_prime_tab.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_prime_tab.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_PRIME_TAB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> const mp_digit __prime_tab[] = { 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, @@ -53,3 +54,4 @@ 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 #endif }; +#endif
--- a/bn_reverse.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_reverse.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_REVERSE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* reverse an array, used for radix code */ void @@ -31,3 +32,4 @@ --iy; } } +#endif
--- a/bn_s_mp_add.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_s_mp_add.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_S_MP_ADD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* low level addition, based on HAC pp.594, Algorithm 14.7 */ int @@ -101,3 +102,4 @@ mp_clamp (c); return MP_OKAY; } +#endif
--- a/bn_s_mp_exptmod.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_s_mp_exptmod.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_S_MP_EXPTMOD_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> #ifdef MP_LOW_MEM #define TAB_SIZE 32 @@ -232,3 +233,4 @@ } return err; } +#endif
--- a/bn_s_mp_mul_digs.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_s_mp_mul_digs.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_S_MP_MUL_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* multiplies |a| * |b| and only computes upto digs digits of result * HAC pp. 595, Algorithm 14.12 Modified so you can control how @@ -83,3 +84,4 @@ mp_clear (&t); return MP_OKAY; } +#endif
--- a/bn_s_mp_mul_high_digs.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_s_mp_mul_high_digs.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_S_MP_MUL_HIGH_DIGS_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* multiplies |a| * |b| and does not compute the lower digs digits * [meant to get the higher part of the product] @@ -27,10 +28,12 @@ mp_digit tmpx, *tmpt, *tmpy; /* can we use the fast multiplier? */ +#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C if (((a->used + b->used + 1) < MP_WARRAY) && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { return fast_s_mp_mul_high_digs (a, b, c, digs); } +#endif if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) { return res; @@ -71,3 +74,4 @@ mp_clear (&t); return MP_OKAY; } +#endif
--- a/bn_s_mp_sqr.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_s_mp_sqr.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_S_MP_SQR_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ int @@ -77,3 +78,4 @@ mp_clear (&t); return MP_OKAY; } +#endif
--- a/bn_s_mp_sub.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bn_s_mp_sub.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BN_S_MP_SUB_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,7 +14,6 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ int @@ -81,3 +82,4 @@ return MP_OKAY; } +#endif
--- a/bncore.c Tue Jun 15 14:42:57 2004 +0000 +++ b/bncore.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,5 @@ +#include <tommath.h> +#ifdef BNCORE_C /* LibTomMath, multiple-precision integer library -- Tom St Denis * * LibTomMath is a library that provides multiple-precision @@ -12,20 +14,18 @@ * * Tom St Denis, [email protected], http://math.libtomcrypt.org */ -#include <tommath.h> /* Known optimal configurations CPU /Compiler /MUL CUTOFF/SQR CUTOFF ------------------------------------------------------------- - Intel P4 /GCC v3.2 / 70/ 108 - AMD Athlon XP /GCC v3.2 / 109/ 127 - + Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) + */ -/* configured for a AMD XP Thoroughbred core with etc/tune.c */ -int KARATSUBA_MUL_CUTOFF = 109, /* Min. number of digits before Karatsuba multiplication is used. */ - KARATSUBA_SQR_CUTOFF = 127, /* Min. number of digits before Karatsuba squaring is used. */ +int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */ + KARATSUBA_SQR_CUTOFF = 128, /* Min. number of digits before Karatsuba squaring is used. */ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ TOOM_SQR_CUTOFF = 400; +#endif
--- a/booker.pl Tue Jun 15 14:42:57 2004 +0000 +++ b/booker.pl Sun Dec 19 11:33:56 2004 +0000 @@ -82,8 +82,9 @@ # scan till next end of comment, e.g. skip license while (<SRC>) { $text[$line++] = $_; - last if ($_ =~ /tommath\.h/); + last if ($_ =~ /math\.libtomcrypt\.org/); } + <SRC>; } $inline = 0;
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/callgraph.txt Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,10168 @@ +BN_PRIME_TAB_C + + +BN_MP_SQRT_C ++--->BN_MP_N_ROOT_C +| +--->BN_MP_INIT_C +| +--->BN_MP_SET_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_EXPT_D_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_SQR_C +| | | +--->BN_MP_TOOM_SQR_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_KARATSUBA_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_FAST_S_MP_SQR_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| +--->BN_MP_MUL_C +| | +--->BN_MP_TOOM_MUL_C +| | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_KARATSUBA_MUL_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_MUL_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_CMP_C +| | +--->BN_MP_CMP_MAG_C +| +--->BN_MP_SUB_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_ZERO_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_RSHD_C ++--->BN_MP_DIV_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_SET_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_SIZE_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_MUL_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_ADD_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_DIV_2_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_MAG_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_CMP_D_C + + +BN_MP_EXCH_C + + +BN_MP_IS_SQUARE_C ++--->BN_MP_MOD_D_C +| +--->BN_MP_DIV_D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_INIT_SET_INT_C +| +--->BN_MP_INIT_C +| +--->BN_MP_SET_INT_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_MOD_C +| +--->BN_MP_INIT_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_GET_INT_C ++--->BN_MP_SQRT_C +| +--->BN_MP_N_ROOT_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_EXPT_D_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_SQR_C +| | | | +--->BN_MP_TOOM_SQR_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_FAST_S_MP_SQR_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_CMP_C +| | | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_SUB_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_2_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_SQR_C +| +--->BN_MP_TOOM_SQR_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_KARATSUBA_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | +--->BN_MP_ADD_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_SQR_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_CMP_MAG_C ++--->BN_MP_CLEAR_C + + +BN_MP_NEG_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C + + +BN_MP_EXPTMOD_C ++--->BN_MP_INIT_C ++--->BN_MP_INVMOD_C +| +--->BN_FAST_MP_INVMOD_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ABS_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_CMP_D_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_INVMOD_SLOW_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_CMP_D_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_C ++--->BN_MP_ABS_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_CLEAR_MULTI_C ++--->BN_MP_DR_IS_MODULUS_C ++--->BN_MP_REDUCE_IS_2K_C +| +--->BN_MP_REDUCE_2K_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_COUNT_BITS_C ++--->BN_MP_EXPTMOD_FAST_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_MONTGOMERY_SETUP_C +| +--->BN_FAST_MP_MONTGOMERY_REDUCE_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| +--->BN_MP_MONTGOMERY_REDUCE_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| +--->BN_MP_DR_SETUP_C +| +--->BN_MP_DR_REDUCE_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| +--->BN_MP_REDUCE_2K_SETUP_C +| | +--->BN_MP_2EXPT_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_GROW_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_REDUCE_2K_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +| | +--->BN_MP_2EXPT_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_MULMOD_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2D_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_COPY_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_SET_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_MOD_C +| | +--->BN_MP_DIV_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_SQR_C +| | +--->BN_MP_TOOM_SQR_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_KARATSUBA_SQR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | +--->BN_FAST_S_MP_SQR_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SQR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_MUL_C +| | +--->BN_MP_TOOM_MUL_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_KARATSUBA_MUL_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_EXCH_C ++--->BN_S_MP_EXPTMOD_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_REDUCE_SETUP_C +| | +--->BN_MP_2EXPT_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_DIV_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_SET_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_MOD_C +| | +--->BN_MP_DIV_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_SET_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_SQR_C +| | +--->BN_MP_TOOM_SQR_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_KARATSUBA_SQR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | +--->BN_FAST_S_MP_SQR_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SQR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_REDUCE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_D_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_MUL_C +| | +--->BN_MP_TOOM_MUL_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_KARATSUBA_MUL_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_SET_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_EXCH_C + + +BN_MP_OR_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_ZERO_C + + +BN_MP_GROW_C + + +BN_MP_COUNT_BITS_C + + +BN_MP_PRIME_FERMAT_C ++--->BN_MP_CMP_D_C ++--->BN_MP_INIT_C ++--->BN_MP_EXPTMOD_C +| +--->BN_MP_INVMOD_C +| | +--->BN_FAST_MP_INVMOD_C +| | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ABS_C +| | | +--->BN_MP_SET_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INVMOD_SLOW_C +| | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SET_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_ABS_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_DR_IS_MODULUS_C +| +--->BN_MP_REDUCE_IS_2K_C +| | +--->BN_MP_REDUCE_2K_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_EXPTMOD_FAST_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MONTGOMERY_SETUP_C +| | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | +--->BN_MP_MONTGOMERY_REDUCE_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | +--->BN_MP_DR_SETUP_C +| | +--->BN_MP_DR_REDUCE_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | +--->BN_MP_REDUCE_2K_SETUP_C +| | | +--->BN_MP_2EXPT_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_REDUCE_2K_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +| | | +--->BN_MP_2EXPT_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SET_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MULMOD_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_SET_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2D_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_INIT_COPY_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2D_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_COPY_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_SQR_C +| | | +--->BN_MP_TOOM_SQR_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | +--->BN_FAST_S_MP_SQR_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| +--->BN_S_MP_EXPTMOD_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_REDUCE_SETUP_C +| | | +--->BN_MP_2EXPT_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2D_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_COPY_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2D_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_COPY_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_SQR_C +| | | +--->BN_MP_TOOM_SQR_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | +--->BN_FAST_S_MP_SQR_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_REDUCE_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SET_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_EXCH_C ++--->BN_MP_CMP_C +| +--->BN_MP_CMP_MAG_C ++--->BN_MP_CLEAR_C + + +BN_MP_SUBMOD_C ++--->BN_MP_INIT_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_CLEAR_C ++--->BN_MP_MOD_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C + + +BN_MP_MOD_2D_C ++--->BN_MP_ZERO_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C + + +BN_MP_TORADIX_N_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_DIV_D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_DIV_3_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_SIZE_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_C + + +BN_MP_CMP_C ++--->BN_MP_CMP_MAG_C + + +BNCORE_C + + +BN_MP_TORADIX_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_DIV_D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_DIV_3_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_SIZE_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_C + + +BN_MP_ADD_D_C ++--->BN_MP_GROW_C ++--->BN_MP_SUB_D_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLAMP_C + + +BN_MP_DIV_3_C ++--->BN_MP_INIT_SIZE_C +| +--->BN_MP_INIT_C ++--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_FAST_S_MP_MUL_DIGS_C ++--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C + + +BN_MP_SQRMOD_C ++--->BN_MP_INIT_C ++--->BN_MP_SQR_C +| +--->BN_MP_TOOM_SQR_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_KARATSUBA_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | +--->BN_MP_ADD_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_SQR_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_C ++--->BN_MP_MOD_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C + + +BN_MP_INVMOD_C ++--->BN_FAST_MP_INVMOD_C +| +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ABS_C +| +--->BN_MP_SET_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_DIV_2_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_C +| | +--->BN_MP_CMP_MAG_C +| +--->BN_MP_CMP_D_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_INVMOD_SLOW_C +| +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_SET_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_DIV_2_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_C +| | +--->BN_MP_CMP_MAG_C +| +--->BN_MP_CMP_D_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_CLEAR_C + + +BN_MP_AND_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_MUL_D_C ++--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C + + +BN_FAST_MP_INVMOD_C ++--->BN_MP_INIT_MULTI_C +| +--->BN_MP_INIT_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_ABS_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_DIV_2_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_C +| +--->BN_MP_CMP_MAG_C ++--->BN_MP_CMP_D_C ++--->BN_MP_ADD_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_CLEAR_C + + +BN_MP_FWRITE_C ++--->BN_MP_RADIX_SIZE_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_DIV_D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_TORADIX_C +| +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_DIV_D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C + + +BN_S_MP_SQR_C ++--->BN_MP_INIT_SIZE_C +| +--->BN_MP_INIT_C ++--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_N_ROOT_C ++--->BN_MP_INIT_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_EXPT_D_C +| +--->BN_MP_INIT_COPY_C +| +--->BN_MP_SQR_C +| | +--->BN_MP_TOOM_SQR_C +| | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_KARATSUBA_SQR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_FAST_S_MP_SQR_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SQR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_MUL_C +| | +--->BN_MP_TOOM_MUL_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_KARATSUBA_MUL_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C ++--->BN_MP_MUL_C +| +--->BN_MP_TOOM_MUL_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_KARATSUBA_MUL_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_MUL_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_DIV_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_SIZE_C +| +--->BN_MP_INIT_COPY_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_CMP_C +| +--->BN_MP_CMP_MAG_C ++--->BN_MP_SUB_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_ADD_D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_PRIME_RABIN_MILLER_TRIALS_C + + +BN_MP_RADIX_SIZE_C ++--->BN_MP_COUNT_BITS_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_DIV_D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_DIV_3_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_SIZE_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_C + + +BN_MP_READ_SIGNED_BIN_C ++--->BN_MP_READ_UNSIGNED_BIN_C +| +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C + + +BN_MP_PRIME_RANDOM_EX_C ++--->BN_MP_READ_UNSIGNED_BIN_C +| +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_PRIME_IS_PRIME_C +| +--->BN_MP_CMP_D_C +| +--->BN_MP_PRIME_IS_DIVISIBLE_C +| | +--->BN_MP_MOD_D_C +| | | +--->BN_MP_DIV_D_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_DIV_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_INIT_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_INIT_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_C +| +--->BN_MP_SET_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_PRIME_MILLER_RABIN_C +| | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_SUB_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CNT_LSB_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXPTMOD_C +| | | +--->BN_MP_INVMOD_C +| | | | +--->BN_FAST_MP_INVMOD_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ABS_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_INVMOD_SLOW_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_ABS_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_DR_IS_MODULUS_C +| | | +--->BN_MP_REDUCE_IS_2K_C +| | | | +--->BN_MP_REDUCE_2K_C +| | | | | +--->BN_MP_COUNT_BITS_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_EXPTMOD_FAST_C +| | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_MONTGOMERY_SETUP_C +| | | | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_MONTGOMERY_REDUCE_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_DR_SETUP_C +| | | | +--->BN_MP_DR_REDUCE_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_REDUCE_2K_SETUP_C +| | | | | +--->BN_MP_2EXPT_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_REDUCE_2K_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +| | | | | +--->BN_MP_2EXPT_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MULMOD_C +| | | | | +--->BN_MP_MUL_C +| | | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | | | | +--->BN_MP_COPY_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_MUL_2_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_DIV_2_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_MUL_D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_DIV_3_C +| | | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_EXCH_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_MOD_C +| | | | | | +--->BN_MP_DIV_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_MUL_D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_MOD_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_SQR_C +| | | | | +--->BN_MP_TOOM_SQR_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_FAST_S_MP_SQR_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SQR_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_S_MP_EXPTMOD_C +| | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_REDUCE_SETUP_C +| | | | | +--->BN_MP_2EXPT_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MOD_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_SQR_C +| | | | | +--->BN_MP_TOOM_SQR_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_FAST_S_MP_SQR_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SQR_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_REDUCE_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_C +| | | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_MUL_2_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_DIV_2_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_MUL_D_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_DIV_3_C +| | | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | | +--->BN_MP_EXCH_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_SUB_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_ADD_C +| | | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_CMP_C +| | | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_SQRMOD_C +| | | +--->BN_MP_SQR_C +| | | | +--->BN_MP_TOOM_SQR_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_FAST_S_MP_SQR_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_COUNT_BITS_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_SUB_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_ADD_D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_DIV_2_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_MUL_2_C +| +--->BN_MP_GROW_C ++--->BN_MP_ADD_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C + + +BN_MP_KARATSUBA_SQR_C ++--->BN_MP_INIT_SIZE_C +| +--->BN_MP_INIT_C ++--->BN_MP_CLAMP_C ++--->BN_MP_SQR_C +| +--->BN_MP_TOOM_SQR_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_SQR_C +| | +--->BN_MP_GROW_C +| +--->BN_S_MP_SQR_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C ++--->BN_S_MP_ADD_C +| +--->BN_MP_GROW_C ++--->BN_MP_LSHD_C +| +--->BN_MP_GROW_C +| +--->BN_MP_RSHD_C +| | +--->BN_MP_ZERO_C ++--->BN_MP_ADD_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C ++--->BN_MP_CLEAR_C + + +BN_MP_INIT_COPY_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C + + +BN_MP_CLAMP_C + + +BN_MP_TOOM_SQR_C ++--->BN_MP_INIT_MULTI_C +| +--->BN_MP_INIT_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_MOD_2D_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_RSHD_C +| +--->BN_MP_ZERO_C ++--->BN_MP_SQR_C +| +--->BN_MP_KARATSUBA_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_SQR_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_MUL_2_C +| +--->BN_MP_GROW_C ++--->BN_MP_ADD_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_DIV_2_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_MUL_2D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_LSHD_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_MUL_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_DIV_3_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_LSHD_C +| +--->BN_MP_GROW_C ++--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_CLEAR_C + + +BN_MP_MOD_C ++--->BN_MP_INIT_C ++--->BN_MP_DIV_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_SET_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_SIZE_C +| +--->BN_MP_INIT_COPY_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_MUL_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_C ++--->BN_MP_ADD_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C + + +BN_MP_INIT_C + + +BN_MP_TOOM_MUL_C ++--->BN_MP_INIT_MULTI_C +| +--->BN_MP_INIT_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_MOD_2D_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_RSHD_C +| +--->BN_MP_ZERO_C ++--->BN_MP_MUL_C +| +--->BN_MP_KARATSUBA_MUL_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_MUL_2_C +| +--->BN_MP_GROW_C ++--->BN_MP_ADD_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_DIV_2_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_MUL_2D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_LSHD_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_MUL_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_DIV_3_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_LSHD_C +| +--->BN_MP_GROW_C ++--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_CLEAR_C + + +BN_MP_PRIME_IS_PRIME_C ++--->BN_MP_CMP_D_C ++--->BN_MP_PRIME_IS_DIVISIBLE_C +| +--->BN_MP_MOD_D_C +| | +--->BN_MP_DIV_D_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_INIT_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C ++--->BN_MP_INIT_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_PRIME_MILLER_RABIN_C +| +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_SUB_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CNT_LSB_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_EXPTMOD_C +| | +--->BN_MP_INVMOD_C +| | | +--->BN_FAST_MP_INVMOD_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ABS_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_INVMOD_SLOW_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_ABS_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_DR_IS_MODULUS_C +| | +--->BN_MP_REDUCE_IS_2K_C +| | | +--->BN_MP_REDUCE_2K_C +| | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_EXPTMOD_FAST_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_MONTGOMERY_SETUP_C +| | | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_MONTGOMERY_REDUCE_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_DR_SETUP_C +| | | +--->BN_MP_DR_REDUCE_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_REDUCE_2K_SETUP_C +| | | | +--->BN_MP_2EXPT_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_REDUCE_2K_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +| | | | +--->BN_MP_2EXPT_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MULMOD_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_MOD_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SQR_C +| | | | +--->BN_MP_TOOM_SQR_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_FAST_S_MP_SQR_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_S_MP_EXPTMOD_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_REDUCE_SETUP_C +| | | | +--->BN_MP_2EXPT_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SQR_C +| | | | +--->BN_MP_TOOM_SQR_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_FAST_S_MP_SQR_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_REDUCE_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_CMP_C +| | +--->BN_MP_CMP_MAG_C +| +--->BN_MP_SQRMOD_C +| | +--->BN_MP_SQR_C +| | | +--->BN_MP_TOOM_SQR_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_KARATSUBA_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_FAST_S_MP_SQR_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_C + + +BN_MP_COPY_C ++--->BN_MP_GROW_C + + +BN_S_MP_SUB_C ++--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C + + +BN_MP_READ_UNSIGNED_BIN_C ++--->BN_MP_GROW_C ++--->BN_MP_ZERO_C ++--->BN_MP_MUL_2D_C +| +--->BN_MP_COPY_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLAMP_C + + +BN_MP_EXPTMOD_FAST_C ++--->BN_MP_COUNT_BITS_C ++--->BN_MP_INIT_C ++--->BN_MP_CLEAR_C ++--->BN_MP_MONTGOMERY_SETUP_C ++--->BN_FAST_MP_MONTGOMERY_REDUCE_C +| +--->BN_MP_GROW_C +| +--->BN_MP_RSHD_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C ++--->BN_MP_MONTGOMERY_REDUCE_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_RSHD_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C ++--->BN_MP_DR_SETUP_C ++--->BN_MP_DR_REDUCE_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C ++--->BN_MP_REDUCE_2K_SETUP_C +| +--->BN_MP_2EXPT_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_GROW_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_REDUCE_2K_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_MUL_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +| +--->BN_MP_2EXPT_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_SET_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_MUL_2_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_MULMOD_C +| +--->BN_MP_MUL_C +| | +--->BN_MP_TOOM_MUL_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_KARATSUBA_MUL_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_MOD_C +| | +--->BN_MP_DIV_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_SET_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2D_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_COPY_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_MOD_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_SQR_C +| +--->BN_MP_TOOM_SQR_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_KARATSUBA_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | +--->BN_MP_ADD_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| +--->BN_FAST_S_MP_SQR_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C ++--->BN_MP_MUL_C +| +--->BN_MP_TOOM_MUL_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_KARATSUBA_MUL_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C ++--->BN_MP_EXCH_C + + +BN_MP_TO_UNSIGNED_BIN_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_DIV_2D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_SET_INT_C ++--->BN_MP_ZERO_C ++--->BN_MP_MUL_2D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_GROW_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLAMP_C + + +BN_MP_MOD_D_C ++--->BN_MP_DIV_D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_DIV_3_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C + + +BN_MP_SQR_C ++--->BN_MP_TOOM_SQR_C +| +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_RSHD_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_MUL_2_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_2_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_MUL_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_3_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_KARATSUBA_SQR_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| +--->BN_MP_ADD_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_CLEAR_C ++--->BN_FAST_S_MP_SQR_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_S_MP_SQR_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C + + +BN_MP_MULMOD_C ++--->BN_MP_INIT_C ++--->BN_MP_MUL_C +| +--->BN_MP_TOOM_MUL_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_KARATSUBA_MUL_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_C ++--->BN_MP_MOD_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C + + +BN_MP_DIV_2D_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_ZERO_C ++--->BN_MP_INIT_C ++--->BN_MP_MOD_2D_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLEAR_C ++--->BN_MP_RSHD_C ++--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C + + +BN_S_MP_ADD_C ++--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C + + +BN_FAST_S_MP_SQR_C ++--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C + + +BN_S_MP_MUL_DIGS_C ++--->BN_FAST_S_MP_MUL_DIGS_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_INIT_SIZE_C +| +--->BN_MP_INIT_C ++--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_XOR_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_RADIX_SMAP_C + + +BN_MP_DR_IS_MODULUS_C + + +BN_MP_MONTGOMERY_CALC_NORMALIZATION_C ++--->BN_MP_COUNT_BITS_C ++--->BN_MP_2EXPT_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_GROW_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_MUL_2_C +| +--->BN_MP_GROW_C ++--->BN_MP_CMP_MAG_C ++--->BN_S_MP_SUB_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C + + +BN_MP_SUB_C ++--->BN_S_MP_ADD_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_MAG_C ++--->BN_S_MP_SUB_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C + + +BN_MP_INIT_MULTI_C ++--->BN_MP_INIT_C ++--->BN_MP_CLEAR_C + + +BN_S_MP_MUL_HIGH_DIGS_C ++--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_INIT_SIZE_C +| +--->BN_MP_INIT_C ++--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_PRIME_NEXT_PRIME_C ++--->BN_MP_CMP_D_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_SUB_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_ADD_D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_MOD_D_C +| +--->BN_MP_DIV_D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_INIT_C ++--->BN_MP_ADD_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_PRIME_MILLER_RABIN_C +| +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_CNT_LSB_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_EXPTMOD_C +| | +--->BN_MP_INVMOD_C +| | | +--->BN_FAST_MP_INVMOD_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ABS_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_INVMOD_SLOW_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_ABS_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_DR_IS_MODULUS_C +| | +--->BN_MP_REDUCE_IS_2K_C +| | | +--->BN_MP_REDUCE_2K_C +| | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_EXPTMOD_FAST_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_MONTGOMERY_SETUP_C +| | | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_MONTGOMERY_REDUCE_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_DR_SETUP_C +| | | +--->BN_MP_DR_REDUCE_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_REDUCE_2K_SETUP_C +| | | | +--->BN_MP_2EXPT_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_REDUCE_2K_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +| | | | +--->BN_MP_2EXPT_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MULMOD_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_COPY_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_MOD_C +| | | | | +--->BN_MP_DIV_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SQR_C +| | | | +--->BN_MP_TOOM_SQR_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_FAST_S_MP_SQR_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_S_MP_EXPTMOD_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_REDUCE_SETUP_C +| | | | +--->BN_MP_2EXPT_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SQR_C +| | | | +--->BN_MP_TOOM_SQR_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_FAST_S_MP_SQR_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SQR_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_REDUCE_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_C +| | | | | +--->BN_MP_TOOM_MUL_C +| | | | | | +--->BN_MP_INIT_MULTI_C +| | | | | | +--->BN_MP_MOD_2D_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_2_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_2D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_MUL_D_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_DIV_3_C +| | | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | | +--->BN_MP_EXCH_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_SUB_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_ADD_C +| | | | | | | +--->BN_S_MP_ADD_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | | +--->BN_S_MP_SUB_C +| | | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_CMP_C +| | +--->BN_MP_CMP_MAG_C +| +--->BN_MP_SQRMOD_C +| | +--->BN_MP_SQR_C +| | | +--->BN_MP_TOOM_SQR_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_CLEAR_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_KARATSUBA_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_FAST_S_MP_SQR_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_COUNT_BITS_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_C + + +BN_MP_SIGNED_BIN_SIZE_C ++--->BN_MP_UNSIGNED_BIN_SIZE_C +| +--->BN_MP_COUNT_BITS_C + + +BN_MP_INVMOD_SLOW_C ++--->BN_MP_INIT_MULTI_C +| +--->BN_MP_INIT_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_DIV_2_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_ADD_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_C +| +--->BN_MP_CMP_MAG_C ++--->BN_MP_CMP_D_C ++--->BN_MP_CMP_MAG_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_CLEAR_C + + +BN_MP_LCM_C ++--->BN_MP_INIT_MULTI_C +| +--->BN_MP_INIT_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_GCD_C +| +--->BN_MP_ABS_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_CNT_LSB_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_MP_EXCH_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_CMP_MAG_C ++--->BN_MP_DIV_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_SET_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_INIT_C +| +--->BN_MP_INIT_COPY_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_MUL_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_MUL_C +| +--->BN_MP_TOOM_MUL_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_KARATSUBA_MUL_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_CLEAR_C + + +BN_REVERSE_C + + +BN_MP_PRIME_IS_DIVISIBLE_C ++--->BN_MP_MOD_D_C +| +--->BN_MP_DIV_D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C + + +BN_MP_SET_C ++--->BN_MP_ZERO_C + + +BN_MP_GCD_C ++--->BN_MP_ABS_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_ZERO_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_CNT_LSB_C ++--->BN_MP_DIV_2D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_CMP_MAG_C ++--->BN_MP_EXCH_C ++--->BN_S_MP_SUB_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_MUL_2D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_GROW_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLEAR_C + + +BN_MP_READ_RADIX_C ++--->BN_MP_ZERO_C ++--->BN_MP_MUL_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_ADD_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_SUB_D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C + + +BN_FAST_S_MP_MUL_HIGH_DIGS_C ++--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C + + +BN_FAST_MP_MONTGOMERY_REDUCE_C ++--->BN_MP_GROW_C ++--->BN_MP_RSHD_C +| +--->BN_MP_ZERO_C ++--->BN_MP_CLAMP_C ++--->BN_MP_CMP_MAG_C ++--->BN_S_MP_SUB_C + + +BN_MP_DIV_D_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_DIV_2D_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_INIT_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_DIV_3_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_INIT_SIZE_C +| +--->BN_MP_INIT_C ++--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_REDUCE_2K_SETUP_C ++--->BN_MP_INIT_C ++--->BN_MP_COUNT_BITS_C ++--->BN_MP_2EXPT_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_GROW_C ++--->BN_MP_CLEAR_C ++--->BN_S_MP_SUB_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C + + +BN_MP_INIT_SET_C ++--->BN_MP_INIT_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C + + +BN_MP_REDUCE_2K_C ++--->BN_MP_INIT_C ++--->BN_MP_COUNT_BITS_C ++--->BN_MP_DIV_2D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_MUL_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_S_MP_ADD_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_MAG_C ++--->BN_S_MP_SUB_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLEAR_C + + +BN_ERROR_C + + +BN_MP_EXPT_D_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_SQR_C +| +--->BN_MP_TOOM_SQR_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_KARATSUBA_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | +--->BN_MP_ADD_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_SQR_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_CLEAR_C ++--->BN_MP_MUL_C +| +--->BN_MP_TOOM_MUL_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_KARATSUBA_MUL_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C + + +BN_S_MP_EXPTMOD_C ++--->BN_MP_COUNT_BITS_C ++--->BN_MP_INIT_C ++--->BN_MP_CLEAR_C ++--->BN_MP_REDUCE_SETUP_C +| +--->BN_MP_2EXPT_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_MOD_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_SQR_C +| +--->BN_MP_TOOM_SQR_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_KARATSUBA_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | +--->BN_MP_ADD_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| +--->BN_FAST_S_MP_SQR_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_SQR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C ++--->BN_MP_REDUCE_C +| +--->BN_MP_INIT_COPY_C +| +--->BN_MP_RSHD_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_MUL_C +| | +--->BN_MP_TOOM_MUL_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_KARATSUBA_MUL_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_MUL_DIGS_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| +--->BN_S_MP_MUL_HIGH_DIGS_C +| | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_D_C +| +--->BN_MP_SET_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_C +| | +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_MUL_C +| +--->BN_MP_TOOM_MUL_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_KARATSUBA_MUL_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_EXCH_C + + +BN_MP_ABS_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C + + +BN_MP_INIT_SET_INT_C ++--->BN_MP_INIT_C ++--->BN_MP_SET_INT_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C + + +BN_MP_SUB_D_C ++--->BN_MP_GROW_C ++--->BN_MP_ADD_D_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLAMP_C + + +BN_MP_TO_SIGNED_BIN_C ++--->BN_MP_TO_UNSIGNED_BIN_C +| +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C + + +BN_MP_DIV_2_C ++--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C + + +BN_MP_REDUCE_IS_2K_C ++--->BN_MP_REDUCE_2K_C +| +--->BN_MP_INIT_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_MUL_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_COUNT_BITS_C + + +BN_MP_INIT_SIZE_C ++--->BN_MP_INIT_C + + +BN_MP_DIV_C ++--->BN_MP_CMP_MAG_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_ZERO_C ++--->BN_MP_INIT_MULTI_C +| +--->BN_MP_INIT_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_SET_C ++--->BN_MP_COUNT_BITS_C ++--->BN_MP_MUL_2D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_ADD_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_DIV_2D_C +| +--->BN_MP_INIT_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_INIT_SIZE_C +| +--->BN_MP_INIT_C ++--->BN_MP_INIT_C ++--->BN_MP_INIT_COPY_C ++--->BN_MP_LSHD_C +| +--->BN_MP_GROW_C +| +--->BN_MP_RSHD_C ++--->BN_MP_RSHD_C ++--->BN_MP_MUL_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLAMP_C ++--->BN_MP_CLEAR_C + + +BN_MP_CLEAR_C + + +BN_MP_MONTGOMERY_REDUCE_C ++--->BN_FAST_MP_MONTGOMERY_REDUCE_C +| +--->BN_MP_GROW_C +| +--->BN_MP_RSHD_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C ++--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C ++--->BN_MP_RSHD_C +| +--->BN_MP_ZERO_C ++--->BN_MP_CMP_MAG_C ++--->BN_S_MP_SUB_C + + +BN_MP_MUL_2_C ++--->BN_MP_GROW_C + + +BN_MP_UNSIGNED_BIN_SIZE_C ++--->BN_MP_COUNT_BITS_C + + +BN_MP_ADDMOD_C ++--->BN_MP_INIT_C ++--->BN_MP_ADD_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_CLEAR_C ++--->BN_MP_MOD_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C + + +BN_MP_ADD_C ++--->BN_S_MP_ADD_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_MAG_C ++--->BN_S_MP_SUB_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C + + +BN_MP_RAND_C ++--->BN_MP_ZERO_C ++--->BN_MP_ADD_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_SUB_D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_LSHD_C +| +--->BN_MP_GROW_C +| +--->BN_MP_RSHD_C + + +BN_MP_CNT_LSB_C + + +BN_MP_2EXPT_C ++--->BN_MP_ZERO_C ++--->BN_MP_GROW_C + + +BN_MP_RSHD_C ++--->BN_MP_ZERO_C + + +BN_MP_SHRINK_C + + +BN_MP_REDUCE_C ++--->BN_MP_REDUCE_SETUP_C +| +--->BN_MP_2EXPT_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2D_C +| | | +--->BN_MP_INIT_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_INIT_COPY_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_RSHD_C +| +--->BN_MP_ZERO_C ++--->BN_MP_MUL_C +| +--->BN_MP_TOOM_MUL_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_KARATSUBA_MUL_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_S_MP_MUL_HIGH_DIGS_C +| +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_INIT_SIZE_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_MOD_2D_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_S_MP_MUL_DIGS_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_INIT_SIZE_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_D_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_LSHD_C +| +--->BN_MP_GROW_C ++--->BN_MP_ADD_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_C +| +--->BN_MP_CMP_MAG_C ++--->BN_S_MP_SUB_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CLEAR_C + + +BN_MP_MUL_2D_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_GROW_C ++--->BN_MP_LSHD_C +| +--->BN_MP_RSHD_C +| | +--->BN_MP_ZERO_C ++--->BN_MP_CLAMP_C + + +BN_MP_GET_INT_C + + +BN_MP_JACOBI_C ++--->BN_MP_CMP_D_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_CNT_LSB_C ++--->BN_MP_DIV_2D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_MOD_C +| +--->BN_MP_DIV_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_SET_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_CLEAR_MULTI_C ++--->BN_MP_CLEAR_C + + +BN_MP_MUL_C ++--->BN_MP_TOOM_MUL_C +| +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_ZERO_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_RSHD_C +| | +--->BN_MP_ZERO_C +| +--->BN_MP_MUL_2_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_2_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_MUL_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_3_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_KARATSUBA_MUL_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CMP_MAG_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| +--->BN_MP_CLEAR_C ++--->BN_FAST_S_MP_MUL_DIGS_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_S_MP_MUL_DIGS_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_C + + +BN_MP_EXTEUCLID_C ++--->BN_MP_INIT_MULTI_C +| +--->BN_MP_INIT_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_SET_C +| +--->BN_MP_ZERO_C ++--->BN_MP_COPY_C +| +--->BN_MP_GROW_C ++--->BN_MP_DIV_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_INIT_C +| +--->BN_MP_INIT_COPY_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_MUL_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C ++--->BN_MP_MUL_C +| +--->BN_MP_TOOM_MUL_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_KARATSUBA_MUL_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C ++--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_CLEAR_C + + +BN_MP_DR_REDUCE_C ++--->BN_MP_GROW_C ++--->BN_MP_CLAMP_C ++--->BN_MP_CMP_MAG_C ++--->BN_S_MP_SUB_C + + +BN_MP_FREAD_C ++--->BN_MP_ZERO_C ++--->BN_MP_MUL_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_ADD_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_SUB_D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CMP_D_C + + +BN_MP_REDUCE_SETUP_C ++--->BN_MP_2EXPT_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_GROW_C ++--->BN_MP_DIV_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_INIT_MULTI_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_SET_C +| +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_MUL_2D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CMP_C +| +--->BN_MP_SUB_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_ADD_C +| | +--->BN_S_MP_ADD_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SUB_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| +--->BN_MP_DIV_2D_C +| | +--->BN_MP_INIT_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_CLEAR_C +| | +--->BN_MP_RSHD_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| +--->BN_MP_EXCH_C +| +--->BN_MP_CLEAR_MULTI_C +| | +--->BN_MP_CLEAR_C +| +--->BN_MP_INIT_SIZE_C +| | +--->BN_MP_INIT_C +| +--->BN_MP_INIT_C +| +--->BN_MP_INIT_COPY_C +| +--->BN_MP_LSHD_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_MUL_D_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C + + +BN_MP_MONTGOMERY_SETUP_C + + +BN_MP_KARATSUBA_MUL_C ++--->BN_MP_MUL_C +| +--->BN_MP_TOOM_MUL_C +| | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_MOD_2D_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_RSHD_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MUL_2_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_SUB_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_2_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_2D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_D_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_DIV_3_C +| | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_INIT_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_LSHD_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_FAST_S_MP_MUL_DIGS_C +| | +--->BN_MP_GROW_C +| | +--->BN_MP_CLAMP_C +| +--->BN_S_MP_MUL_DIGS_C +| | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_INIT_C +| | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C +| | +--->BN_MP_CLEAR_C ++--->BN_MP_INIT_SIZE_C +| +--->BN_MP_INIT_C ++--->BN_MP_CLAMP_C ++--->BN_MP_SUB_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C ++--->BN_MP_ADD_C +| +--->BN_S_MP_ADD_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_CMP_MAG_C +| +--->BN_S_MP_SUB_C +| | +--->BN_MP_GROW_C ++--->BN_MP_LSHD_C +| +--->BN_MP_GROW_C +| +--->BN_MP_RSHD_C +| | +--->BN_MP_ZERO_C ++--->BN_MP_CLEAR_C + + +BN_MP_LSHD_C ++--->BN_MP_GROW_C ++--->BN_MP_RSHD_C +| +--->BN_MP_ZERO_C + + +BN_MP_PRIME_MILLER_RABIN_C ++--->BN_MP_CMP_D_C ++--->BN_MP_INIT_COPY_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C ++--->BN_MP_SUB_D_C +| +--->BN_MP_GROW_C +| +--->BN_MP_ADD_D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLAMP_C ++--->BN_MP_CNT_LSB_C ++--->BN_MP_DIV_2D_C +| +--->BN_MP_COPY_C +| | +--->BN_MP_GROW_C +| +--->BN_MP_ZERO_C +| +--->BN_MP_MOD_2D_C +| | +--->BN_MP_CLAMP_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_RSHD_C +| +--->BN_MP_CLAMP_C +| +--->BN_MP_EXCH_C ++--->BN_MP_EXPTMOD_C +| +--->BN_MP_INVMOD_C +| | +--->BN_FAST_MP_INVMOD_C +| | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ABS_C +| | | +--->BN_MP_SET_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_INVMOD_SLOW_C +| | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SET_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_ABS_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| +--->BN_MP_CLEAR_MULTI_C +| +--->BN_MP_DR_IS_MODULUS_C +| +--->BN_MP_REDUCE_IS_2K_C +| | +--->BN_MP_REDUCE_2K_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_COUNT_BITS_C +| +--->BN_MP_EXPTMOD_FAST_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_MONTGOMERY_SETUP_C +| | +--->BN_FAST_MP_MONTGOMERY_REDUCE_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | +--->BN_MP_MONTGOMERY_REDUCE_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | +--->BN_MP_DR_SETUP_C +| | +--->BN_MP_DR_REDUCE_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | +--->BN_MP_REDUCE_2K_SETUP_C +| | | +--->BN_MP_2EXPT_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_REDUCE_2K_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +| | | +--->BN_MP_2EXPT_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_SET_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MULMOD_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_COPY_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_MOD_C +| | | | +--->BN_MP_DIV_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_MP_COPY_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_SET_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_SQR_C +| | | +--->BN_MP_TOOM_SQR_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | +--->BN_FAST_S_MP_SQR_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_EXCH_C +| +--->BN_S_MP_EXPTMOD_C +| | +--->BN_MP_COUNT_BITS_C +| | +--->BN_MP_REDUCE_SETUP_C +| | | +--->BN_MP_2EXPT_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MOD_C +| | | +--->BN_MP_DIV_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_SET_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | +--->BN_MP_COPY_C +| | | +--->BN_MP_GROW_C +| | +--->BN_MP_SQR_C +| | | +--->BN_MP_TOOM_SQR_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | +--->BN_FAST_S_MP_SQR_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_SQR_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_REDUCE_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_C +| | | | +--->BN_MP_TOOM_MUL_C +| | | | | +--->BN_MP_INIT_MULTI_C +| | | | | +--->BN_MP_MOD_2D_C +| | | | | | +--->BN_MP_ZERO_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_2_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_2D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_MUL_D_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_DIV_3_C +| | | | | | +--->BN_MP_INIT_SIZE_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | | +--->BN_MP_EXCH_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_KARATSUBA_MUL_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_SUB_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_ADD_C +| | | | | | +--->BN_S_MP_ADD_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CMP_MAG_C +| | | | | | +--->BN_S_MP_SUB_C +| | | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | +--->BN_S_MP_MUL_HIGH_DIGS_C +| | | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_FAST_S_MP_MUL_HIGH_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SET_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_MUL_C +| | | +--->BN_MP_TOOM_MUL_C +| | | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_MOD_2D_C +| | | | | +--->BN_MP_ZERO_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_MUL_2_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_2_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_2D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_MUL_D_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_DIV_3_C +| | | | | +--->BN_MP_INIT_SIZE_C +| | | | | +--->BN_MP_CLAMP_C +| | | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_KARATSUBA_MUL_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_SUB_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_ADD_C +| | | | | +--->BN_S_MP_ADD_C +| | | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CMP_MAG_C +| | | | | +--->BN_S_MP_SUB_C +| | | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_RSHD_C +| | | | | | +--->BN_MP_ZERO_C +| | | +--->BN_FAST_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_S_MP_MUL_DIGS_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | +--->BN_MP_SET_C +| | | +--->BN_MP_ZERO_C +| | +--->BN_MP_EXCH_C ++--->BN_MP_CMP_C +| +--->BN_MP_CMP_MAG_C ++--->BN_MP_SQRMOD_C +| +--->BN_MP_SQR_C +| | +--->BN_MP_TOOM_SQR_C +| | | +--->BN_MP_INIT_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_MOD_2D_C +| | | | +--->BN_MP_ZERO_C +| | | | +--->BN_MP_COPY_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_MUL_2_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_2_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_DIV_3_C +| | | | +--->BN_MP_INIT_SIZE_C +| | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_MP_EXCH_C +| | | | +--->BN_MP_CLEAR_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | | +--->BN_MP_CLEAR_C +| | +--->BN_MP_KARATSUBA_SQR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_MP_CMP_MAG_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLEAR_C +| | +--->BN_FAST_S_MP_SQR_C +| | | +--->BN_MP_GROW_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_S_MP_SQR_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_C +| +--->BN_MP_CLEAR_C +| +--->BN_MP_MOD_C +| | +--->BN_MP_DIV_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_MP_COPY_C +| | | | +--->BN_MP_GROW_C +| | | +--->BN_MP_ZERO_C +| | | +--->BN_MP_INIT_MULTI_C +| | | +--->BN_MP_SET_C +| | | +--->BN_MP_COUNT_BITS_C +| | | +--->BN_MP_MUL_2D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_LSHD_C +| | | | | +--->BN_MP_RSHD_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_SUB_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_ADD_C +| | | | +--->BN_S_MP_ADD_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | | +--->BN_S_MP_SUB_C +| | | | | +--->BN_MP_GROW_C +| | | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_EXCH_C +| | | +--->BN_MP_CLEAR_MULTI_C +| | | +--->BN_MP_INIT_SIZE_C +| | | +--->BN_MP_LSHD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_RSHD_C +| | | +--->BN_MP_MUL_D_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_ADD_C +| | | +--->BN_S_MP_ADD_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | | +--->BN_MP_CMP_MAG_C +| | | +--->BN_S_MP_SUB_C +| | | | +--->BN_MP_GROW_C +| | | | +--->BN_MP_CLAMP_C +| | +--->BN_MP_EXCH_C ++--->BN_MP_CLEAR_C + + +BN_MP_DR_SETUP_C + + +BN_MP_CMP_MAG_C + +
--- a/changes.txt Tue Jun 15 14:42:57 2004 +0000 +++ b/changes.txt Sun Dec 19 11:33:56 2004 +0000 @@ -1,3 +1,27 @@ +October 29th, 2004 +v0.32 -- Added "makefile.shared" for shared object support + -- Added more to the build options/configs in the manual + -- Started the Depends framework, wrote dep.pl to scan deps and + produce "callgraph.txt" ;-) + -- Wrote SC_RSA_1 which will enable close to the minimum required to perform + RSA on 32-bit [or 64-bit] platforms with LibTomCrypt + -- Merged in the small/slower mp_div replacement. You can now toggle which + you want to use as your mp_div() at build time. Saves roughly 8KB or so. + -- Renamed a few files and changed some comments to make depends system work better. + (No changes to function names) + -- Merged in new Combas that perform 2 reads per inner loop instead of the older + 3reads/2writes per inner loop of the old code. Really though if you want speed + learn to use TomsFastMath ;-) + +August 9th, 2004 +v0.31 -- "profiled" builds now :-) new timings for Intel Northwoods + -- Added "pretty" build target + -- Update mp_init() to actually assign 0's instead of relying on calloc() + -- "Wolfgang Ehrhardt" <[email protected]> found a bug in mp_mul() where if + you multiply a negative by zero you get negative zero as the result. Oops. + -- J Harper from PeerSec let me toy with his AMD64 and I got 60-bit digits working properly + [this also means that I fixed a bug where if sizeof(int) < sizeof(mp_digit) it would bug] + April 11th, 2004 v0.30 -- Added "mp_toradix_n" which stores upto "n-1" least significant digits of an mp_int -- Johan Lindh sent a patch so MSVC wouldn't whine about redefining malloc [in weird dll modes]
--- a/demo/demo.c Tue Jun 15 14:42:57 2004 +0000 +++ b/demo/demo.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,7 +1,5 @@ #include <time.h> -#define TESTING - #ifdef IOWNANATHLON #include <unistd.h> #define SLEEP sleep(4) @@ -11,49 +9,6 @@ #include "tommath.h" -#ifdef TIMER -ulong64 _tt; - -#if defined(__i386__) || defined(_M_IX86) || defined(_M_AMD64) -/* RDTSC from Scott Duplichan */ -static ulong64 TIMFUNC (void) - { - #if defined __GNUC__ - #ifdef __i386__ - ulong64 a; - __asm__ __volatile__ ("rdtsc ":"=A" (a)); - return a; - #else /* gcc-IA64 version */ - unsigned long result; - __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory"); - while (__builtin_expect ((int) result == -1, 0)) - __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory"); - return result; - #endif - - // Microsoft and Intel Windows compilers - #elif defined _M_IX86 - __asm rdtsc - #elif defined _M_AMD64 - return __rdtsc (); - #elif defined _M_IA64 - #if defined __INTEL_COMPILER - #include <ia64intrin.h> - #endif - return __getReg (3116); - #else - #error need rdtsc function for this build - #endif - } -#else -#define TIMFUNC clock -#endif - -ulong64 rdtsc(void) { return TIMFUNC() - _tt; } -void reset(void) { _tt = TIMFUNC(); } - -#endif - void ndraw(mp_int *a, char *name) { char buf[4096]; @@ -89,10 +44,6 @@ } -#define DO2(x) x; x; -#define DO4(x) DO2(x); DO2(x); -#define DO8(x) DO4(x); DO4(x); -#define DO(x) DO8(x); DO8(x); char cmd[4096], buf[4096]; int main(void) @@ -103,10 +54,6 @@ unsigned rr; int i, n, err, cnt, ix, old_kara_m, old_kara_s; -#ifdef TIMER - ulong64 tt, CLK_PER_SEC; - FILE *log, *logb, *logc; -#endif mp_init(&a); mp_init(&b); @@ -117,11 +64,11 @@ srand(time(NULL)); -#ifdef TESTING +#if 0 // test mp_get_int printf("Testing: mp_get_int\n"); for(i=0;i<1000;++i) { - t = (unsigned long)rand()*rand()+1; + t = ((unsigned long)rand()*rand()+1)&0xFFFFFFFF; mp_set_int(&a,t); if (t!=mp_get_int(&a)) { printf("mp_get_int() bad result!\n"); @@ -141,7 +88,7 @@ // test mp_sqrt printf("Testing: mp_sqrt\n"); - for (i=0;i<10000;++i) { + for (i=0;i<1000;++i) { printf("%6d\r", i); fflush(stdout); n = (rand()&15)+1; mp_rand(&a,n); @@ -157,7 +104,7 @@ } printf("\nTesting: mp_is_square\n"); - for (i=0;i<100000;++i) { + for (i=0;i<1000;++i) { printf("%6d\r", i); fflush(stdout); /* test mp_is_square false negatives */ @@ -186,11 +133,9 @@ } printf("\n\n"); -#endif -#ifdef TESTING /* test for size */ - for (ix = 16; ix < 512; ix++) { + for (ix = 10; ix < 256; ix++) { printf("Testing (not safe-prime): %9d bits \r", ix); fflush(stdout); err = mp_prime_random_ex(&a, 8, ix, (rand()&1)?LTM_PRIME_2MSB_OFF:LTM_PRIME_2MSB_ON, myrng, NULL); if (err != MP_OKAY) { @@ -203,7 +148,7 @@ } } - for (ix = 16; ix < 512; ix++) { + for (ix = 16; ix < 256; ix++) { printf("Testing ( safe-prime): %9d bits \r", ix); fflush(stdout); err = mp_prime_random_ex(&a, 8, ix, ((rand()&1)?LTM_PRIME_2MSB_OFF:LTM_PRIME_2MSB_ON)|LTM_PRIME_SAFE, myrng, NULL); if (err != MP_OKAY) { @@ -225,9 +170,7 @@ } printf("\n\n"); -#endif -#ifdef TESTING mp_read_radix(&a, "123456", 10); mp_toradix_n(&a, buf, 10, 3); printf("a == %s\n", buf); @@ -235,7 +178,6 @@ printf("a == %s\n", buf); mp_toradix_n(&a, buf, 10, 30); printf("a == %s\n", buf); -#endif #if 0 @@ -248,22 +190,6 @@ } #endif -#if 0 -{ - mp_word aa, bb; - - for (;;) { - aa = abs(rand()) & MP_MASK; - bb = abs(rand()) & MP_MASK; - if (MULT(aa,bb) != (aa*bb)) { - printf("%llu * %llu == %llu or %llu?\n", aa, bb, (ulong64)MULT(aa,bb), (ulong64)(aa*bb)); - return 0; - } - } -} -#endif - -#ifdef TESTING /* test mp_cnt_lsb */ printf("testing mp_cnt_lsb...\n"); mp_set(&a, 1); @@ -274,12 +200,10 @@ } mp_mul_2(&a, &a); } -#endif /* test mp_reduce_2k */ -#ifdef TESTING printf("Testing mp_reduce_2k...\n"); - for (cnt = 3; cnt <= 384; ++cnt) { + for (cnt = 3; cnt <= 128; ++cnt) { mp_digit tmp; mp_2expt(&a, cnt); mp_sub_d(&a, 2, &a); /* a = 2**cnt - 2 */ @@ -289,7 +213,7 @@ printf("(%d)", mp_reduce_is_2k(&a)); mp_reduce_2k_setup(&a, &tmp); printf("(%d)", tmp); - for (ix = 0; ix < 10000; ix++) { + for (ix = 0; ix < 1000; ix++) { if (!(ix & 127)) {printf("."); fflush(stdout); } mp_rand(&b, (cnt/DIGIT_BIT + 1) * 2); mp_copy(&c, &b); @@ -301,14 +225,11 @@ } } } -#endif - /* test mp_div_3 */ -#ifdef TESTING printf("Testing mp_div_3...\n"); mp_set(&d, 3); - for (cnt = 0; cnt < 1000000; ) { + for (cnt = 0; cnt < 10000; ) { mp_digit r1, r2; if (!(++cnt & 127)) printf("%9d\r", cnt); @@ -321,12 +242,10 @@ } } printf("\n\nPassed div_3 testing\n"); -#endif /* test the DR reduction */ -#ifdef TESTING printf("testing mp_dr_reduce...\n"); - for (cnt = 2; cnt < 128; cnt++) { + for (cnt = 2; cnt < 32; cnt++) { printf("%d digit modulus\n", cnt); mp_grow(&a, cnt); mp_zero(&a); @@ -334,7 +253,7 @@ a.dp[ix] = MP_MASK; } a.used = cnt; - mp_prime_next_prime(&a, 3, 0); + a.dp[0] = 3; mp_rand(&b, cnt - 1); mp_copy(&b, &c); @@ -346,204 +265,15 @@ mp_copy(&b, &c); mp_mod(&b, &a, &b); - mp_dr_reduce(&c, &a, (1<<DIGIT_BIT)-a.dp[0]); + mp_dr_reduce(&c, &a, (((mp_digit)1)<<DIGIT_BIT)-a.dp[0]); if (mp_cmp(&b, &c) != MP_EQ) { printf("Failed on trial %lu\n", rr); exit(-1); } - } while (++rr < 100000); + } while (++rr < 500); printf("Passed DR test for %d digits\n", cnt); } -#endif - -#ifdef TIMER - /* temp. turn off TOOM */ - TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000; - - reset(); - sleep(1); - CLK_PER_SEC = rdtsc(); - - printf("CLK_PER_SEC == %lu\n", CLK_PER_SEC); - - - log = fopen("logs/add.log", "w"); - for (cnt = 8; cnt <= 128; cnt += 8) { - SLEEP; - mp_rand(&a, cnt); - mp_rand(&b, cnt); - reset(); - rr = 0; - do { - DO(mp_add(&a,&b,&c)); - rr += 16; - } while (rdtsc() < (CLK_PER_SEC * 2)); - tt = rdtsc(); - printf("Adding\t\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt); - fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, (((ulong64)rr)*CLK_PER_SEC)/tt); fflush(log); - } - fclose(log); - - log = fopen("logs/sub.log", "w"); - for (cnt = 8; cnt <= 128; cnt += 8) { - SLEEP; - mp_rand(&a, cnt); - mp_rand(&b, cnt); - reset(); - rr = 0; - do { - DO(mp_sub(&a,&b,&c)); - rr += 16; - } while (rdtsc() < (CLK_PER_SEC * 2)); - tt = rdtsc(); - printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt); - fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, (((ulong64)rr)*CLK_PER_SEC)/tt); fflush(log); - } - fclose(log); - - /* do mult/square twice, first without karatsuba and second with */ -mult_test: - old_kara_m = KARATSUBA_MUL_CUTOFF; - old_kara_s = KARATSUBA_SQR_CUTOFF; - for (ix = 0; ix < 2; ix++) { - printf("With%s Karatsuba\n", (ix==0)?"out":""); - - KARATSUBA_MUL_CUTOFF = (ix==0)?9999:old_kara_m; - KARATSUBA_SQR_CUTOFF = (ix==0)?9999:old_kara_s; - - log = fopen((ix==0)?"logs/mult.log":"logs/mult_kara.log", "w"); - for (cnt = 32; cnt <= 288; cnt += 8) { - SLEEP; - mp_rand(&a, cnt); - mp_rand(&b, cnt); - reset(); - rr = 0; - do { - DO(mp_mul(&a, &b, &c)); - rr += 16; - } while (rdtsc() < (CLK_PER_SEC * 2)); - tt = rdtsc(); - printf("Multiplying\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt); - fprintf(log, "%d %9llu\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt); fflush(log); - } - fclose(log); - - log = fopen((ix==0)?"logs/sqr.log":"logs/sqr_kara.log", "w"); - for (cnt = 32; cnt <= 288; cnt += 8) { - SLEEP; - mp_rand(&a, cnt); - reset(); - rr = 0; - do { - DO(mp_sqr(&a, &b)); - rr += 16; - } while (rdtsc() < (CLK_PER_SEC * 2)); - tt = rdtsc(); - printf("Squaring\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt); - fprintf(log, "%d %9llu\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt); fflush(log); - } - fclose(log); - - } -expt_test: - { - char *primes[] = { - /* 2K moduli mersenne primes */ - "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", - "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127", - "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087", - "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007", - "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071", - "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991", - - /* DR moduli */ - "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079", - "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039", - "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431", - "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783", - "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147", - "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503", - "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679", - - /* generic unrestricted moduli */ - "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203", - "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487", - "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319", - "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887", - "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227", - "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207", - "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979", - NULL - }; - log = fopen("logs/expt.log", "w"); - logb = fopen("logs/expt_dr.log", "w"); - logc = fopen("logs/expt_2k.log", "w"); - for (n = 0; primes[n]; n++) { - SLEEP; - mp_read_radix(&a, primes[n], 10); - mp_zero(&b); - for (rr = 0; rr < mp_count_bits(&a); rr++) { - mp_mul_2(&b, &b); - b.dp[0] |= lbit(); - b.used += 1; - } - mp_sub_d(&a, 1, &c); - mp_mod(&b, &c, &b); - mp_set(&c, 3); - reset(); - rr = 0; - do { - DO(mp_exptmod(&c, &b, &a, &d)); - rr += 16; - } while (rdtsc() < (CLK_PER_SEC * 2)); - tt = rdtsc(); - mp_sub_d(&a, 1, &e); - mp_sub(&e, &b, &b); - mp_exptmod(&c, &b, &a, &e); /* c^(p-1-b) mod a */ - mp_mulmod(&e, &d, &a, &d); /* c^b * c^(p-1-b) == c^p-1 == 1 */ - if (mp_cmp_d(&d, 1)) { - printf("Different (%d)!!!\n", mp_count_bits(&a)); - draw(&d); - exit(0); - } - printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt); - fprintf((n < 6) ? logc : (n < 13) ? logb : log, "%d %9llu\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt); - } - } - fclose(log); - fclose(logb); - fclose(logc); - - log = fopen("logs/invmod.log", "w"); - for (cnt = 4; cnt <= 128; cnt += 4) { - SLEEP; - mp_rand(&a, cnt); - mp_rand(&b, cnt); - - do { - mp_add_d(&b, 1, &b); - mp_gcd(&a, &b, &c); - } while (mp_cmp_d(&c, 1) != MP_EQ); - - reset(); - rr = 0; - do { - DO(mp_invmod(&b, &a, &c)); - rr += 16; - } while (rdtsc() < (CLK_PER_SEC * 2)); - tt = rdtsc(); - mp_mulmod(&b, &c, &a, &d); - if (mp_cmp_d(&d, 1) != MP_EQ) { - printf("Failed to invert\n"); - return 0; - } - printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu ticks\n", mp_count_bits(&a), (((ulong64)rr)*CLK_PER_SEC)/tt, tt); - fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, (((ulong64)rr)*CLK_PER_SEC)/tt); - } - fclose(log); - - return 0; #endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/demo/timing.c Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,291 @@ +#include <tommath.h> +#include <time.h> + +ulong64 _tt; + +#ifdef IOWNANATHLON +#include <unistd.h> +#define SLEEP sleep(4) +#else +#define SLEEP +#endif + + +void ndraw(mp_int *a, char *name) +{ + char buf[4096]; + printf("%s: ", name); + mp_toradix(a, buf, 64); + printf("%s\n", buf); +} + +static void draw(mp_int *a) +{ + ndraw(a, ""); +} + + +unsigned long lfsr = 0xAAAAAAAAUL; + +int lbit(void) +{ + if (lfsr & 0x80000000UL) { + lfsr = ((lfsr << 1) ^ 0x8000001BUL) & 0xFFFFFFFFUL; + return 1; + } else { + lfsr <<= 1; + return 0; + } +} + +#if defined(__i386__) || defined(_M_IX86) || defined(_M_AMD64) +/* RDTSC from Scott Duplichan */ +static ulong64 TIMFUNC (void) + { + #if defined __GNUC__ + #ifdef __i386__ + ulong64 a; + __asm__ __volatile__ ("rdtsc ":"=A" (a)); + return a; + #else /* gcc-IA64 version */ + unsigned long result; + __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory"); + while (__builtin_expect ((int) result == -1, 0)) + __asm__ __volatile__("mov %0=ar.itc" : "=r"(result) :: "memory"); + return result; + #endif + + // Microsoft and Intel Windows compilers + #elif defined _M_IX86 + __asm rdtsc + #elif defined _M_AMD64 + return __rdtsc (); + #elif defined _M_IA64 + #if defined __INTEL_COMPILER + #include <ia64intrin.h> + #endif + return __getReg (3116); + #else + #error need rdtsc function for this build + #endif + } +#else +#define TIMFUNC clock +#endif + +#define DO(x) x; x; +//#define DO4(x) DO2(x); DO2(x); +//#define DO8(x) DO4(x); DO4(x); +//#define DO(x) DO8(x); DO8(x); + +int main(void) +{ + ulong64 tt, gg, CLK_PER_SEC; + FILE *log, *logb, *logc; + mp_int a, b, c, d, e, f; + int n, cnt, ix, old_kara_m, old_kara_s; + unsigned rr; + + mp_init(&a); + mp_init(&b); + mp_init(&c); + mp_init(&d); + mp_init(&e); + mp_init(&f); + + srand(time(NULL)); + + + /* temp. turn off TOOM */ + TOOM_MUL_CUTOFF = TOOM_SQR_CUTOFF = 100000; + + CLK_PER_SEC = TIMFUNC(); + sleep(1); + CLK_PER_SEC = TIMFUNC() - CLK_PER_SEC; + + printf("CLK_PER_SEC == %llu\n", CLK_PER_SEC); + + log = fopen("logs/add.log", "w"); + for (cnt = 8; cnt <= 128; cnt += 8) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_add(&a,&b,&c)); + gg = (TIMFUNC() - gg)>>1; + if (tt > gg) tt = gg; + } while (++rr < 100000); + printf("Adding\t\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); + fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt); fflush(log); + } + fclose(log); + + log = fopen("logs/sub.log", "w"); + for (cnt = 8; cnt <= 128; cnt += 8) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_sub(&a,&b,&c)); + gg = (TIMFUNC() - gg)>>1; + if (tt > gg) tt = gg; + } while (++rr < 100000); + + printf("Subtracting\t\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); + fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt); fflush(log); + } + fclose(log); + + /* do mult/square twice, first without karatsuba and second with */ + old_kara_m = KARATSUBA_MUL_CUTOFF; + old_kara_s = KARATSUBA_SQR_CUTOFF; + for (ix = 0; ix < 1; ix++) { + printf("With%s Karatsuba\n", (ix==0)?"out":""); + + KARATSUBA_MUL_CUTOFF = (ix==0)?9999:old_kara_m; + KARATSUBA_SQR_CUTOFF = (ix==0)?9999:old_kara_s; + + log = fopen((ix==0)?"logs/mult.log":"logs/mult_kara.log", "w"); + for (cnt = 4; cnt <= 288; cnt += 2) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_mul(&a, &b, &c)); + gg = (TIMFUNC() - gg)>>1; + if (tt > gg) tt = gg; + } while (++rr < 100); + printf("Multiplying\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); + fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt); fflush(log); + } + fclose(log); + + log = fopen((ix==0)?"logs/sqr.log":"logs/sqr_kara.log", "w"); + for (cnt = 4; cnt <= 288; cnt += 2) { + SLEEP; + mp_rand(&a, cnt); + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_sqr(&a, &b)); + gg = (TIMFUNC() - gg)>>1; + if (tt > gg) tt = gg; + } while (++rr < 100); + printf("Squaring\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); + fprintf(log, "%d %9llu\n", mp_count_bits(&a), tt); fflush(log); + } + fclose(log); + + } + + { + char *primes[] = { + /* 2K moduli mersenne primes */ + "6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151", + "531137992816767098689588206552468627329593117727031923199444138200403559860852242739162502265229285668889329486246501015346579337652707239409519978766587351943831270835393219031728127", + "10407932194664399081925240327364085538615262247266704805319112350403608059673360298012239441732324184842421613954281007791383566248323464908139906605677320762924129509389220345773183349661583550472959420547689811211693677147548478866962501384438260291732348885311160828538416585028255604666224831890918801847068222203140521026698435488732958028878050869736186900714720710555703168729087", + "1475979915214180235084898622737381736312066145333169775147771216478570297878078949377407337049389289382748507531496480477281264838760259191814463365330269540496961201113430156902396093989090226259326935025281409614983499388222831448598601834318536230923772641390209490231836446899608210795482963763094236630945410832793769905399982457186322944729636418890623372171723742105636440368218459649632948538696905872650486914434637457507280441823676813517852099348660847172579408422316678097670224011990280170474894487426924742108823536808485072502240519452587542875349976558572670229633962575212637477897785501552646522609988869914013540483809865681250419497686697771007", + "259117086013202627776246767922441530941818887553125427303974923161874019266586362086201209516800483406550695241733194177441689509238807017410377709597512042313066624082916353517952311186154862265604547691127595848775610568757931191017711408826252153849035830401185072116424747461823031471398340229288074545677907941037288235820705892351068433882986888616658650280927692080339605869308790500409503709875902119018371991620994002568935113136548829739112656797303241986517250116412703509705427773477972349821676443446668383119322540099648994051790241624056519054483690809616061625743042361721863339415852426431208737266591962061753535748892894599629195183082621860853400937932839420261866586142503251450773096274235376822938649407127700846077124211823080804139298087057504713825264571448379371125032081826126566649084251699453951887789613650248405739378594599444335231188280123660406262468609212150349937584782292237144339628858485938215738821232393687046160677362909315071", + "190797007524439073807468042969529173669356994749940177394741882673528979787005053706368049835514900244303495954950709725762186311224148828811920216904542206960744666169364221195289538436845390250168663932838805192055137154390912666527533007309292687539092257043362517857366624699975402375462954490293259233303137330643531556539739921926201438606439020075174723029056838272505051571967594608350063404495977660656269020823960825567012344189908927956646011998057988548630107637380993519826582389781888135705408653045219655801758081251164080554609057468028203308718724654081055323215860189611391296030471108443146745671967766308925858547271507311563765171008318248647110097614890313562856541784154881743146033909602737947385055355960331855614540900081456378659068370317267696980001187750995491090350108417050917991562167972281070161305972518044872048331306383715094854938415738549894606070722584737978176686422134354526989443028353644037187375385397838259511833166416134323695660367676897722287918773420968982326089026150031515424165462111337527431154890666327374921446276833564519776797633875503548665093914556482031482248883127023777039667707976559857333357013727342079099064400455741830654320379350833236245819348824064783585692924881021978332974949906122664421376034687815350484991", + + /* DR moduli */ + "14059105607947488696282932836518693308967803494693489478439861164411992439598399594747002144074658928593502845729752797260025831423419686528151609940203368612079", + "101745825697019260773923519755878567461315282017759829107608914364075275235254395622580447400994175578963163918967182013639660669771108475957692810857098847138903161308502419410142185759152435680068435915159402496058513611411688900243039", + "736335108039604595805923406147184530889923370574768772191969612422073040099331944991573923112581267542507986451953227192970402893063850485730703075899286013451337291468249027691733891486704001513279827771740183629161065194874727962517148100775228363421083691764065477590823919364012917984605619526140821797602431", + "38564998830736521417281865696453025806593491967131023221754800625044118265468851210705360385717536794615180260494208076605798671660719333199513807806252394423283413430106003596332513246682903994829528690198205120921557533726473585751382193953592127439965050261476810842071573684505878854588706623484573925925903505747545471088867712185004135201289273405614415899438276535626346098904241020877974002916168099951885406379295536200413493190419727789712076165162175783", + "542189391331696172661670440619180536749994166415993334151601745392193484590296600979602378676624808129613777993466242203025054573692562689251250471628358318743978285860720148446448885701001277560572526947619392551574490839286458454994488665744991822837769918095117129546414124448777033941223565831420390846864429504774477949153794689948747680362212954278693335653935890352619041936727463717926744868338358149568368643403037768649616778526013610493696186055899318268339432671541328195724261329606699831016666359440874843103020666106568222401047720269951530296879490444224546654729111504346660859907296364097126834834235287147", + "1487259134814709264092032648525971038895865645148901180585340454985524155135260217788758027400478312256339496385275012465661575576202252063145698732079880294664220579764848767704076761853197216563262660046602703973050798218246170835962005598561669706844469447435461092542265792444947706769615695252256130901271870341005768912974433684521436211263358097522726462083917939091760026658925757076733484173202927141441492573799914240222628795405623953109131594523623353044898339481494120112723445689647986475279242446083151413667587008191682564376412347964146113898565886683139407005941383669325997475076910488086663256335689181157957571445067490187939553165903773554290260531009121879044170766615232300936675369451260747671432073394867530820527479172464106442450727640226503746586340279816318821395210726268291535648506190714616083163403189943334431056876038286530365757187367147446004855912033137386225053275419626102417236133948503", + "1095121115716677802856811290392395128588168592409109494900178008967955253005183831872715423151551999734857184538199864469605657805519106717529655044054833197687459782636297255219742994736751541815269727940751860670268774903340296040006114013971309257028332849679096824800250742691718610670812374272414086863715763724622797509437062518082383056050144624962776302147890521249477060215148275163688301275847155316042279405557632639366066847442861422164832655874655824221577849928863023018366835675399949740429332468186340518172487073360822220449055340582568461568645259954873303616953776393853174845132081121976327462740354930744487429617202585015510744298530101547706821590188733515880733527449780963163909830077616357506845523215289297624086914545378511082534229620116563260168494523906566709418166011112754529766183554579321224940951177394088465596712620076240067370589036924024728375076210477267488679008016579588696191194060127319035195370137160936882402244399699172017835144537488486396906144217720028992863941288217185353914991583400421682751000603596655790990815525126154394344641336397793791497068253936771017031980867706707490224041075826337383538651825493679503771934836094655802776331664261631740148281763487765852746577808019633679", + + /* generic unrestricted moduli */ + "17933601194860113372237070562165128350027320072176844226673287945873370751245439587792371960615073855669274087805055507977323024886880985062002853331424203", + "2893527720709661239493896562339544088620375736490408468011883030469939904368086092336458298221245707898933583190713188177399401852627749210994595974791782790253946539043962213027074922559572312141181787434278708783207966459019479487", + "347743159439876626079252796797422223177535447388206607607181663903045907591201940478223621722118173270898487582987137708656414344685816179420855160986340457973820182883508387588163122354089264395604796675278966117567294812714812796820596564876450716066283126720010859041484786529056457896367683122960411136319", + "47266428956356393164697365098120418976400602706072312735924071745438532218237979333351774907308168340693326687317443721193266215155735814510792148768576498491199122744351399489453533553203833318691678263241941706256996197460424029012419012634671862283532342656309677173602509498417976091509154360039893165037637034737020327399910409885798185771003505320583967737293415979917317338985837385734747478364242020380416892056650841470869294527543597349250299539682430605173321029026555546832473048600327036845781970289288898317888427517364945316709081173840186150794397479045034008257793436817683392375274635794835245695887", + "436463808505957768574894870394349739623346440601945961161254440072143298152040105676491048248110146278752857839930515766167441407021501229924721335644557342265864606569000117714935185566842453630868849121480179691838399545644365571106757731317371758557990781880691336695584799313313687287468894148823761785582982549586183756806449017542622267874275103877481475534991201849912222670102069951687572917937634467778042874315463238062009202992087620963771759666448266532858079402669920025224220613419441069718482837399612644978839925207109870840278194042158748845445131729137117098529028886770063736487420613144045836803985635654192482395882603511950547826439092832800532152534003936926017612446606135655146445620623395788978726744728503058670046885876251527122350275750995227", + "11424167473351836398078306042624362277956429440521137061889702611766348760692206243140413411077394583180726863277012016602279290144126785129569474909173584789822341986742719230331946072730319555984484911716797058875905400999504305877245849119687509023232790273637466821052576859232452982061831009770786031785669030271542286603956118755585683996118896215213488875253101894663403069677745948305893849505434201763745232895780711972432011344857521691017896316861403206449421332243658855453435784006517202894181640562433575390821384210960117518650374602256601091379644034244332285065935413233557998331562749140202965844219336298970011513882564935538704289446968322281451907487362046511461221329799897350993370560697505809686438782036235372137015731304779072430260986460269894522159103008260495503005267165927542949439526272736586626709581721032189532726389643625590680105784844246152702670169304203783072275089194754889511973916207", + "1214855636816562637502584060163403830270705000634713483015101384881871978446801224798536155406895823305035467591632531067547890948695117172076954220727075688048751022421198712032848890056357845974246560748347918630050853933697792254955890439720297560693579400297062396904306270145886830719309296352765295712183040773146419022875165382778007040109957609739589875590885701126197906063620133954893216612678838507540777138437797705602453719559017633986486649523611975865005712371194067612263330335590526176087004421363598470302731349138773205901447704682181517904064735636518462452242791676541725292378925568296858010151852326316777511935037531017413910506921922450666933202278489024521263798482237150056835746454842662048692127173834433089016107854491097456725016327709663199738238442164843147132789153725513257167915555162094970853584447993125488607696008169807374736711297007473812256272245489405898470297178738029484459690836250560495461579533254473316340608217876781986188705928270735695752830825527963838355419762516246028680280988020401914551825487349990306976304093109384451438813251211051597392127491464898797406789175453067960072008590614886532333015881171367104445044718144312416815712216611576221546455968770801413440778423979", + NULL + }; + log = fopen("logs/expt.log", "w"); + logb = fopen("logs/expt_dr.log", "w"); + logc = fopen("logs/expt_2k.log", "w"); + for (n = 0; primes[n]; n++) { + SLEEP; + mp_read_radix(&a, primes[n], 10); + mp_zero(&b); + for (rr = 0; rr < (unsigned)mp_count_bits(&a); rr++) { + mp_mul_2(&b, &b); + b.dp[0] |= lbit(); + b.used += 1; + } + mp_sub_d(&a, 1, &c); + mp_mod(&b, &c, &b); + mp_set(&c, 3); + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_exptmod(&c, &b, &a, &d)); + gg = (TIMFUNC() - gg)>>1; + if (tt > gg) tt = gg; + } while (++rr < 10); + mp_sub_d(&a, 1, &e); + mp_sub(&e, &b, &b); + mp_exptmod(&c, &b, &a, &e); /* c^(p-1-b) mod a */ + mp_mulmod(&e, &d, &a, &d); /* c^b * c^(p-1-b) == c^p-1 == 1 */ + if (mp_cmp_d(&d, 1)) { + printf("Different (%d)!!!\n", mp_count_bits(&a)); + draw(&d); + exit(0); + } + printf("Exponentiating\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); + fprintf((n < 6) ? logc : (n < 13) ? logb : log, "%d %9llu\n", mp_count_bits(&a), tt); + } + } + fclose(log); + fclose(logb); + fclose(logc); + + log = fopen("logs/invmod.log", "w"); + for (cnt = 4; cnt <= 128; cnt += 4) { + SLEEP; + mp_rand(&a, cnt); + mp_rand(&b, cnt); + + do { + mp_add_d(&b, 1, &b); + mp_gcd(&a, &b, &c); + } while (mp_cmp_d(&c, 1) != MP_EQ); + + rr = 0; + tt = -1; + do { + gg = TIMFUNC(); + DO(mp_invmod(&b, &a, &c)); + gg = (TIMFUNC() - gg)>>1; + if (tt > gg) tt = gg; + } while (++rr < 1000); + mp_mulmod(&b, &c, &a, &d); + if (mp_cmp_d(&d, 1) != MP_EQ) { + printf("Failed to invert\n"); + return 0; + } + printf("Inverting mod\t%4d-bit => %9llu/sec, %9llu cycles\n", mp_count_bits(&a), CLK_PER_SEC/tt, tt); + fprintf(log, "%d %9llu\n", cnt*DIGIT_BIT, tt); + } + fclose(log); + + return 0; +} +
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/dep.pl Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,121 @@ +#!/usr/bin/perl +# +# Walk through source, add labels and make classes +# +#use strict; + +my %deplist; + +#open class file and write preamble +open(CLASS, ">tommath_class.h") or die "Couldn't open tommath_class.h for writing\n"; +print CLASS "#if !(defined(LTM1) && defined(LTM2) && defined(LTM3))\n#if defined(LTM2)\n#define LTM3\n#endif\n#if defined(LTM1)\n#define LTM2\n#endif\n#define LTM1\n\n#if defined(LTM_ALL)\n"; + +foreach my $filename (glob "bn*.c") { + my $define = $filename; + + # convert filename to upper case so we can use it as a define + $define =~ tr/[a-z]/[A-Z]/; + $define =~ tr/\./_/; + print CLASS "#define $define\n"; + + # now copy text and apply #ifdef as required + my $apply = 0; + open(SRC, "<$filename"); + open(OUT, ">tmp"); + + # first line will be the #ifdef + my $line = <SRC>; + if ($line =~ /include/) { + print OUT $line; + } else { + print OUT "#include <tommath.h>\n#ifdef $define\n$line"; + $apply = 1; + } + while (<SRC>) { + if (!($_ =~ /tommath\.h/)) { + print OUT $_; + } + } + if ($apply == 1) { + print OUT "#endif\n"; + } + close SRC; + close OUT; + + unlink($filename); + rename("tmp", $filename); +} +print CLASS "#endif\n\n"; + +# now do classes + +foreach my $filename (glob "bn*.c") { + open(SRC, "<$filename") or die "Can't open source file!\n"; + + # convert filename to upper case so we can use it as a define + $filename =~ tr/[a-z]/[A-Z]/; + $filename =~ tr/\./_/; + + print CLASS "#if defined($filename)\n"; + my $list = $filename; + + # scan for mp_* and make classes + while (<SRC>) { + my $line = $_; + while ($line =~ m/(fast_)*(s_)*mp\_[a-z_0-9]*/) { + $line = $'; + # now $& is the match, we want to skip over LTM keywords like + # mp_int, mp_word, mp_digit + if (!($& eq "mp_digit") && !($& eq "mp_word") && !($& eq "mp_int")) { + my $a = $&; + $a =~ tr/[a-z]/[A-Z]/; + $a = "BN_" . $a . "_C"; + if (!($list =~ /$a/)) { + print CLASS " #define $a\n"; + } + $list = $list . "," . $a; + } + } + } + @deplist{$filename} = $list; + + print CLASS "#endif\n\n"; + close SRC; +} + +print CLASS "#ifdef LTM3\n#define LTM_LAST\n#endif\n#include <tommath_superclass.h>\n#include <tommath_class.h>\n#else\n#define LTM_LAST\n#endif\n"; +close CLASS; + +#now let's make a cool call graph... + +open(OUT,">callgraph.txt"); +$indent = 0; +foreach (keys %deplist) { + $list = ""; + draw_func(@deplist{$_}); + print OUT "\n\n"; +} +close(OUT); + +sub draw_func() +{ + my @funcs = split(",", $_[0]); + if ($list =~ /@funcs[0]/) { + return; + } else { + $list = $list . @funcs[0]; + } + if ($indent == 0) { } + elsif ($indent >= 1) { print OUT "| " x ($indent - 1) . "+--->"; } + print OUT @funcs[0] . "\n"; + shift @funcs; + my $temp = $list; + foreach my $i (@funcs) { + ++$indent; + draw_func(@deplist{$i}); + --$indent; + } + $list = $temp; +} + +
--- a/etc/makefile Tue Jun 15 14:42:57 2004 +0000 +++ b/etc/makefile Sun Dec 19 11:33:56 2004 +0000 @@ -46,4 +46,5 @@ clean: - rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat + rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat \ + *.da *.dyn *.dpi *~
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/etc/makefile.icc Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,67 @@ +CC = icc + +CFLAGS += -I../ + +# optimize for SPEED +# +# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4 +# -ax? specifies make code specifically for ? but compatible with IA-32 +# -x? specifies compile solely for ? [not specifically IA-32 compatible] +# +# where ? is +# K - PIII +# W - first P4 [Williamette] +# N - P4 Northwood +# P - P4 Prescott +# B - Blend of P4 and PM [mobile] +# +# Default to just generic max opts +CFLAGS += -O3 -xN -ip + +# default lib name (requires install with root) +# LIBNAME=-ltommath + +# libname when you can't install the lib with install +LIBNAME=../libtommath.a + +#provable primes +pprime: pprime.o + $(CC) pprime.o $(LIBNAME) -o pprime + +# portable [well requires clock()] tuning app +tune: tune.o + $(CC) tune.o $(LIBNAME) -o tune + +# same app but using RDTSC for higher precision [requires 80586+], coff based gcc installs [e.g. ming, cygwin, djgpp] +tune86: tune.c + nasm -f coff timer.asm + $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86 + +# for cygwin +tune86c: tune.c + nasm -f gnuwin32 timer.asm + $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86 + +#make tune86 for linux or any ELF format +tune86l: tune.c + nasm -f elf -DUSE_ELF timer.asm + $(CC) -DX86_TIMER $(CFLAGS) tune.c timer.o $(LIBNAME) -o tune86l + +# spits out mersenne primes +mersenne: mersenne.o + $(CC) mersenne.o $(LIBNAME) -o mersenne + +# fines DR safe primes for the given config +drprime: drprime.o + $(CC) drprime.o $(LIBNAME) -o drprime + +# fines 2k safe primes for the given config +2kprime: 2kprime.o + $(CC) 2kprime.o $(LIBNAME) -o 2kprime + +mont: mont.o + $(CC) mont.o $(LIBNAME) -o mont + + +clean: + rm -f *.log *.o *.obj *.exe pprime tune mersenne drprime tune86 tune86l mont 2kprime pprime.dat *.il
--- a/etc/tune.c Tue Jun 15 14:42:57 2004 +0000 +++ b/etc/tune.c Sun Dec 19 11:33:56 2004 +0000 @@ -8,7 +8,7 @@ /* how many times todo each size mult. Depends on your computer. For slow computers * this can be low like 5 or 10. For fast [re: Athlon] should be 25 - 50 or so */ -#define TIMES 50 +#define TIMES (1UL<<14UL) #ifndef X86_TIMER @@ -23,154 +23,85 @@ extern ulong64 t_read(void); #endif -ulong64 -time_mult (int max) +ulong64 time_mult(int size, int s) { - int x, y; + unsigned long x; mp_int a, b, c; + ulong64 t1; mp_init (&a); mp_init (&b); mp_init (&c); + mp_rand (&a, size); + mp_rand (&b, size); + + if (s == 1) { + KARATSUBA_MUL_CUTOFF = size; + } else { + KARATSUBA_MUL_CUTOFF = 100000; + } + t_start(); - for (x = 32; x <= max; x += 4) { - mp_rand (&a, x); - mp_rand (&b, x); - for (y = 0; y < TIMES; y++) { - mp_mul (&a, &b, &c); - } + for (x = 0; x < TIMES; x++) { + mp_mul(&a,&b,&c); } + t1 = t_read(); mp_clear (&a); mp_clear (&b); mp_clear (&c); - return t_read(); + return t1; } -ulong64 -time_sqr (int max) +ulong64 time_sqr(int size, int s) { - int x, y; + unsigned long x; mp_int a, b; + ulong64 t1; mp_init (&a); mp_init (&b); + mp_rand (&a, size); + + if (s == 1) { + KARATSUBA_SQR_CUTOFF = size; + } else { + KARATSUBA_SQR_CUTOFF = 100000; + } + t_start(); - for (x = 32; x <= max; x += 4) { - mp_rand (&a, x); - for (y = 0; y < TIMES; y++) { - mp_sqr (&a, &b); - } + for (x = 0; x < TIMES; x++) { + mp_sqr(&a,&b); } + t1 = t_read(); mp_clear (&a); mp_clear (&b); - return t_read(); + return t1; } int main (void) { - int best_kmult, best_tmult, best_ksquare, best_tsquare, counter; - ulong64 best, ti; - FILE *log; + ulong64 t1, t2; + int x, y; - best_kmult = best_ksquare = best_tmult = best_tsquare = 0; - /* tune multiplication first */ - - /* effectively turn TOOM off */ - TOOM_SQR_CUTOFF = TOOM_MUL_CUTOFF = 100000; - - log = fopen ("mult.log", "w"); - best = -1; - counter = 16; - for (KARATSUBA_MUL_CUTOFF = 8; KARATSUBA_MUL_CUTOFF <= 200; KARATSUBA_MUL_CUTOFF++) { - ti = time_mult (300); - printf ("%4d : %9llu \r", KARATSUBA_MUL_CUTOFF, ti); - fprintf (log, "%d, %llu\n", KARATSUBA_MUL_CUTOFF, ti); - fflush (stdout); - if (ti < best) { - printf ("New best: %llu, %d \r", ti, KARATSUBA_MUL_CUTOFF); - best = ti; - best_kmult = KARATSUBA_MUL_CUTOFF; - counter = 16; - } else if (--counter == 0) { - printf("No better found in 16 trials.\n"); - break; - } - } - fclose (log); - printf("Karatsuba Multiplier Cutoff (KARATSUBA_MUL_CUTOFF) == %d\n", best_kmult); - - /* tune squaring */ - log = fopen ("sqr.log", "w"); - best = -1; - counter = 16; - for (KARATSUBA_SQR_CUTOFF = 8; KARATSUBA_SQR_CUTOFF <= 200; KARATSUBA_SQR_CUTOFF++) { - ti = time_sqr (300); - printf ("%4d : %9llu \r", KARATSUBA_SQR_CUTOFF, ti); - fprintf (log, "%d, %llu\n", KARATSUBA_SQR_CUTOFF, ti); - fflush (stdout); - if (ti < best) { - printf ("New best: %llu, %d \r", ti, KARATSUBA_SQR_CUTOFF); - best = ti; - best_ksquare = KARATSUBA_SQR_CUTOFF; - counter = 16; - } else if (--counter == 0) { - printf("No better found in 16 trials.\n"); - break; - } + for (x = 8; ; x += 2) { + t1 = time_mult(x, 0); + t2 = time_mult(x, 1); + printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1); + if (t2 < t1) break; } - fclose (log); - printf("Karatsuba Squaring Cutoff (KARATSUBA_SQR_CUTOFF) == %d\n", best_ksquare); - - KARATSUBA_MUL_CUTOFF = best_kmult; - KARATSUBA_SQR_CUTOFF = best_ksquare; - - /* tune TOOM mult */ - counter = 16; - log = fopen ("tmult.log", "w"); - best = -1; - for (TOOM_MUL_CUTOFF = best_kmult*5; TOOM_MUL_CUTOFF <= 800; TOOM_MUL_CUTOFF++) { - ti = time_mult (1200); - printf ("%4d : %9llu \r", TOOM_MUL_CUTOFF, ti); - fprintf (log, "%d, %llu\n", TOOM_MUL_CUTOFF, ti); - fflush (stdout); - if (ti < best) { - printf ("New best: %llu, %d \r", ti, TOOM_MUL_CUTOFF); - best = ti; - best_tmult = TOOM_MUL_CUTOFF; - counter = 16; - } else if (--counter == 0) { - printf("No better found in 16 trials.\n"); - break; - } + y = x; + + for (x = 8; ; x += 2) { + t1 = time_sqr(x, 0); + t2 = time_sqr(x, 1); + printf("%d: %9llu %9llu, %9llu\n", x, t1, t2, t2 - t1); + if (t2 < t1) break; } - fclose (log); - printf("Toom-Cook Multiplier Cutoff (TOOM_MUL_CUTOFF) == %d\n", best_tmult); - - /* tune TOOM sqr */ - log = fopen ("tsqr.log", "w"); - best = -1; - counter = 16; - for (TOOM_SQR_CUTOFF = best_ksquare*3; TOOM_SQR_CUTOFF <= 800; TOOM_SQR_CUTOFF++) { - ti = time_sqr (1200); - printf ("%4d : %9llu \r", TOOM_SQR_CUTOFF, ti); - fprintf (log, "%d, %llu\n", TOOM_SQR_CUTOFF, ti); - fflush (stdout); - if (ti < best) { - printf ("New best: %llu, %d \r", ti, TOOM_SQR_CUTOFF); - best = ti; - best_tsquare = TOOM_SQR_CUTOFF; - counter = 16; - } else if (--counter == 0) { - printf("No better found in 16 trials.\n"); - break; - } - } - fclose (log); - printf("Toom-Cook Squaring Cutoff (TOOM_SQR_CUTOFF) == %d\n", best_tsquare); - + printf("KARATSUBA_MUL_CUTOFF = %d\n", y); + printf("KARATSUBA_SQR_CUTOFF = %d\n", x); return 0; }
--- a/logs/add.log Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/add.log Sun Dec 19 11:33:56 2004 +0000 @@ -1,16 +1,16 @@ -224 20297071 -448 15151383 -672 13088682 -896 11111587 -1120 9240621 -1344 8221878 -1568 7227434 -1792 6718051 -2016 6042524 -2240 5685200 -2464 5240465 -2688 4818032 -2912 4412794 -3136 4155883 -3360 3927078 -3584 3722138 +224 222 +448 330 +672 436 +896 520 +1120 612 +1344 696 +1568 810 +1792 912 +2016 1006 +2240 1116 +2464 1152 +2688 1284 +2912 1348 +3136 1486 +3360 1580 +3584 1636
--- a/logs/expt.log Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/expt.log Sun Dec 19 11:33:56 2004 +0000 @@ -1,7 +0,0 @@ -513 745 -769 282 -1025 130 -2049 20 -2561 11 -3073 6 -4097 2
--- a/logs/expt_2k.log Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/expt_2k.log Sun Dec 19 11:33:56 2004 +0000 @@ -1,6 +0,0 @@ -521 783 -607 585 -1279 138 -2203 39 -3217 15 -4253 6
--- a/logs/expt_dr.log Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/expt_dr.log Sun Dec 19 11:33:56 2004 +0000 @@ -1,7 +0,0 @@ -532 1296 -784 551 -1036 283 -1540 109 -2072 52 -3080 18 -4116 7
--- a/logs/graphs.dem Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/graphs.dem Sun Dec 19 11:33:56 2004 +0000 @@ -1,17 +1,17 @@ -set terminal png -set size 1.75 -set ylabel "Operations per Second" -set xlabel "Operand size (bits)" - -set output "addsub.png" -plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction" - -set output "mult.png" -plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)" - -set output "expt.png" -plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)", 'expt_2k.log' smooth bezier title "Exptmod (2k Reduction)" - -set output "invmod.png" -plot 'invmod.log' smooth bezier title "Modular Inverse" - +set terminal png +set size 1.75 +set ylabel "Cycles per Operation" +set xlabel "Operand size (bits)" + +set output "addsub.png" +plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction" + +set output "mult.png" +plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)" + +set output "expt.png" +plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)", 'expt_2k.log' smooth bezier title "Exptmod (2k Reduction)" + +set output "invmod.png" +plot 'invmod.log' smooth bezier title "Modular Inverse" +
--- a/logs/invmod.log Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/invmod.log Sun Dec 19 11:33:56 2004 +0000 @@ -1,32 +0,0 @@ -112 17364 -224 8643 -336 8867 -448 6228 -560 4737 -672 2259 -784 2899 -896 1497 -1008 1238 -1120 1010 -1232 870 -1344 1265 -1456 1102 -1568 981 -1680 539 -1792 484 -1904 722 -2016 392 -2128 604 -2240 551 -2352 511 -2464 469 -2576 263 -2688 247 -2800 227 -2912 354 -3024 336 -3136 312 -3248 296 -3360 166 -3472 155 -3584 248
--- a/logs/k7/README Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,13 +0,0 @@ -To use the pretty graphs you have to first build/run the ltmtest from the root directory of the package. -Todo this type - -make timing ; ltmtest - -in the root. It will run for a while [about ten minutes on most PCs] and produce a series of .log files in logs/. - -After doing that run "gnuplot graphs.dem" to make the PNGs. If you managed todo that all so far just open index.html to view -them all :-) - -Have fun - -Tom \ No newline at end of file
--- a/logs/k7/add.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,16 +0,0 @@ -224 11069160 -448 9156136 -672 8089755 -896 7399424 -1120 6389352 -1344 5818648 -1568 5257112 -1792 4982160 -2016 4527856 -2240 4325312 -2464 4051760 -2688 3767640 -2912 3612520 -3136 3415208 -3360 3258656 -3584 3113360
--- a/logs/k7/expt.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,7 +0,0 @@ -513 664 -769 256 -1025 117 -2049 17 -2561 9 -3073 5 -4097 2
--- a/logs/k7/expt_dr.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,7 +0,0 @@ -532 1088 -784 460 -1036 240 -1540 92 -2072 43 -3080 15 -4116 6
--- a/logs/k7/graphs.dem Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -set terminal png color -set size 1.75 -set ylabel "Operations per Second" -set xlabel "Operand size (bits)" - -set output "addsub.png" -plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction" - -set output "mult.png" -plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)" - -set output "expt.png" -plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)" - -set output "invmod.png" -plot 'invmod.log' smooth bezier title "Modular Inverse" -
--- a/logs/k7/index.html Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,24 +0,0 @@ -<html> -<head> -<title>LibTomMath Log Plots</title> -</head> -<body> - -<h1>Addition and Subtraction</h1> -<center><img src=addsub.png></center> -<hr> - -<h1>Multipliers</h1> -<center><img src=mult.png></center> -<hr> - -<h1>Exptmod</h1> -<center><img src=expt.png></center> -<hr> - -<h1>Modular Inverse</h1> -<center><img src=invmod.png></center> -<hr> - -</body> -</html> \ No newline at end of file
--- a/logs/k7/invmod.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,32 +0,0 @@ -112 16248 -224 8192 -336 5320 -448 3560 -560 2728 -672 2064 -784 1704 -896 2176 -1008 1184 -1120 976 -1232 1280 -1344 1176 -1456 624 -1568 912 -1680 504 -1792 452 -1904 658 -2016 608 -2128 336 -2240 312 -2352 288 -2464 264 -2576 408 -2688 376 -2800 354 -2912 198 -3024 307 -3136 173 -3248 162 -3360 256 -3472 145 -3584 226
--- a/logs/k7/mult.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -896 322904 -1344 151592 -1792 90472 -2240 59984 -2688 42624 -3136 31872 -3584 24704 -4032 19704 -4480 16096 -4928 13376 -5376 11272 -5824 9616 -6272 8360 -6720 7304 -7168 1664 -7616 1472 -8064 1328
--- a/logs/k7/mult_kara.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -896 322872 -1344 151688 -1792 90480 -2240 59984 -2688 42656 -3136 32144 -3584 25840 -4032 21328 -4480 17856 -4928 14928 -5376 12856 -5824 11256 -6272 9880 -6720 8984 -7168 7928 -7616 7200 -8064 6576
--- a/logs/k7/sqr.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -896 415472 -1344 223736 -1792 141232 -2240 97624 -2688 71400 -3136 54800 -3584 16904 -4032 13528 -4480 10968 -4928 9128 -5376 7784 -5824 6672 -6272 5760 -6720 5056 -7168 4440 -7616 3952 -8064 3512
--- a/logs/k7/sqr_kara.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -896 420464 -1344 224800 -1792 142808 -2240 97704 -2688 71416 -3136 54504 -3584 38320 -4032 32360 -4480 27576 -4928 23840 -5376 20688 -5824 18264 -6272 16176 -6720 14440 -7168 11688 -7616 10752 -8064 9936
--- a/logs/k7/sub.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,16 +0,0 @@ -224 9728504 -448 8573648 -672 7488096 -896 6714064 -1120 5950472 -1344 5457400 -1568 5038896 -1792 4683632 -2016 4384656 -2240 4105976 -2464 3871608 -2688 3650680 -2912 3463552 -3136 3290016 -3360 3135272 -3584 2993848
--- a/logs/mult.log Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/mult.log Sun Dec 19 11:33:56 2004 +0000 @@ -1,33 +1,143 @@ -920 374785 -1142 242737 -1371 176704 -1596 134341 -1816 105537 -2044 85089 -2268 70051 -2490 58671 -2716 49851 -2937 42881 -3162 37288 -3387 32697 -3608 28915 -3836 25759 -4057 23088 -4284 20800 -4508 18827 -4730 17164 -4956 15689 -5180 14397 -5398 13260 -5628 12249 -5852 11346 -6071 10537 -6298 9812 -6522 9161 -6742 8572 -6971 8038 -7195 2915 -7419 2744 -7644 2587 -7866 2444 -8090 2311 +140 1272 +195 1428 +252 1996 +307 2586 +364 3464 +420 4420 +476 5260 +532 6430 +588 7692 +644 8704 +699 10226 +755 11670 +812 13190 +865 14834 +924 16738 +979 18362 +1036 20660 +1092 22776 +1148 24848 +1204 27168 +1260 29930 +1316 32258 +1370 35172 +1422 37534 +1482 40390 +1537 43990 +1589 46946 +1652 50438 +1703 52902 +1764 56646 +1820 59892 +1876 63248 +1932 66872 +1988 72596 +2042 74662 +2100 78512 +2156 82944 +2211 87444 +2268 92170 +2324 95534 +2380 100484 +2435 105024 +2491 109460 +2546 114154 +2603 118946 +2660 124110 +2716 129300 +2771 134274 +2828 139594 +2883 145234 +2939 150332 +2996 155750 +3048 161718 +3108 167492 +3162 173882 +3219 179766 +3276 185560 +3330 191826 +3388 197822 +3442 204176 +3500 210682 +3556 217236 +3612 223484 +3666 230714 +3724 237744 +3779 244080 +3835 250970 +3890 257914 +3947 265162 +4001 272128 +4060 279108 +4116 287606 +4171 294716 +4227 302806 +4284 310260 +4340 318564 +4395 326164 +4443 334034 +4508 342108 +4561 351810 +4618 358828 +4675 367332 +4732 376140 +4787 384172 +4841 393308 +4899 402036 +4955 411286 +5010 420290 +5067 429688 +5124 438810 +5180 448130 +5235 457264 +5290 467390 +5348 476586 +5404 486120 +5459 496512 +5516 506624 +5569 516346 +5628 526604 +5684 536544 +5740 546936 +5796 557284 +5852 568106 +5907 578824 +5963 589204 +6019 600176 +6076 610564 +6127 621972 +6188 633564 +6244 644730 +6300 655288 +6354 667402 +6412 678824 +6467 690594 +6522 702718 +6580 714148 +6636 725608 +6690 737834 +6747 750100 +6804 762202 +6860 774184 +6916 787298 +6971 798734 +7028 811162 +7083 824570 +7139 837738 +7196 2579488 +7245 2626714 +7308 2643582 +7364 2698746 +7416 2734106 +7476 2773372 +7530 2816738 +7588 2859204 +7643 2938596 +7698 2919716 +7754 2988542 +7812 3026520 +7867 3058304 +7924 3115790 +7977 3161450 +8035 3203138 +8092 3244056
--- a/logs/mult_kara.log Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/mult_kara.log Sun Dec 19 11:33:56 2004 +0000 @@ -1,33 +1,33 @@ -924 374171 -1147 243163 -1371 177111 -1596 134465 -1819 105619 -2044 85145 -2266 70086 -2488 58717 -2715 49869 -2939 42894 -3164 37389 -3387 33510 -3610 29993 -3836 27205 -4060 24751 -4281 22576 -4508 20670 -4732 19019 -4954 17527 -5180 16217 -5404 15044 -5624 14003 -5849 13051 -6076 12067 -6300 11438 -6524 10772 -6748 10298 -6972 9715 -7195 9330 -7416 8836 -7644 8465 -7864 8042 -8091 7735 +924 16686 +1146 25334 +1371 35304 +1591 47122 +1820 61500 +2044 75254 +2266 91732 +2492 111656 +2716 129428 +2937 147508 +3164 167758 +3388 188248 +3612 210826 +3836 233814 +4059 256898 +4284 280210 +4508 310372 +4731 333902 +4955 376502 +5179 402854 +5404 432004 +5626 459010 +5849 491868 +6076 520550 +6300 547400 +6524 575968 +6747 608482 +6971 642850 +7196 673670 +7419 710680 +7644 743942 +7868 780394 +8092 817342
--- a/logs/p4/README Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,13 +0,0 @@ -To use the pretty graphs you have to first build/run the ltmtest from the root directory of the package. -Todo this type - -make timing ; ltmtest - -in the root. It will run for a while [about ten minutes on most PCs] and produce a series of .log files in logs/. - -After doing that run "gnuplot graphs.dem" to make the PNGs. If you managed todo that all so far just open index.html to view -them all :-) - -Have fun - -Tom \ No newline at end of file
--- a/logs/p4/add.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,16 +0,0 @@ -224 8113248 -448 6585584 -672 5687678 -896 4761144 -1120 4111592 -1344 3995154 -1568 3532387 -1792 3225400 -2016 2963960 -2240 2720112 -2464 2533952 -2688 2307168 -2912 2287064 -3136 2150160 -3360 2035992 -3584 1936304
--- a/logs/p4/expt.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,7 +0,0 @@ -513 195 -769 68 -1025 31 -2049 4 -2561 2 -3073 1 -4097 0
--- a/logs/p4/expt_dr.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,7 +0,0 @@ -532 393 -784 158 -1036 79 -1540 27 -2072 12 -3080 4 -4116 1
--- a/logs/p4/graphs.dem Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -set terminal png color -set size 1.75 -set ylabel "Operations per Second" -set xlabel "Operand size (bits)" - -set output "addsub.png" -plot 'add.log' smooth bezier title "Addition", 'sub.log' smooth bezier title "Subtraction" - -set output "mult.png" -plot 'sqr.log' smooth bezier title "Squaring (without Karatsuba)", 'sqr_kara.log' smooth bezier title "Squaring (Karatsuba)", 'mult.log' smooth bezier title "Multiplication (without Karatsuba)", 'mult_kara.log' smooth bezier title "Multiplication (Karatsuba)" - -set output "expt.png" -plot 'expt.log' smooth bezier title "Exptmod (Montgomery)", 'expt_dr.log' smooth bezier title "Exptmod (Dimminished Radix)" - -set output "invmod.png" -plot 'invmod.log' smooth bezier title "Modular Inverse" -
--- a/logs/p4/index.html Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,24 +0,0 @@ -<html> -<head> -<title>LibTomMath Log Plots</title> -</head> -<body> - -<h1>Addition and Subtraction</h1> -<center><img src=addsub.png></center> -<hr> - -<h1>Multipliers</h1> -<center><img src=mult.png></center> -<hr> - -<h1>Exptmod</h1> -<center><img src=expt.png></center> -<hr> - -<h1>Modular Inverse</h1> -<center><img src=invmod.png></center> -<hr> - -</body> -</html> \ No newline at end of file
--- a/logs/p4/invmod.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,32 +0,0 @@ -112 13608 -224 6872 -336 4264 -448 2792 -560 2144 -672 1560 -784 1296 -896 1672 -1008 896 -1120 736 -1232 1024 -1344 888 -1456 472 -1568 680 -1680 373 -1792 328 -1904 484 -2016 436 -2128 232 -2240 211 -2352 200 -2464 177 -2576 293 -2688 262 -2800 251 -2912 137 -3024 216 -3136 117 -3248 113 -3360 181 -3472 98 -3584 158
--- a/logs/p4/mult.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -896 77600 -1344 35776 -1792 19688 -2240 13248 -2688 9424 -3136 7056 -3584 5464 -4032 4368 -4480 3568 -4928 2976 -5376 2520 -5824 2152 -6272 1872 -6720 1632 -7168 650 -7616 576 -8064 515
--- a/logs/p4/mult_kara.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -896 77752 -1344 35832 -1792 19688 -2240 14704 -2688 10832 -3136 8336 -3584 6600 -4032 5424 -4480 4648 -4928 3976 -5376 3448 -5824 3016 -6272 2664 -6720 2384 -7168 2120 -7616 1912 -8064 1752
--- a/logs/p4/sqr.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -896 128088 -1344 63640 -1792 37968 -2240 25488 -2688 18176 -3136 13672 -3584 4920 -4032 3912 -4480 3160 -4928 2616 -5376 2216 -5824 1896 -6272 1624 -6720 1408 -7168 1240 -7616 1096 -8064 984
--- a/logs/p4/sqr_kara.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,17 +0,0 @@ -896 127456 -1344 63752 -1792 37920 -2240 25440 -2688 18200 -3136 13728 -3584 10968 -4032 9072 -4480 7608 -4928 6440 -5376 5528 -5824 4768 -6272 4328 -6720 3888 -7168 3504 -7616 3176 -8064 2896
--- a/logs/p4/sub.log Tue Jun 15 14:42:57 2004 +0000 +++ /dev/null Thu Jan 01 00:00:00 1970 +0000 @@ -1,16 +0,0 @@ -224 7355896 -448 6162880 -672 5218984 -896 4622776 -1120 3999320 -1344 3629480 -1568 3290384 -1792 2954752 -2016 2737056 -2240 2563320 -2464 2451928 -2688 2310920 -2912 2139048 -3136 2034080 -3360 1890800 -3584 1808624
--- a/logs/sqr.log Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/sqr.log Sun Dec 19 11:33:56 2004 +0000 @@ -1,33 +1,143 @@ -922 471095 -1147 337137 -1366 254327 -1596 199732 -1819 161225 -2044 132852 -2268 111493 -2490 94864 -2715 81745 -2940 71187 -3162 62575 -3387 55418 -3612 14540 -3836 12944 -4060 11627 -4281 10546 -4508 9502 -4730 8688 -4954 7937 -5180 7273 -5402 6701 -5627 6189 -5850 5733 -6076 5310 -6300 4933 -6522 4631 -6748 4313 -6971 4064 -7196 3801 -7420 3576 -7642 3388 -7868 3191 -8092 3020 +139 806 +195 1212 +252 1604 +307 2260 +364 2892 +420 3308 +476 4152 +532 4814 +588 5754 +644 6684 +700 7226 +756 8324 +808 9092 +866 10068 +924 11204 +976 12918 +1036 13656 +1092 15248 +1148 15956 +1204 17270 +1260 19894 +1316 20516 +1370 21864 +1428 25554 +1483 26138 +1540 27086 +1596 29246 +1652 32210 +1707 32704 +1764 35142 +1820 39050 +1876 39256 +1931 41574 +1985 45070 +2044 46352 +2099 48114 +2155 51332 +2212 53268 +2267 55890 +2324 59054 +2380 60206 +2434 63540 +2491 66084 +2547 68590 +2604 74332 +2660 74784 +2715 77974 +2772 79924 +2826 82914 +2884 87210 +2929 89076 +2996 92480 +3052 96814 +3108 99990 +3162 102550 +3219 105396 +3276 109284 +3332 113752 +3387 116628 +3444 120782 +3500 122938 +3556 127940 +3612 303656 +3667 312212 +3724 324376 +3779 329204 +3833 340910 +3892 353850 +3943 362348 +4003 367780 +4056 380448 +4114 393616 +4172 404104 +4227 415148 +4284 409770 +4339 436648 +4394 442970 +4451 463096 +4507 472056 +4564 485780 +4616 496286 +4675 507612 +4732 519524 +4788 536768 +4843 542754 +4899 553090 +4956 571986 +5012 586340 +5068 599606 +5124 613670 +5179 624256 +5235 636266 +5292 655518 +5348 668142 +5403 677266 +5460 696040 +5516 712772 +5570 723942 +5628 739052 +5684 755350 +5739 769962 +5790 775258 +5851 790128 +5908 814536 +5962 827278 +6018 844510 +6076 851606 +6130 865748 +6188 894752 +6244 900474 +6300 928174 +6356 928440 +6410 957758 +6468 981134 +6524 994088 +6580 1011124 +6636 1027178 +6692 1045466 +6747 1056910 +6804 1083784 +6860 1104706 +6915 1116450 +6972 1137894 +7028 1154670 +7084 1158064 +7138 1188734 +7196 1214218 +7249 1226822 +7307 1247528 +7363 1255338 +7420 1291104 +7475 1297940 +7532 1324994 +7587 1340274 +7644 1342596 +7698 1381418 +7756 1382904 +7812 1432588 +7867 1443632 +7922 1465092 +7979 1496804 +8036 1520142 +8092 1539566
--- a/logs/sqr_kara.log Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/sqr_kara.log Sun Dec 19 11:33:56 2004 +0000 @@ -1,33 +1,33 @@ -922 470930 -1148 337217 -1372 254433 -1596 199827 -1820 161204 -2043 132871 -2267 111522 -2488 94932 -2714 81814 -2939 71231 -3164 62616 -3385 55467 -3611 44426 -3836 40695 -4060 37391 -4283 34371 -4508 31779 -4732 29499 -4956 27426 -5177 25598 -5403 23944 -5628 22416 -5851 21052 -6076 19781 -6299 18588 -6523 17539 -6746 16618 -6972 15705 -7196 13582 -7420 13004 -7643 12496 -7868 11963 -8092 11497 +922 11272 +1148 16004 +1370 21958 +1596 28684 +1817 37832 +2044 46386 +2262 56218 +2492 66388 +2716 77478 +2940 89380 +3163 103680 +3385 116274 +3612 135334 +3836 151332 +4057 164938 +4284 183178 +4508 198864 +4731 215222 +4954 231986 +5180 251660 +5404 269414 +5626 288454 +5850 307806 +6076 329458 +6299 347726 +6523 369864 +6748 387832 +6971 413010 +7194 453310 +7415 476936 +7643 497118 +7867 521394 +8091 540224
--- a/logs/sub.log Tue Jun 15 14:42:57 2004 +0000 +++ b/logs/sub.log Sun Dec 19 11:33:56 2004 +0000 @@ -1,16 +1,16 @@ -224 16370431 -448 13327848 -672 11009401 -896 9125342 -1120 7930419 -1344 7114040 -1568 6506998 -1792 5899346 -2016 5435327 -2240 5038931 -2464 4696364 -2688 4425678 -2912 4134476 -3136 3913280 -3360 3692536 -3584 3505219 +224 216 +448 324 +672 428 +896 532 +1120 648 +1344 766 +1568 862 +1792 928 +2016 1070 +2240 1128 +2464 1250 +2688 1344 +2912 1436 +3136 1542 +3360 1628 +3584 1696
--- a/makefile Tue Jun 15 14:42:57 2004 +0000 +++ b/makefile Sun Dec 19 11:33:56 2004 +0000 @@ -12,7 +12,10 @@ #x86 optimizations [should be valid for any GCC install though] CFLAGS += -fomit-frame-pointer -VERSION=0.30 +#debug +#CFLAGS += -g3 + +VERSION=0.32 default: libtommath.a @@ -20,7 +23,7 @@ LIBNAME=libtommath.a HEADERS=tommath.h -#LIBPATH-The directory for libtomcrypt to be installed to. +#LIBPATH-The directory for libtommath to be installed to. #INCPATH-The directory to install the header files for libtommath. #DATAPATH-The directory to install the pdf docs. DESTDIR= @@ -50,14 +53,38 @@ bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \ bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ -bn_mp_init_multi.o bn_mp_clear_multi.o bn_prime_sizes_tab.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ +bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ -bn_mp_init_set_int.o +bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o libtommath.a: $(OBJECTS) $(AR) $(ARFLAGS) libtommath.a $(OBJECTS) ranlib libtommath.a + +#make a profiled library (takes a while!!!) +# +# This will build the library with profile generation +# then run the test demo and rebuild the library. +# +# So far I've seen improvements in the MP math +profiled: + make CFLAGS="$(CFLAGS) -fprofile-arcs -DTESTING" timing + ./ltmtest + rm -f *.a *.o ltmtest + make CFLAGS="$(CFLAGS) -fbranch-probabilities" + +#make a single object profiled library +profiled_single: + perl gen.pl + $(CC) $(CFLAGS) -fprofile-arcs -DTESTING -c mpi.c -o mpi.o + $(CC) $(CFLAGS) -DTESTING -DTIMER demo/timing.c mpi.o -o ltmtest + ./ltmtest + rm -f *.o ltmtest + $(CC) $(CFLAGS) -fbranch-probabilities -DTESTING -c mpi.c -o mpi.o + $(AR) $(ARFLAGS) libtommath.a mpi.o + ranlib libtommath.a + install: libtommath.a install -d -g root -o root $(DESTDIR)$(LIBPATH) install -d -g root -o root $(DESTDIR)$(INCPATH) @@ -71,7 +98,7 @@ cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest -s timing: libtommath.a - $(CC) $(CFLAGS) -DTIMER demo/demo.c libtommath.a -o ltmtest -s + $(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest -s # makes the LTM book DVI file, requires tetex, perl and makeindex [part of tetex I think] docdvi: tommath.src @@ -106,10 +133,14 @@ manual: mandvi pdflatex bn >/dev/null rm -f bn.aux bn.dvi bn.log bn.idx bn.lof bn.out bn.toc - + +pretty: + perl pretty.build + clean: rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \ - *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c + *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.da *.dyn *.dpi tommath.tex `find -type f | grep [~] | xargs` *.lo *.la + rm -rf .libs cd etc ; make clean cd pics ; make clean
--- a/makefile.bcc Tue Jun 15 14:42:57 2004 +0000 +++ b/makefile.bcc Sun Dec 19 11:33:56 2004 +0000 @@ -29,8 +29,9 @@ bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \ bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \ bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \ -bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_prime_sizes_tab.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \ -bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj +bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \ +bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \ +bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj TARGET = libtommath.lib
--- a/makefile.cygwin_dll Tue Jun 15 14:42:57 2004 +0000 +++ b/makefile.cygwin_dll Sun Dec 19 11:33:56 2004 +0000 @@ -34,8 +34,9 @@ bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \ bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ -bn_mp_init_multi.o bn_mp_clear_multi.o bn_prime_sizes_tab.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ -bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o +bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ +bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ +bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o # make a Windows DLL via Cygwin windll: $(OBJECTS)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/makefile.icc Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,110 @@ +#Makefile for ICC +# +#Tom St Denis +CC=icc + +CFLAGS += -I./ + +# optimize for SPEED +# +# -mcpu= can be pentium, pentiumpro (covers PII through PIII) or pentium4 +# -ax? specifies make code specifically for ? but compatible with IA-32 +# -x? specifies compile solely for ? [not specifically IA-32 compatible] +# +# where ? is +# K - PIII +# W - first P4 [Williamette] +# N - P4 Northwood +# P - P4 Prescott +# B - Blend of P4 and PM [mobile] +# +# Default to just generic max opts +CFLAGS += -O3 -xN + +default: libtommath.a + +#default files to install +LIBNAME=libtommath.a +HEADERS=tommath.h + +#LIBPATH-The directory for libtomcrypt to be installed to. +#INCPATH-The directory to install the header files for libtommath. +#DATAPATH-The directory to install the pdf docs. +DESTDIR= +LIBPATH=/usr/lib +INCPATH=/usr/include +DATAPATH=/usr/share/doc/libtommath/pdf + +OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \ +bn_mp_clamp.o bn_mp_zero.o bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \ +bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \ +bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \ +bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \ +bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \ +bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \ +bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \ +bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \ +bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \ +bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \ +bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \ +bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \ +bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o \ +bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \ +bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \ +bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \ +bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \ +bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \ +bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \ +bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ +bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ +bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ +bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ +bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o + +libtommath.a: $(OBJECTS) + $(AR) $(ARFLAGS) libtommath.a $(OBJECTS) + ranlib libtommath.a + +#make a profiled library (takes a while!!!) +# +# This will build the library with profile generation +# then run the test demo and rebuild the library. +# +# So far I've seen improvements in the MP math +profiled: + make -f makefile.icc CFLAGS="$(CFLAGS) -prof_gen -DTESTING" timing + ./ltmtest + rm -f *.a *.o ltmtest + make -f makefile.icc CFLAGS="$(CFLAGS) -prof_use" + +#make a single object profiled library +profiled_single: + perl gen.pl + $(CC) $(CFLAGS) -prof_gen -DTESTING -c mpi.c -o mpi.o + $(CC) $(CFLAGS) -DTESTING -DTIMER demo/demo.c mpi.o -o ltmtest + ./ltmtest + rm -f *.o ltmtest + $(CC) $(CFLAGS) -prof_use -ip -DTESTING -c mpi.c -o mpi.o + $(AR) $(ARFLAGS) libtommath.a mpi.o + ranlib libtommath.a + +install: libtommath.a + install -d -g root -o root $(DESTDIR)$(LIBPATH) + install -d -g root -o root $(DESTDIR)$(INCPATH) + install -g root -o root $(LIBNAME) $(DESTDIR)$(LIBPATH) + install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH) + +test: libtommath.a demo/demo.o + $(CC) demo/demo.o libtommath.a -o test + +mtest: test + cd mtest ; $(CC) $(CFLAGS) mtest.c -o mtest + +timing: libtommath.a + $(CC) $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest + +clean: + rm -f *.bat *.pdf *.o *.a *.obj *.lib *.exe *.dll etclib/*.o demo/demo.o test ltmtest mpitest mtest/mtest mtest/mtest.exe \ + *.idx *.toc *.log *.aux *.dvi *.lof *.ind *.ilg *.ps *.log *.s mpi.c *.il etc/*.il *.dyn + cd etc ; make clean + cd pics ; make clean
--- a/makefile.msvc Tue Jun 15 14:42:57 2004 +0000 +++ b/makefile.msvc Sun Dec 19 11:33:56 2004 +0000 @@ -28,8 +28,9 @@ bn_mp_reduce_2k.obj bn_mp_reduce_is_2k.obj bn_mp_reduce_2k_setup.obj \ bn_mp_radix_smap.obj bn_mp_read_radix.obj bn_mp_toradix.obj bn_mp_radix_size.obj \ bn_mp_fread.obj bn_mp_fwrite.obj bn_mp_cnt_lsb.obj bn_error.obj \ -bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_prime_sizes_tab.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \ -bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj +bn_mp_init_multi.obj bn_mp_clear_multi.obj bn_mp_exteuclid.obj bn_mp_toradix_n.obj \ +bn_mp_prime_random_ex.obj bn_mp_get_int.obj bn_mp_sqrt.obj bn_mp_is_square.obj \ +bn_mp_init_set.obj bn_mp_init_set_int.obj bn_mp_invmod_slow.obj bn_mp_prime_rabin_miller_trials.obj library: $(OBJECTS) lib /out:tommath.lib $(OBJECTS)
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/makefile.shared Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,74 @@ +#Makefile for GCC +# +#Tom St Denis +VERSION=0:32 + +CC = libtool --mode=compile gcc + +CFLAGS += -I./ -Wall -W -Wshadow -Wsign-compare + +#for speed +CFLAGS += -O3 -funroll-loops + +#for size +#CFLAGS += -Os + +#x86 optimizations [should be valid for any GCC install though] +CFLAGS += -fomit-frame-pointer + +default: libtommath.la + +#default files to install +LIBNAME=libtommath.la +HEADERS=tommath.h + +#LIBPATH-The directory for libtommath to be installed to. +#INCPATH-The directory to install the header files for libtommath. +#DATAPATH-The directory to install the pdf docs. +DESTDIR= +LIBPATH=/usr/lib +INCPATH=/usr/include +DATAPATH=/usr/share/doc/libtommath/pdf + +OBJECTS=bncore.o bn_mp_init.o bn_mp_clear.o bn_mp_exch.o bn_mp_grow.o bn_mp_shrink.o \ +bn_mp_clamp.o bn_mp_zero.o bn_mp_set.o bn_mp_set_int.o bn_mp_init_size.o bn_mp_copy.o \ +bn_mp_init_copy.o bn_mp_abs.o bn_mp_neg.o bn_mp_cmp_mag.o bn_mp_cmp.o bn_mp_cmp_d.o \ +bn_mp_rshd.o bn_mp_lshd.o bn_mp_mod_2d.o bn_mp_div_2d.o bn_mp_mul_2d.o bn_mp_div_2.o \ +bn_mp_mul_2.o bn_s_mp_add.o bn_s_mp_sub.o bn_fast_s_mp_mul_digs.o bn_s_mp_mul_digs.o \ +bn_fast_s_mp_mul_high_digs.o bn_s_mp_mul_high_digs.o bn_fast_s_mp_sqr.o bn_s_mp_sqr.o \ +bn_mp_add.o bn_mp_sub.o bn_mp_karatsuba_mul.o bn_mp_mul.o bn_mp_karatsuba_sqr.o \ +bn_mp_sqr.o bn_mp_div.o bn_mp_mod.o bn_mp_add_d.o bn_mp_sub_d.o bn_mp_mul_d.o \ +bn_mp_div_d.o bn_mp_mod_d.o bn_mp_expt_d.o bn_mp_addmod.o bn_mp_submod.o \ +bn_mp_mulmod.o bn_mp_sqrmod.o bn_mp_gcd.o bn_mp_lcm.o bn_fast_mp_invmod.o bn_mp_invmod.o \ +bn_mp_reduce.o bn_mp_montgomery_setup.o bn_fast_mp_montgomery_reduce.o bn_mp_montgomery_reduce.o \ +bn_mp_exptmod_fast.o bn_mp_exptmod.o bn_mp_2expt.o bn_mp_n_root.o bn_mp_jacobi.o bn_reverse.o \ +bn_mp_count_bits.o bn_mp_read_unsigned_bin.o bn_mp_read_signed_bin.o bn_mp_to_unsigned_bin.o \ +bn_mp_to_signed_bin.o bn_mp_unsigned_bin_size.o bn_mp_signed_bin_size.o \ +bn_mp_xor.o bn_mp_and.o bn_mp_or.o bn_mp_rand.o bn_mp_montgomery_calc_normalization.o \ +bn_mp_prime_is_divisible.o bn_prime_tab.o bn_mp_prime_fermat.o bn_mp_prime_miller_rabin.o \ +bn_mp_prime_is_prime.o bn_mp_prime_next_prime.o bn_mp_dr_reduce.o \ +bn_mp_dr_is_modulus.o bn_mp_dr_setup.o bn_mp_reduce_setup.o \ +bn_mp_toom_mul.o bn_mp_toom_sqr.o bn_mp_div_3.o bn_s_mp_exptmod.o \ +bn_mp_reduce_2k.o bn_mp_reduce_is_2k.o bn_mp_reduce_2k_setup.o \ +bn_mp_radix_smap.o bn_mp_read_radix.o bn_mp_toradix.o bn_mp_radix_size.o \ +bn_mp_fread.o bn_mp_fwrite.o bn_mp_cnt_lsb.o bn_error.o \ +bn_mp_init_multi.o bn_mp_clear_multi.o bn_mp_exteuclid.o bn_mp_toradix_n.o \ +bn_mp_prime_random_ex.o bn_mp_get_int.o bn_mp_sqrt.o bn_mp_is_square.o bn_mp_init_set.o \ +bn_mp_init_set_int.o bn_mp_invmod_slow.o bn_mp_prime_rabin_miller_trials.o + +libtommath.la: $(OBJECTS) + libtool --mode=link gcc *.lo -o libtommath.la -rpath $(LIBPATH) -version-info $(VERSION) + libtool --mode=link gcc *.o -o libtommath.a + libtool --mode=install install -c libtommath.la $(LIBPATH)/libtommath.la + install -d -g root -o root $(DESTDIR)$(INCPATH) + install -g root -o root $(HEADERS) $(DESTDIR)$(INCPATH) + +test: libtommath.a demo/demo.o + gcc $(CFLAGS) -c demo/demo.c -o demo/demo.o + libtool --mode=link gcc -o test demo/demo.o libtommath.la + +mtest: test + cd mtest ; gcc $(CFLAGS) mtest.c -o mtest -s + +timing: libtommath.la + gcc $(CFLAGS) -DTIMER demo/timing.c libtommath.a -o ltmtest -s
--- a/mtest/mtest.c Tue Jun 15 14:42:57 2004 +0000 +++ b/mtest/mtest.c Sun Dec 19 11:33:56 2004 +0000 @@ -58,7 +58,7 @@ int n, size; unsigned char buf[2048]; - size = 1 + ((fgetc(rng)<<8) + fgetc(rng)) % 97; + size = 10 + ((fgetc(rng)<<8) + fgetc(rng)) % 97; buf[0] = (fgetc(rng)&1)?1:0; fread(buf+1, 1, size, rng); while (buf[1] == 0) buf[1] = fgetc(rng); @@ -109,11 +109,12 @@ t1 = clock(); for (;;) { +#if 0 if (clock() - t1 > CLOCKS_PER_SEC) { sleep(2); t1 = clock(); } - +#endif n = fgetc(rng) % 15; if (n == 0) {
--- a/pre_gen/mpi.c Tue Jun 15 14:42:57 2004 +0000 +++ b/pre_gen/mpi.c Sun Dec 19 11:33:56 2004 +0000 @@ -1,19 +1,20 @@ /* Start: bn_error.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_ERROR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ static const struct { int code; @@ -40,30 +41,32 @@ return "Invalid error code"; } +#endif /* End: bn_error.c */ /* Start: bn_fast_mp_invmod.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_FAST_MP_INVMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* computes the modular inverse via binary extended euclidean algorithm, * that is c = 1/a mod b * - * Based on mp_invmod except this is optimized for the case where b is + * Based on slow invmod except this is optimized for the case where b is * odd as per HAC Note 14.64 on pp. 610 */ int @@ -187,29 +190,31 @@ __ERR:mp_clear_multi (&x, &y, &u, &v, &B, &D, NULL); return res; } +#endif /* End: bn_fast_mp_invmod.c */ /* Start: bn_fast_mp_montgomery_reduce.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* computes xR**-1 == x (mod N) via Montgomery Reduction * - * This is an optimized implementation of mp_montgomery_reduce + * This is an optimized implementation of montgomery_reduce * which uses the comba method to quickly calculate the columns of the * reduction. * @@ -358,25 +363,27 @@ } return MP_OKAY; } +#endif /* End: bn_fast_mp_montgomery_reduce.c */ /* Start: bn_fast_s_mp_mul_digs.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_FAST_S_MP_MUL_DIGS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* Fast (comba) multiplier * @@ -397,8 +404,9 @@ int fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { - int olduse, res, pa, ix; - mp_word W[MP_WARRAY]; + int olduse, res, pa, ix, iz; + mp_digit W[MP_WARRAY]; + register mp_word _W; /* grow the destination as required */ if (c->alloc < digs) { @@ -407,82 +415,52 @@ } } - /* clear temp buf (the columns) */ - memset (W, 0, sizeof (mp_word) * digs); - - /* calculate the columns */ - pa = a->used; - for (ix = 0; ix < pa; ix++) { - /* this multiplier has been modified to allow you to - * control how many digits of output are produced. - * So at most we want to make upto "digs" digits of output. - * - * this adds products to distinct columns (at ix+iy) of W - * note that each step through the loop is not dependent on - * the previous which means the compiler can easily unroll - * the loop without scheduling problems - */ - { - register mp_digit tmpx, *tmpy; - register mp_word *_W; - register int iy, pb; - - /* alias for the the word on the left e.g. A[ix] * A[iy] */ - tmpx = a->dp[ix]; - - /* alias for the right side */ - tmpy = b->dp; - - /* alias for the columns, each step through the loop adds a new - term to each column + /* number of output digits to produce */ + pa = MIN(digs, a->used + b->used); + + /* clear the carry */ + _W = 0; + for (ix = 0; ix <= pa; ix++) { + int tx, ty; + int iy; + mp_digit *tmpx, *tmpy; + + /* get offsets into the two bignums */ + ty = MIN(b->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = b->dp + ty; + + /* this is the number of times the loop will iterrate, essentially its + while (tx++ < a->used && ty-- >= 0) { ... } */ - _W = W + ix; - - /* the number of digits is limited by their placement. E.g. - we avoid multiplying digits that will end up above the # of - digits of precision requested - */ - pb = MIN (b->used, digs - ix); - - for (iy = 0; iy < pb; iy++) { - *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++); + iy = MIN(a->used-tx, ty+1); + + /* execute loop */ + for (iz = 0; iz < iy; ++iz) { + _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); } - } - + + /* store term */ + W[ix] = ((mp_digit)_W) & MP_MASK; + + /* make next carry */ + _W = _W >> ((mp_word)DIGIT_BIT); } /* setup dest */ - olduse = c->used; + olduse = c->used; c->used = digs; { register mp_digit *tmpc; - - /* At this point W[] contains the sums of each column. To get the - * correct result we must take the extra bits from each column and - * carry them down - * - * Note that while this adds extra code to the multiplier it - * saves time since the carry propagation is removed from the - * above nested loop.This has the effect of reducing the work - * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the - * cost of the shifting. On very small numbers this is slower - * but on most cryptographic size numbers it is faster. - * - * In this particular implementation we feed the carries from - * behind which means when the loop terminates we still have one - * last digit to copy - */ tmpc = c->dp; - for (ix = 1; ix < digs; ix++) { - /* forward the carry from the previous temp */ - W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT)); - + for (ix = 0; ix < digs; ix++) { /* now extract the previous digit [below the carry] */ - *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); - } - /* fetch the last digit */ - *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK)); + *tmpc++ = W[ix]; + } /* clear unused digits [that existed in the old copy of c] */ for (; ix < olduse; ix++) { @@ -492,28 +470,30 @@ mp_clamp (c); return MP_OKAY; } +#endif /* End: bn_fast_s_mp_mul_digs.c */ /* Start: bn_fast_s_mp_mul_high_digs.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ - #include <tommath.h> - -/* this is a modified version of fast_s_mp_mul_digs that only produces - * output digits *above* digs. See the comments for fast_s_mp_mul_digs +#include <tommath.h> +#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* this is a modified version of fast_s_mul_digs that only produces + * output digits *above* digs. See the comments for fast_s_mul_digs * to see how it works. * * This is used in the Barrett reduction since for one of the multiplications @@ -524,95 +504,92 @@ int fast_s_mp_mul_high_digs (mp_int * a, mp_int * b, mp_int * c, int digs) { - int oldused, newused, res, pa, pb, ix; - mp_word W[MP_WARRAY]; - - /* calculate size of product and allocate more space if required */ - newused = a->used + b->used + 1; - if (c->alloc < newused) { - if ((res = mp_grow (c, newused)) != MP_OKAY) { + int olduse, res, pa, ix, iz; + mp_digit W[MP_WARRAY]; + mp_word _W; + + /* grow the destination as required */ + pa = a->used + b->used; + if (c->alloc < pa) { + if ((res = mp_grow (c, pa)) != MP_OKAY) { return res; } } - /* like the other comba method we compute the columns first */ - pa = a->used; - pb = b->used; - memset (W + digs, 0, (pa + pb + 1 - digs) * sizeof (mp_word)); - for (ix = 0; ix < pa; ix++) { - { - register mp_digit tmpx, *tmpy; - register int iy; - register mp_word *_W; - - /* work todo, that is we only calculate digits that are at "digs" or above */ - iy = digs - ix; - - /* copy of word on the left of A[ix] * B[iy] */ - tmpx = a->dp[ix]; - - /* alias for right side */ - tmpy = b->dp + iy; - - /* alias for the columns of output. Offset to be equal to or above the - * smallest digit place requested + /* number of output digits to produce */ + pa = a->used + b->used; + _W = 0; + for (ix = digs; ix <= pa; ix++) { + int tx, ty, iy; + mp_digit *tmpx, *tmpy; + + /* get offsets into the two bignums */ + ty = MIN(b->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = b->dp + ty; + + /* this is the number of times the loop will iterrate, essentially its + while (tx++ < a->used && ty-- >= 0) { ... } */ - _W = W + digs; - - /* skip cases below zero where ix > digs */ - if (iy < 0) { - iy = abs(iy); - tmpy += iy; - _W += iy; - iy = 0; + iy = MIN(a->used-tx, ty+1); + + /* execute loop */ + for (iz = 0; iz < iy; iz++) { + _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); } - /* compute column products for digits above the minimum */ - for (; iy < pb; iy++) { - *_W++ += ((mp_word) tmpx) * ((mp_word)*tmpy++); - } - } + /* store term */ + W[ix] = ((mp_digit)_W) & MP_MASK; + + /* make next carry */ + _W = _W >> ((mp_word)DIGIT_BIT); } /* setup dest */ - oldused = c->used; - c->used = newused; - - /* now convert the array W downto what we need - * - * See comments in bn_fast_s_mp_mul_digs.c - */ - for (ix = digs + 1; ix < newused; ix++) { - W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT)); - c->dp[ix - 1] = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); - } - c->dp[newused - 1] = (mp_digit) (W[newused - 1] & ((mp_word) MP_MASK)); - - for (; ix < oldused; ix++) { - c->dp[ix] = 0; + olduse = c->used; + c->used = pa; + + { + register mp_digit *tmpc; + + tmpc = c->dp + digs; + for (ix = digs; ix <= pa; ix++) { + /* now extract the previous digit [below the carry] */ + *tmpc++ = W[ix]; + } + + /* clear unused digits [that existed in the old copy of c] */ + for (; ix < olduse; ix++) { + *tmpc++ = 0; + } } mp_clamp (c); return MP_OKAY; } +#endif /* End: bn_fast_s_mp_mul_high_digs.c */ /* Start: bn_fast_s_mp_sqr.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_FAST_S_MP_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* fast squaring * @@ -631,131 +608,121 @@ * Based on Algorithm 14.16 on pp.597 of HAC. * */ +/* the jist of squaring... + +you do like mult except the offset of the tmpx [one that starts closer to zero] +can't equal the offset of tmpy. So basically you set up iy like before then you min it with +(ty-tx) so that it never happens. You double all those you add in the inner loop + +After that loop you do the squares and add them in. + +Remove W2 and don't memset W + +*/ + int fast_s_mp_sqr (mp_int * a, mp_int * b) { - int olduse, newused, res, ix, pa; - mp_word W2[MP_WARRAY], W[MP_WARRAY]; - - /* calculate size of product and allocate as required */ - pa = a->used; - newused = pa + pa + 1; - if (b->alloc < newused) { - if ((res = mp_grow (b, newused)) != MP_OKAY) { + int olduse, res, pa, ix, iz; + mp_digit W[MP_WARRAY], *tmpx; + mp_word W1; + + /* grow the destination as required */ + pa = a->used + a->used; + if (b->alloc < pa) { + if ((res = mp_grow (b, pa)) != MP_OKAY) { return res; } } - /* zero temp buffer (columns) - * Note that there are two buffers. Since squaring requires - * a outer and inner product and the inner product requires - * computing a product and doubling it (a relatively expensive - * op to perform n**2 times if you don't have to) the inner and - * outer products are computed in different buffers. This way - * the inner product can be doubled using n doublings instead of - * n**2 - */ - memset (W, 0, newused * sizeof (mp_word)); - memset (W2, 0, newused * sizeof (mp_word)); - - /* This computes the inner product. To simplify the inner N**2 loop - * the multiplication by two is done afterwards in the N loop. - */ - for (ix = 0; ix < pa; ix++) { - /* compute the outer product - * - * Note that every outer product is computed - * for a particular column only once which means that - * there is no need todo a double precision addition - * into the W2[] array. - */ - W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]); - - { - register mp_digit tmpx, *tmpy; - register mp_word *_W; - register int iy; - - /* copy of left side */ - tmpx = a->dp[ix]; - - /* alias for right side */ - tmpy = a->dp + (ix + 1); - - /* the column to store the result in */ - _W = W + (ix + ix + 1); - - /* inner products */ - for (iy = ix + 1; iy < pa; iy++) { - *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++); + /* number of output digits to produce */ + W1 = 0; + for (ix = 0; ix <= pa; ix++) { + int tx, ty, iy; + mp_word _W; + mp_digit *tmpy; + + /* clear counter */ + _W = 0; + + /* get offsets into the two bignums */ + ty = MIN(a->used-1, ix); + tx = ix - ty; + + /* setup temp aliases */ + tmpx = a->dp + tx; + tmpy = a->dp + ty; + + /* this is the number of times the loop will iterrate, essentially its + while (tx++ < a->used && ty-- >= 0) { ... } + */ + iy = MIN(a->used-tx, ty+1); + + /* now for squaring tx can never equal ty + * we halve the distance since they approach at a rate of 2x + * and we have to round because odd cases need to be executed + */ + iy = MIN(iy, (ty-tx+1)>>1); + + /* execute loop */ + for (iz = 0; iz < iy; iz++) { + _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); } - } + + /* double the inner product and add carry */ + _W = _W + _W + W1; + + /* even columns have the square term in them */ + if ((ix&1) == 0) { + _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]); + } + + /* store it */ + W[ix] = _W; + + /* make next carry */ + W1 = _W >> ((mp_word)DIGIT_BIT); } /* setup dest */ olduse = b->used; - b->used = newused; - - /* now compute digits - * - * We have to double the inner product sums, add in the - * outer product sums, propagate carries and convert - * to single precision. - */ + b->used = a->used+a->used; + { - register mp_digit *tmpb; - - /* double first value, since the inner products are - * half of what they should be - */ - W[0] += W[0] + W2[0]; - + mp_digit *tmpb; tmpb = b->dp; - for (ix = 1; ix < newused; ix++) { - /* double/add next digit */ - W[ix] += W[ix] + W2[ix]; - - /* propagate carry forwards [from the previous digit] */ - W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT)); - - /* store the current digit now that the carry isn't - * needed - */ - *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); - } - /* set the last value. Note even if the carry is zero - * this is required since the next step will not zero - * it if b originally had a value at b->dp[2*a.used] - */ - *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK)); - - /* clear high digits of b if there were any originally */ + for (ix = 0; ix < pa; ix++) { + *tmpb++ = W[ix] & MP_MASK; + } + + /* clear unused digits [that existed in the old copy of c] */ for (; ix < olduse; ix++) { *tmpb++ = 0; } } - mp_clamp (b); return MP_OKAY; } +#endif /* End: bn_fast_s_mp_sqr.c */ /* Start: bn_mp_2expt.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_2EXPT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* computes a = 2**b * @@ -779,29 +746,31 @@ a->used = b / DIGIT_BIT + 1; /* put the single bit in its place */ - a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT); + a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); return MP_OKAY; } +#endif /* End: bn_mp_2expt.c */ /* Start: bn_mp_abs.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_ABS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* b = |a| * @@ -824,25 +793,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_abs.c */ /* Start: bn_mp_add.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_ADD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* high level addition (handles signs) */ int mp_add (mp_int * a, mp_int * b, mp_int * c) @@ -875,25 +846,27 @@ return res; } +#endif /* End: bn_mp_add.c */ /* Start: bn_mp_add_d.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_ADD_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* single digit addition */ int @@ -982,25 +955,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_add_d.c */ /* Start: bn_mp_addmod.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_ADDMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* d = a + b (mod c) */ int @@ -1021,25 +996,27 @@ mp_clear (&t); return res; } +#endif /* End: bn_mp_addmod.c */ /* Start: bn_mp_and.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_AND_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* AND two ints together */ int @@ -1076,25 +1053,27 @@ mp_clear (&t); return MP_OKAY; } +#endif /* End: bn_mp_and.c */ /* Start: bn_mp_clamp.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_CLAMP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* trim unused digits * @@ -1118,34 +1097,40 @@ a->sign = MP_ZPOS; } } +#endif /* End: bn_mp_clamp.c */ /* Start: bn_mp_clear.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_CLEAR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* clear one (frees) */ void mp_clear (mp_int * a) { + int i; + /* only do anything if a hasn't been freed previously */ if (a->dp != NULL) { /* first zero the digits */ - memset (a->dp, 0, sizeof (mp_digit) * a->used); + for (i = 0; i < a->used; i++) { + a->dp[i] = 0; + } /* free ram */ XFREE(a->dp); @@ -1156,25 +1141,27 @@ a->sign = MP_ZPOS; } } +#endif /* End: bn_mp_clear.c */ /* Start: bn_mp_clear_multi.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_CLEAR_MULTI_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ #include <stdarg.h> void mp_clear_multi(mp_int *mp, ...) @@ -1188,25 +1175,27 @@ } va_end(args); } +#endif /* End: bn_mp_clear_multi.c */ /* Start: bn_mp_cmp.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_CMP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* compare two ints (signed)*/ int @@ -1229,25 +1218,27 @@ return mp_cmp_mag(a, b); } } +#endif /* End: bn_mp_cmp.c */ /* Start: bn_mp_cmp_d.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_CMP_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* compare a digit */ int mp_cmp_d(mp_int * a, mp_digit b) @@ -1271,25 +1262,27 @@ return MP_EQ; } } +#endif /* End: bn_mp_cmp_d.c */ /* Start: bn_mp_cmp_mag.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_CMP_MAG_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* compare maginitude of two ints (unsigned) */ int mp_cmp_mag (mp_int * a, mp_int * b) @@ -1324,25 +1317,27 @@ } return MP_EQ; } +#endif /* End: bn_mp_cmp_mag.c */ /* Start: bn_mp_cnt_lsb.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_CNT_LSB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ static const int lnz[16] = { 4, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0 @@ -1375,25 +1370,27 @@ return x; } +#endif /* End: bn_mp_cnt_lsb.c */ /* Start: bn_mp_copy.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_COPY_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* copy, b = a */ int @@ -1441,25 +1438,27 @@ b->sign = a->sign; return MP_OKAY; } +#endif /* End: bn_mp_copy.c */ /* Start: bn_mp_count_bits.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_COUNT_BITS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* returns the number of bits in an int */ int @@ -1484,25 +1483,99 @@ } return r; } +#endif /* End: bn_mp_count_bits.c */ /* Start: bn_mp_div.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_DIV_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +#ifdef BN_MP_DIV_SMALL + +/* slower bit-bang division... also smaller */ +int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d) +{ + mp_int ta, tb, tq, q; + int res, n, n2; + + /* is divisor zero ? */ + if (mp_iszero (b) == 1) { + return MP_VAL; + } + + /* if a < b then q=0, r = a */ + if (mp_cmp_mag (a, b) == MP_LT) { + if (d != NULL) { + res = mp_copy (a, d); + } else { + res = MP_OKAY; + } + if (c != NULL) { + mp_zero (c); + } + return res; + } + + /* init our temps */ + if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) { + return res; + } + + + mp_set(&tq, 1); + n = mp_count_bits(a) - mp_count_bits(b); + if (((res = mp_copy(a, &ta)) != MP_OKAY) || + ((res = mp_copy(b, &tb)) != MP_OKAY) || + ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || + ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) { + goto __ERR; + } + + while (n-- >= 0) { + if (mp_cmp(&tb, &ta) != MP_GT) { + if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || + ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) { + goto __ERR; + } + } + if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) || + ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) { + goto __ERR; + } + } + + /* now q == quotient and ta == remainder */ + n = a->sign; + n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG); + if (c != NULL) { + mp_exch(c, &q); + c->sign = n2; + } + if (d != NULL) { + mp_exch(d, &ta); + d->sign = n; + } +__ERR: + mp_clear_multi(&ta, &tb, &tq, &q, NULL); + return res; +} + +#else /* integer signed division. * c*b + d == a [e.g. a/b, c=quotient, d=remainder] @@ -1677,7 +1750,7 @@ */ /* get sign before writing to c */ - x.sign = a->sign; + x.sign = x.used == 0 ? MP_ZPOS : a->sign; if (c != NULL) { mp_clamp (&q); @@ -1700,24 +1773,29 @@ return res; } +#endif + +#endif + /* End: bn_mp_div.c */ /* Start: bn_mp_div_2.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_DIV_2_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* b = a/2 */ int mp_div_2(mp_int * a, mp_int * b) @@ -1765,25 +1843,27 @@ mp_clamp (b); return MP_OKAY; } +#endif /* End: bn_mp_div_2.c */ /* Start: bn_mp_div_2d.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_DIV_2D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* shift right by a certain bit count (store quotient in c, optional remainder in d) */ int mp_div_2d (mp_int * a, int b, mp_int * c, mp_int * d) @@ -1860,25 +1940,27 @@ mp_clear (&t); return MP_OKAY; } +#endif /* End: bn_mp_div_2d.c */ /* Start: bn_mp_div_3.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_DIV_3_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* divide by three (based on routine from MPI and the GMP manual) */ int @@ -1937,25 +2019,27 @@ return res; } +#endif /* End: bn_mp_div_3.c */ /* Start: bn_mp_div_d.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_DIV_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ static int s_is_power_of_two(mp_digit b, int *p) { @@ -1997,7 +2081,7 @@ /* power of two ? */ if (s_is_power_of_two(b, &ix) == 1) { if (d != NULL) { - *d = a->dp[0] & ((1<<ix) - 1); + *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1); } if (c != NULL) { return mp_div_2d(a, ix, c, NULL); @@ -2005,10 +2089,12 @@ return MP_OKAY; } +#ifdef BN_MP_DIV_3_C /* three? */ if (b == 3) { return mp_div_3(a, c, d); } +#endif /* no easy answer [c'est la vie]. Just division */ if ((res = mp_init_size(&q, a->used)) != MP_OKAY) { @@ -2043,25 +2129,27 @@ return res; } +#endif /* End: bn_mp_div_d.c */ /* Start: bn_mp_dr_is_modulus.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_DR_IS_MODULUS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* determines if a number is a valid DR modulus */ int mp_dr_is_modulus(mp_int *a) @@ -2084,25 +2172,27 @@ return 1; } +#endif /* End: bn_mp_dr_is_modulus.c */ /* Start: bn_mp_dr_reduce.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_DR_REDUCE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* reduce "x" in place modulo "n" using the Diminished Radix algorithm. * @@ -2176,25 +2266,27 @@ } return MP_OKAY; } +#endif /* End: bn_mp_dr_reduce.c */ /* Start: bn_mp_dr_setup.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_DR_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* determines the setup value */ void mp_dr_setup(mp_int *a, mp_digit *d) @@ -2206,25 +2298,27 @@ ((mp_word)a->dp[0])); } +#endif /* End: bn_mp_dr_setup.c */ /* Start: bn_mp_exch.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_EXCH_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* swap the elements of two integers, for cases where you can't simply swap the * mp_int pointers around @@ -2238,25 +2332,27 @@ *a = *b; *b = t; } +#endif /* End: bn_mp_exch.c */ /* Start: bn_mp_expt_d.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_EXPT_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* calculate c = a**b using a square-multiply algorithm */ int mp_expt_d (mp_int * a, mp_digit b, mp_int * c) @@ -2293,25 +2389,27 @@ mp_clear (&g); return MP_OKAY; } +#endif /* End: bn_mp_expt_d.c */ /* Start: bn_mp_exptmod.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_EXPTMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* this is a shell function that calls either the normal or Montgomery @@ -2330,6 +2428,7 @@ /* if exponent X is negative we have to recurse */ if (X->sign == MP_NEG) { +#ifdef BN_MP_INVMOD_C mp_int tmpG, tmpX; int err; @@ -2356,44 +2455,65 @@ err = mp_exptmod(&tmpG, &tmpX, P, Y); mp_clear_multi(&tmpG, &tmpX, NULL); return err; - } - +#else + /* no invmod */ + return MP_VAL +#endif + } + +#ifdef BN_MP_DR_IS_MODULUS_C /* is it a DR modulus? */ dr = mp_dr_is_modulus(P); - +#else + dr = 0; +#endif + +#ifdef BN_MP_REDUCE_IS_2K_C /* if not, is it a uDR modulus? */ if (dr == 0) { dr = mp_reduce_is_2k(P) << 1; } +#endif /* if the modulus is odd or dr != 0 use the fast method */ +#ifdef BN_MP_EXPTMOD_FAST_C if (mp_isodd (P) == 1 || dr != 0) { return mp_exptmod_fast (G, X, P, Y, dr); } else { +#endif +#ifdef BN_S_MP_EXPTMOD_C /* otherwise use the generic Barrett reduction technique */ return s_mp_exptmod (G, X, P, Y); - } +#else + /* no exptmod for evens */ + return MP_VAL; +#endif +#ifdef BN_MP_EXPTMOD_FAST_C + } +#endif } +#endif /* End: bn_mp_exptmod.c */ /* Start: bn_mp_exptmod_fast.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_EXPTMOD_FAST_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* computes Y == G**X mod P, HAC pp.616, Algorithm 14.85 * @@ -2465,29 +2585,52 @@ /* determine and setup reduction code */ if (redmode == 0) { +#ifdef BN_MP_MONTGOMERY_SETUP_C /* now setup montgomery */ if ((err = mp_montgomery_setup (P, &mp)) != MP_OKAY) { goto __M; } +#else + err = MP_VAL; + goto __M; +#endif /* automatically pick the comba one if available (saves quite a few calls/ifs) */ +#ifdef BN_FAST_MP_MONTGOMERY_REDUCE_C if (((P->used * 2 + 1) < MP_WARRAY) && P->used < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { redux = fast_mp_montgomery_reduce; - } else { + } else +#endif + { +#ifdef BN_MP_MONTGOMERY_REDUCE_C /* use slower baseline Montgomery method */ redux = mp_montgomery_reduce; +#else + err = MP_VAL; + goto __M; +#endif } } else if (redmode == 1) { +#if defined(BN_MP_DR_SETUP_C) && defined(BN_MP_DR_REDUCE_C) /* setup DR reduction for moduli of the form B**k - b */ mp_dr_setup(P, &mp); redux = mp_dr_reduce; +#else + err = MP_VAL; + goto __M; +#endif } else { +#if defined(BN_MP_REDUCE_2K_SETUP_C) && defined(BN_MP_REDUCE_2K_C) /* setup DR reduction for moduli of the form 2**k - b */ if ((err = mp_reduce_2k_setup(P, &mp)) != MP_OKAY) { goto __M; } redux = mp_reduce_2k; +#else + err = MP_VAL; + goto __M; +#endif } /* setup result */ @@ -2497,16 +2640,21 @@ /* create M table * - * The M table contains powers of the input base, e.g. M[x] = G^x mod P + * * The first half of the table is not computed though accept for M[0] and M[1] */ if (redmode == 0) { +#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C /* now we need R mod m */ if ((err = mp_montgomery_calc_normalization (&res, P)) != MP_OKAY) { goto __RES; } +#else + err = MP_VAL; + goto __RES; +#endif /* now set M[1] to G * R mod m */ if ((err = mp_mulmod (G, &res, P, &M[1])) != MP_OKAY) { @@ -2650,7 +2798,7 @@ * to reduce one more time to cancel out the factor * of R. */ - if ((err = mp_montgomery_reduce (&res, P, mp)) != MP_OKAY) { + if ((err = redux(&res, P, mp)) != MP_OKAY) { goto __RES; } } @@ -2666,25 +2814,28 @@ } return err; } +#endif + /* End: bn_mp_exptmod_fast.c */ /* Start: bn_mp_exteuclid.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_EXTEUCLID_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* Extended euclidean algorithm of (a, b) produces a*u1 + b*u2 = u3 @@ -2739,25 +2890,27 @@ _ERR: mp_clear_multi(&u1, &u2, &u3, &v1, &v2, &v3, &t1, &t2, &t3, &q, &tmp, NULL); return err; } +#endif /* End: bn_mp_exteuclid.c */ /* Start: bn_mp_fread.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_FREAD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* read a bigint from a file stream in ASCII */ int mp_fread(mp_int *a, int radix, FILE *stream) @@ -2804,25 +2957,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_fread.c */ /* Start: bn_mp_fwrite.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_FWRITE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ int mp_fwrite(mp_int *a, int radix, FILE *stream) { @@ -2854,25 +3009,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_fwrite.c */ /* Start: bn_mp_gcd.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_GCD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* Greatest Common Divisor using the binary method */ int mp_gcd (mp_int * a, mp_int * b, mp_int * c) @@ -2965,25 +3122,27 @@ __U:mp_clear (&v); return res; } +#endif /* End: bn_mp_gcd.c */ /* Start: bn_mp_get_int.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_GET_INT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* get the lower 32-bits of an mp_int */ unsigned long mp_get_int(mp_int * a) @@ -3008,25 +3167,27 @@ /* force result to 32-bits always so it is consistent on non 32-bit platforms */ return res & 0xFFFFFFFFUL; } +#endif /* End: bn_mp_get_int.c */ /* Start: bn_mp_grow.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_GROW_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* grow as required */ int mp_grow (mp_int * a, int size) @@ -3063,35 +3224,44 @@ } return MP_OKAY; } +#endif /* End: bn_mp_grow.c */ /* Start: bn_mp_init.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> - -/* init a new bigint */ +#include <tommath.h> +#ifdef BN_MP_INIT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* init a new mp_int */ int mp_init (mp_int * a) { + int i; + /* allocate memory required and clear it */ - a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), MP_PREC); + a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC); if (a->dp == NULL) { return MP_MEM; } + /* set the digits to zero */ + for (i = 0; i < MP_PREC; i++) { + a->dp[i] = 0; + } + /* set the used to zero, allocated digits to the default precision * and sign to positive */ a->used = 0; @@ -3100,25 +3270,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_init.c */ /* Start: bn_mp_init_copy.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_INIT_COPY_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* creates "a" then copies b into it */ int mp_init_copy (mp_int * a, mp_int * b) @@ -3130,25 +3302,27 @@ } return mp_copy (b, a); } +#endif /* End: bn_mp_init_copy.c */ /* Start: bn_mp_init_multi.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_INIT_MULTI_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ #include <stdarg.h> int mp_init_multi(mp_int *mp, ...) @@ -3187,25 +3361,27 @@ return res; /* Assumed ok, if error flagged above. */ } +#endif /* End: bn_mp_init_multi.c */ /* Start: bn_mp_init_set.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_INIT_SET_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* initialize and set a digit */ int mp_init_set (mp_int * a, mp_digit b) @@ -3217,25 +3393,27 @@ mp_set(a, b); return err; } +#endif /* End: bn_mp_init_set.c */ /* Start: bn_mp_init_set_int.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_INIT_SET_INT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* initialize and set a digit */ int mp_init_set_int (mp_int * a, unsigned long b) @@ -3246,66 +3424,122 @@ } return mp_set_int(a, b); } +#endif /* End: bn_mp_init_set_int.c */ /* Start: bn_mp_init_size.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_INIT_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* init an mp_init for a given size */ int mp_init_size (mp_int * a, int size) { + int x; + /* pad size so there are always extra digits */ size += (MP_PREC * 2) - (size % MP_PREC); /* alloc mem */ - a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), size); + a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size); if (a->dp == NULL) { return MP_MEM; } + + /* set the members */ a->used = 0; a->alloc = size; a->sign = MP_ZPOS; + /* zero the digits */ + for (x = 0; x < size; x++) { + a->dp[x] = 0; + } + return MP_OKAY; } +#endif /* End: bn_mp_init_size.c */ /* Start: bn_mp_invmod.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_INVMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* hac 14.61, pp608 */ int mp_invmod (mp_int * a, mp_int * b, mp_int * c) { + /* b cannot be negative */ + if (b->sign == MP_NEG || mp_iszero(b) == 1) { + return MP_VAL; + } + +#ifdef BN_FAST_MP_INVMOD_C + /* if the modulus is odd we can use a faster routine instead */ + if (mp_isodd (b) == 1) { + return fast_mp_invmod (a, b, c); + } +#endif + +#ifdef BN_MP_INVMOD_SLOW_C + return mp_invmod_slow(a, b, c); +#endif + + return MP_VAL; +} +#endif + +/* End: bn_mp_invmod.c */ + +/* Start: bn_mp_invmod_slow.c */ +#include <tommath.h> +#ifdef BN_MP_INVMOD_SLOW_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* hac 14.61, pp608 */ +int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c) +{ mp_int x, y, u, v, A, B, C, D; int res; @@ -3314,11 +3548,6 @@ return MP_VAL; } - /* if the modulus is odd we can use a faster routine instead */ - if (mp_isodd (b) == 1) { - return fast_mp_invmod (a, b, c); - } - /* init temps */ if ((res = mp_init_multi(&x, &y, &u, &v, &A, &B, &C, &D, NULL)) != MP_OKAY) { @@ -3461,25 +3690,27 @@ __ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); return res; } - -/* End: bn_mp_invmod.c */ +#endif + +/* End: bn_mp_invmod_slow.c */ /* Start: bn_mp_is_square.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_IS_SQUARE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* Check if remainders are possible squares - fast exclude non-squares */ static const char rem_128[128] = { @@ -3536,7 +3767,7 @@ return MP_OKAY; } - /* product of primes less than 2^31 */ + if ((res = mp_init_set_int(&t,11L*13L*17L*19L*23L*29L*31L)) != MP_OKAY) { return res; } @@ -3568,25 +3799,27 @@ ERR:mp_clear(&t); return res; } +#endif /* End: bn_mp_is_square.c */ /* Start: bn_mp_jacobi.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_JACOBI_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* computes the jacobi c = (a | n) (or Legendre if n is prime) * HAC pp. 73 Algorithm 2.149 @@ -3671,25 +3904,27 @@ __A1:mp_clear (&a1); return res; } +#endif /* End: bn_mp_jacobi.c */ /* Start: bn_mp_karatsuba_mul.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_KARATSUBA_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* c = |a| * |b| using Karatsuba Multiplication using * three half size multiplications @@ -3753,9 +3988,6 @@ goto X0Y0; /* now shift the digits */ - x0.sign = x1.sign = a->sign; - y0.sign = y1.sign = b->sign; - x0.used = y0.used = B; x1.used = a->used - B; y1.used = b->used - B; @@ -3839,30 +4071,32 @@ ERR: return err; } +#endif /* End: bn_mp_karatsuba_mul.c */ /* Start: bn_mp_karatsuba_sqr.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_KARATSUBA_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* Karatsuba squaring, computes b = a*a using three * half size squarings * - * See comments of mp_karatsuba_mul for details. It + * See comments of karatsuba_mul for details. It * is essentially the same algorithm but merely * tuned to perform recursive squarings. */ @@ -3958,25 +4192,27 @@ ERR: return err; } +#endif /* End: bn_mp_karatsuba_sqr.c */ /* Start: bn_mp_lcm.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_LCM_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* computes least common multiple as |a*b|/(a, b) */ int mp_lcm (mp_int * a, mp_int * b, mp_int * c) @@ -4016,25 +4252,27 @@ mp_clear_multi (&t1, &t2, NULL); return res; } +#endif /* End: bn_mp_lcm.c */ /* Start: bn_mp_lshd.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_LSHD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* shift left a certain amount of digits */ int mp_lshd (mp_int * a, int b) @@ -4081,25 +4319,27 @@ } return MP_OKAY; } +#endif /* End: bn_mp_lshd.c */ /* Start: bn_mp_mod.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_MOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* c = a mod b, 0 <= c < b */ int @@ -4127,25 +4367,27 @@ mp_clear (&t); return res; } +#endif /* End: bn_mp_mod.c */ /* Start: bn_mp_mod_2d.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_MOD_2D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* calc a value mod 2**b */ int @@ -4180,73 +4422,78 @@ mp_clamp (c); return MP_OKAY; } +#endif /* End: bn_mp_mod_2d.c */ /* Start: bn_mp_mod_d.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_MOD_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ int mp_mod_d (mp_int * a, mp_digit b, mp_digit * c) { return mp_div_d(a, b, NULL, c); } +#endif /* End: bn_mp_mod_d.c */ /* Start: bn_mp_montgomery_calc_normalization.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> - -/* calculates a = B^n mod b for Montgomery reduction - * Where B is the base [e.g. 2^DIGIT_BIT]. - * B^n mod b is computed by first computing - * A = B^(n-1) which doesn't require a reduction but a simple OR. - * then C = A * B = B^n is computed by performing upto DIGIT_BIT +#include <tommath.h> +#ifdef BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* * shifts with subtractions when the result is greater than b. * * The method is slightly modified to shift B unconditionally upto just under * the leading bit of b. This saves alot of multiple precision shifting. */ -int -mp_montgomery_calc_normalization (mp_int * a, mp_int * b) +int mp_montgomery_calc_normalization (mp_int * a, mp_int * b) { int x, bits, res; /* how many bits of last digit does b use */ bits = mp_count_bits (b) % DIGIT_BIT; - /* compute A = B^(n-1) * 2^(bits-1) */ - if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { - return res; - } + + if (b->used > 1) { + if ((res = mp_2expt (a, (b->used - 1) * DIGIT_BIT + bits - 1)) != MP_OKAY) { + return res; + } + } else { + mp_set(a, 1); + bits = 1; + } + /* now compute C = A * B mod b */ for (x = bits - 1; x < (int)DIGIT_BIT; x++) { @@ -4262,25 +4509,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_montgomery_calc_normalization.c */ /* Start: bn_mp_montgomery_reduce.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_MONTGOMERY_REDUCE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* computes xR**-1 == x (mod N) via Montgomery Reduction */ int @@ -4291,7 +4540,7 @@ /* can the fast reduction [comba] method be used? * - * Note that unlike in mp_mul you're safely allowed *less* + * Note that unlike in mul you're safely allowed *less* * than the available columns [255 per default] since carries * are fixed up in the inner loop. */ @@ -4314,7 +4563,7 @@ /* mu = ai * rho mod b * * The value of rho must be precalculated via - * bn_mp_montgomery_setup() such that + * montgomery_setup() such that * it equals -1/n0 mod b this allows the * following inner loop to reduce the * input one digit at a time @@ -4378,25 +4627,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_montgomery_reduce.c */ /* Start: bn_mp_montgomery_setup.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_MONTGOMERY_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* setups the montgomery reduction stuff */ int @@ -4431,29 +4682,31 @@ #endif /* rho = -1/m mod b */ - *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK; + *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; return MP_OKAY; } +#endif /* End: bn_mp_montgomery_setup.c */ /* Start: bn_mp_mul.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* high level multiplication (handles sign) */ int mp_mul (mp_int * a, mp_int * b, mp_int * c) @@ -4462,12 +4715,18 @@ neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; /* use Toom-Cook? */ +#ifdef BN_MP_TOOM_MUL_C if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) { res = mp_toom_mul(a, b, c); + } else +#endif +#ifdef BN_MP_KARATSUBA_MUL_C /* use Karatsuba? */ - } else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) { + if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) { res = mp_karatsuba_mul (a, b, c); - } else { + } else +#endif + { /* can we use the fast multiplier? * * The fast multiplier can be used if the output will @@ -4476,36 +4735,44 @@ */ int digs = a->used + b->used + 1; +#ifdef BN_FAST_S_MP_MUL_DIGS_C if ((digs < MP_WARRAY) && MIN(a->used, b->used) <= (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { res = fast_s_mp_mul_digs (a, b, c, digs); - } else { - res = s_mp_mul (a, b, c); - } - } - c->sign = neg; + } else +#endif +#ifdef BN_S_MP_MUL_DIGS_C + res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */ +#else + res = MP_VAL; +#endif + + } + c->sign = (c->used > 0) ? neg : MP_ZPOS; return res; } +#endif /* End: bn_mp_mul.c */ /* Start: bn_mp_mul_2.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_MUL_2_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* b = a*2 */ int mp_mul_2(mp_int * a, mp_int * b) @@ -4567,25 +4834,27 @@ b->sign = a->sign; return MP_OKAY; } +#endif /* End: bn_mp_mul_2.c */ /* Start: bn_mp_mul_2d.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_MUL_2D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* shift left by a certain bit count */ int mp_mul_2d (mp_int * a, int b, mp_int * c) @@ -4650,25 +4919,27 @@ mp_clamp (c); return MP_OKAY; } +#endif /* End: bn_mp_mul_2d.c */ /* Start: bn_mp_mul_d.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_MUL_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* multiply by a digit */ int @@ -4726,25 +4997,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_mul_d.c */ /* Start: bn_mp_mulmod.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_MULMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* d = a * b (mod c) */ int @@ -4765,25 +5038,27 @@ mp_clear (&t); return res; } +#endif /* End: bn_mp_mulmod.c */ /* Start: bn_mp_n_root.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_N_ROOT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* find the n'th root of an integer * @@ -4895,25 +5170,27 @@ __T1:mp_clear (&t1); return res; } +#endif /* End: bn_mp_n_root.c */ /* Start: bn_mp_neg.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_NEG_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* b = -a */ int mp_neg (mp_int * a, mp_int * b) @@ -4927,25 +5204,27 @@ } return MP_OKAY; } +#endif /* End: bn_mp_neg.c */ /* Start: bn_mp_or.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_OR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* OR two ints together */ int mp_or (mp_int * a, mp_int * b, mp_int * c) @@ -4975,25 +5254,27 @@ mp_clear (&t); return MP_OKAY; } +#endif /* End: bn_mp_or.c */ /* Start: bn_mp_prime_fermat.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_PRIME_FERMAT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* performs one Fermat test. * @@ -5035,25 +5316,27 @@ __T:mp_clear (&t); return err; } +#endif /* End: bn_mp_prime_fermat.c */ /* Start: bn_mp_prime_is_divisible.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_PRIME_IS_DIVISIBLE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* determines if an integers is divisible by one * of the first PRIME_SIZE primes or not @@ -5083,30 +5366,32 @@ return MP_OKAY; } +#endif /* End: bn_mp_prime_is_divisible.c */ /* Start: bn_mp_prime_is_prime.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_PRIME_IS_PRIME_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* performs a variable number of rounds of Miller-Rabin * * Probability of error after t rounds is no more than - * (1/4)^t when 1 <= t <= PRIME_SIZE + * * Sets result to 1 if probably prime, 0 otherwise */ @@ -5164,25 +5449,27 @@ __B:mp_clear (&b); return err; } +#endif /* End: bn_mp_prime_is_prime.c */ /* Start: bn_mp_prime_miller_rabin.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_PRIME_MILLER_RABIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* Miller-Rabin test of "a" to the base of "b" as described in * HAC pp. 139 Algorithm 4.24 @@ -5265,25 +5552,27 @@ __N1:mp_clear (&n1); return err; } +#endif /* End: bn_mp_prime_miller_rabin.c */ /* Start: bn_mp_prime_next_prime.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_PRIME_NEXT_PRIME_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* finds the next prime after the number "a" using "t" trials * of Miller-Rabin. @@ -5433,25 +5722,79 @@ return err; } +#endif /* End: bn_mp_prime_next_prime.c */ +/* Start: bn_mp_prime_rabin_miller_trials.c */ +#include <tommath.h> +#ifdef BN_MP_PRIME_RABIN_MILLER_TRIALS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + + +static const struct { + int k, t; +} sizes[] = { +{ 128, 28 }, +{ 256, 16 }, +{ 384, 10 }, +{ 512, 7 }, +{ 640, 6 }, +{ 768, 5 }, +{ 896, 4 }, +{ 1024, 4 } +}; + +/* returns # of RM trials required for a given bit size */ +int mp_prime_rabin_miller_trials(int size) +{ + int x; + + for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) { + if (sizes[x].k == size) { + return sizes[x].t; + } else if (sizes[x].k > size) { + return (x == 0) ? sizes[0].t : sizes[x - 1].t; + } + } + return sizes[x-1].t + 1; +} + + +#endif + +/* End: bn_mp_prime_rabin_miller_trials.c */ + /* Start: bn_mp_prime_random_ex.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_PRIME_RANDOM_EX_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* makes a truly random prime of a given size (bits), * @@ -5531,6 +5874,9 @@ /* is it prime? */ if ((err = mp_prime_is_prime(a, t, &res)) != MP_OKAY) { goto error; } + if (res == MP_NO) { + continue; + } if (flags & LTM_PRIME_SAFE) { /* see if (a-1)/2 is prime */ @@ -5555,25 +5901,27 @@ } +#endif /* End: bn_mp_prime_random_ex.c */ /* Start: bn_mp_radix_size.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_RADIX_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* returns size of ASCII reprensentation */ int mp_radix_size (mp_int * a, int radix, int *size) @@ -5624,47 +5972,51 @@ return MP_OKAY; } +#endif /* End: bn_mp_radix_size.c */ /* Start: bn_mp_radix_smap.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_RADIX_SMAP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* chars used in radix conversions */ const char *mp_s_rmap = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz+/"; +#endif /* End: bn_mp_radix_smap.c */ /* Start: bn_mp_rand.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_RAND_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* makes a pseudo-random int of a given size */ int @@ -5699,25 +6051,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_rand.c */ /* Start: bn_mp_read_radix.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_READ_RADIX_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* read a string [ASCII] in a given radix */ int mp_read_radix (mp_int * a, char *str, int radix) @@ -5779,25 +6133,27 @@ } return MP_OKAY; } +#endif /* End: bn_mp_read_radix.c */ /* Start: bn_mp_read_signed_bin.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_READ_SIGNED_BIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* read signed bin, big endian, first byte is 0==positive or 1==negative */ int @@ -5819,25 +6175,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_read_signed_bin.c */ /* Start: bn_mp_read_unsigned_bin.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_READ_UNSIGNED_BIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* reads a unsigned char array, assumes the msb is stored first [big endian] */ int @@ -5873,25 +6231,27 @@ mp_clamp (a); return MP_OKAY; } +#endif /* End: bn_mp_read_unsigned_bin.c */ /* Start: bn_mp_reduce.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_REDUCE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* reduces x mod m, assumes 0 < x < m**2, mu is * precomputed via mp_reduce_setup. @@ -5917,9 +6277,20 @@ goto CLEANUP; } } else { +#ifdef BN_S_MP_MUL_HIGH_DIGS_C if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { goto CLEANUP; } +#elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) + if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) { + goto CLEANUP; + } +#else + { + res = MP_VAL; + goto CLEANUP; + } +#endif } /* q3 = q2 / b**(k+1) */ @@ -5961,25 +6332,27 @@ return res; } +#endif /* End: bn_mp_reduce.c */ /* Start: bn_mp_reduce_2k.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_REDUCE_2K_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* reduces a modulo n where n is of the form 2**p - d */ int @@ -6021,25 +6394,27 @@ return res; } +#endif /* End: bn_mp_reduce_2k.c */ /* Start: bn_mp_reduce_2k_setup.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_REDUCE_2K_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* determines the setup value */ int @@ -6067,30 +6442,33 @@ mp_clear(&tmp); return MP_OKAY; } +#endif /* End: bn_mp_reduce_2k_setup.c */ /* Start: bn_mp_reduce_is_2k.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_REDUCE_IS_2K_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* determines if mp_reduce_2k can be used */ int mp_reduce_is_2k(mp_int *a) { - int ix, iy, iz, iw; + int ix, iy, iw; + mp_digit iz; if (a->used == 0) { return 0; @@ -6107,7 +6485,7 @@ return 0; } iz <<= 1; - if (iz > (int)MP_MASK) { + if (iz > (mp_digit)MP_MASK) { ++iw; iz = 1; } @@ -6116,31 +6494,32 @@ return 1; } +#endif /* End: bn_mp_reduce_is_2k.c */ /* Start: bn_mp_reduce_setup.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_REDUCE_SETUP_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* pre-calculate the value required for Barrett reduction * For a given modulus "b" it calulates the value required in "a" */ -int -mp_reduce_setup (mp_int * a, mp_int * b) +int mp_reduce_setup (mp_int * a, mp_int * b) { int res; @@ -6149,25 +6528,27 @@ } return mp_div (a, b, a, NULL); } +#endif /* End: bn_mp_reduce_setup.c */ /* Start: bn_mp_rshd.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_RSHD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* shift right a certain amount of digits */ void mp_rshd (mp_int * a, int b) @@ -6219,25 +6600,27 @@ /* remove excess digits */ a->used -= b; } +#endif /* End: bn_mp_rshd.c */ /* Start: bn_mp_set.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_SET_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* set to a digit */ void mp_set (mp_int * a, mp_digit b) @@ -6246,25 +6629,27 @@ a->dp[0] = b & MP_MASK; a->used = (a->dp[0] != 0) ? 1 : 0; } +#endif /* End: bn_mp_set.c */ /* Start: bn_mp_set_int.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_SET_INT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* set a 32-bit const */ int mp_set_int (mp_int * a, unsigned long b) @@ -6292,25 +6677,27 @@ mp_clamp (a); return MP_OKAY; } +#endif /* End: bn_mp_set_int.c */ /* Start: bn_mp_shrink.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_SHRINK_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* shrink a bignum */ int mp_shrink (mp_int * a) @@ -6325,50 +6712,54 @@ } return MP_OKAY; } +#endif /* End: bn_mp_shrink.c */ /* Start: bn_mp_signed_bin_size.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_SIGNED_BIN_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* get the size for an signed equivalent */ int mp_signed_bin_size (mp_int * a) { return 1 + mp_unsigned_bin_size (a); } +#endif /* End: bn_mp_signed_bin_size.c */ /* Start: bn_mp_sqr.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* computes b = a*a */ int @@ -6376,44 +6767,57 @@ { int res; +#ifdef BN_MP_TOOM_SQR_C /* use Toom-Cook? */ if (a->used >= TOOM_SQR_CUTOFF) { res = mp_toom_sqr(a, b); /* Karatsuba? */ - } else if (a->used >= KARATSUBA_SQR_CUTOFF) { + } else +#endif +#ifdef BN_MP_KARATSUBA_SQR_C +if (a->used >= KARATSUBA_SQR_CUTOFF) { res = mp_karatsuba_sqr (a, b); - } else { + } else +#endif + { +#ifdef BN_FAST_S_MP_SQR_C /* can we use the fast comba multiplier? */ if ((a->used * 2 + 1) < MP_WARRAY && a->used < (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) { res = fast_s_mp_sqr (a, b); - } else { + } else +#endif +#ifdef BN_S_MP_SQR_C res = s_mp_sqr (a, b); - } +#else + res = MP_VAL; +#endif } b->sign = MP_ZPOS; return res; } +#endif /* End: bn_mp_sqr.c */ /* Start: bn_mp_sqrmod.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_SQRMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* c = a * a (mod b) */ int @@ -6434,25 +6838,27 @@ mp_clear (&t); return res; } +#endif /* End: bn_mp_sqrmod.c */ /* Start: bn_mp_sqrt.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_SQRT_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* this function is less generic than mp_n_root, simpler and faster */ int mp_sqrt(mp_int *arg, mp_int *ret) @@ -6513,25 +6919,27 @@ return res; } +#endif /* End: bn_mp_sqrt.c */ /* Start: bn_mp_sub.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_SUB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* high level subtraction (handles signs) */ int @@ -6570,25 +6978,27 @@ return res; } +#endif /* End: bn_mp_sub.c */ /* Start: bn_mp_sub_d.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_SUB_D_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* single digit subtraction */ int @@ -6657,25 +7067,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_sub_d.c */ /* Start: bn_mp_submod.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_SUBMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* d = a - b (mod c) */ int @@ -6697,25 +7109,27 @@ mp_clear (&t); return res; } +#endif /* End: bn_mp_submod.c */ /* Start: bn_mp_to_signed_bin.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_TO_SIGNED_BIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* store in signed [big endian] format */ int @@ -6729,25 +7143,27 @@ b[0] = (unsigned char) ((a->sign == MP_ZPOS) ? 0 : 1); return MP_OKAY; } +#endif /* End: bn_mp_to_signed_bin.c */ /* Start: bn_mp_to_unsigned_bin.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_TO_UNSIGNED_BIN_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* store in unsigned [big endian] format */ int @@ -6776,27 +7192,34 @@ mp_clear (&t); return MP_OKAY; } +#endif /* End: bn_mp_to_unsigned_bin.c */ /* Start: bn_mp_toom_mul.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> - -/* multiplication using the Toom-Cook 3-way algorithm */ +#include <tommath.h> +#ifdef BN_MP_TOOM_MUL_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ + +/* multiplication using the Toom-Cook 3-way algorithm + * + * Much more complicated than Karatsuba but has a lower asymptotic running time of + * O(N**1.464). This algorithm is only particularly useful on VERY large + * inputs (we're talking 1000s of digits here...). +*/ int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) { mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; @@ -7052,25 +7475,27 @@ return res; } +#endif /* End: bn_mp_toom_mul.c */ /* Start: bn_mp_toom_sqr.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_TOOM_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* squaring using Toom-Cook 3-way algorithm */ int @@ -7276,25 +7701,27 @@ return res; } +#endif /* End: bn_mp_toom_sqr.c */ /* Start: bn_mp_toradix.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_TORADIX_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* stores a bignum as a ASCII string in a given radix (2..64) */ int mp_toradix (mp_int * a, char *str, int radix) @@ -7349,25 +7776,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_toradix.c */ /* Start: bn_mp_toradix_n.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_TORADIX_N_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* stores a bignum as a ASCII string in a given radix (2..64) * @@ -7436,25 +7865,27 @@ return MP_OKAY; } +#endif /* End: bn_mp_toradix_n.c */ /* Start: bn_mp_unsigned_bin_size.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_UNSIGNED_BIN_SIZE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* get the size for an unsigned equivalent */ int @@ -7463,25 +7894,27 @@ int size = mp_count_bits (a); return (size / 8 + ((size & 7) != 0 ? 1 : 0)); } +#endif /* End: bn_mp_unsigned_bin_size.c */ /* Start: bn_mp_xor.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_XOR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* XOR two ints together */ int @@ -7505,32 +7938,34 @@ } for (ix = 0; ix < px; ix++) { - t.dp[ix] ^= x->dp[ix]; + } mp_clamp (&t); mp_exch (c, &t); mp_clear (&t); return MP_OKAY; } +#endif /* End: bn_mp_xor.c */ /* Start: bn_mp_zero.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_MP_ZERO_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* set to zero */ void @@ -7540,80 +7975,27 @@ a->used = 0; memset (a->dp, 0, sizeof (mp_digit) * a->alloc); } +#endif /* End: bn_mp_zero.c */ -/* Start: bn_prime_sizes_tab.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> - -/* this table gives the # of rabin miller trials for a prob of failure lower than 2^-96 */ -static const struct { - int k, t; -} sizes[] = { -{ 128, 28 }, -{ 256, 16 }, -{ 384, 10 }, -{ 512, 7 }, -{ 640, 6 }, -{ 768, 5 }, -{ 896, 4 }, -{ 1024, 4 }, -{ 1152, 3 }, -{ 1280, 3 }, -{ 1408, 3 }, -{ 1536, 3 }, -{ 1664, 3 }, -{ 1792, 2 } }; - -/* returns # of RM trials required for a given bit size */ -int mp_prime_rabin_miller_trials(int size) -{ - int x; - - for (x = 0; x < (int)(sizeof(sizes)/(sizeof(sizes[0]))); x++) { - if (sizes[x].k == size) { - return sizes[x].t; - } else if (sizes[x].k > size) { - return (x == 0) ? sizes[0].t : sizes[x - 1].t; - } - } - return 1; -} - - - -/* End: bn_prime_sizes_tab.c */ - /* Start: bn_prime_tab.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_PRIME_TAB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ const mp_digit __prime_tab[] = { 0x0002, 0x0003, 0x0005, 0x0007, 0x000B, 0x000D, 0x0011, 0x0013, 0x0017, 0x001D, 0x001F, 0x0025, 0x0029, 0x002B, 0x002F, 0x0035, @@ -7654,25 +8036,27 @@ 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 #endif }; +#endif /* End: bn_prime_tab.c */ /* Start: bn_reverse.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_REVERSE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* reverse an array, used for radix code */ void @@ -7691,25 +8075,27 @@ --iy; } } +#endif /* End: bn_reverse.c */ /* Start: bn_s_mp_add.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_S_MP_ADD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* low level addition, based on HAC pp.594, Algorithm 14.7 */ int @@ -7798,25 +8184,27 @@ mp_clamp (c); return MP_OKAY; } +#endif /* End: bn_s_mp_add.c */ /* Start: bn_s_mp_exptmod.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_S_MP_EXPTMOD_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ #ifdef MP_LOW_MEM #define TAB_SIZE 32 @@ -8036,25 +8424,27 @@ } return err; } +#endif /* End: bn_s_mp_exptmod.c */ /* Start: bn_s_mp_mul_digs.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_S_MP_MUL_DIGS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* multiplies |a| * |b| and only computes upto digs digits of result * HAC pp. 595, Algorithm 14.12 Modified so you can control how @@ -8125,25 +8515,27 @@ mp_clear (&t); return MP_OKAY; } +#endif /* End: bn_s_mp_mul_digs.c */ /* Start: bn_s_mp_mul_high_digs.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_S_MP_MUL_HIGH_DIGS_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* multiplies |a| * |b| and does not compute the lower digs digits * [meant to get the higher part of the product] @@ -8158,10 +8550,12 @@ mp_digit tmpx, *tmpt, *tmpy; /* can we use the fast multiplier? */ +#ifdef BN_FAST_S_MP_MUL_HIGH_DIGS_C if (((a->used + b->used + 1) < MP_WARRAY) && MIN (a->used, b->used) < (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) { return fast_s_mp_mul_high_digs (a, b, c, digs); } +#endif if ((res = mp_init_size (&t, a->used + b->used + 1)) != MP_OKAY) { return res; @@ -8202,25 +8596,27 @@ mp_clear (&t); return MP_OKAY; } +#endif /* End: bn_s_mp_mul_high_digs.c */ /* Start: bn_s_mp_sqr.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_S_MP_SQR_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* low level squaring, b = a*a, HAC pp.596-597, Algorithm 14.16 */ int @@ -8285,25 +8681,27 @@ mp_clear (&t); return MP_OKAY; } +#endif /* End: bn_s_mp_sqr.c */ /* Start: bn_s_mp_sub.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BN_S_MP_SUB_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* low level subtraction (assumes |a| > |b|), HAC pp.595 Algorithm 14.9 */ int @@ -8372,41 +8770,42 @@ return MP_OKAY; } +#endif /* End: bn_s_mp_sub.c */ /* Start: bncore.c */ -/* LibTomMath, multiple-precision integer library -- Tom St Denis - * - * LibTomMath is a library that provides multiple-precision - * integer arithmetic as well as number theoretic functionality. - * - * The library was designed directly after the MPI library by - * Michael Fromberger but has been written from scratch with - * additional optimizations in place. - * - * The library is free for all purposes without any express - * guarantee it works. - * - * Tom St Denis, [email protected], http://math.libtomcrypt.org - */ -#include <tommath.h> +#include <tommath.h> +#ifdef BNCORE_C +/* LibTomMath, multiple-precision integer library -- Tom St Denis + * + * LibTomMath is a library that provides multiple-precision + * integer arithmetic as well as number theoretic functionality. + * + * The library was designed directly after the MPI library by + * Michael Fromberger but has been written from scratch with + * additional optimizations in place. + * + * The library is free for all purposes without any express + * guarantee it works. + * + * Tom St Denis, [email protected], http://math.libtomcrypt.org + */ /* Known optimal configurations CPU /Compiler /MUL CUTOFF/SQR CUTOFF ------------------------------------------------------------- - Intel P4 /GCC v3.2 / 70/ 108 - AMD Athlon XP /GCC v3.2 / 109/ 127 - + Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) + */ -/* configured for a AMD XP Thoroughbred core with etc/tune.c */ -int KARATSUBA_MUL_CUTOFF = 109, /* Min. number of digits before Karatsuba multiplication is used. */ - KARATSUBA_SQR_CUTOFF = 127, /* Min. number of digits before Karatsuba squaring is used. */ +int KARATSUBA_MUL_CUTOFF = 88, /* Min. number of digits before Karatsuba multiplication is used. */ + KARATSUBA_SQR_CUTOFF = 128, /* Min. number of digits before Karatsuba squaring is used. */ TOOM_MUL_CUTOFF = 350, /* no optimal values of these are known yet so set em high */ TOOM_SQR_CUTOFF = 400; +#endif /* End: bncore.c */
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/pretty.build Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,66 @@ +#!/bin/perl -w +# +# Cute little builder for perl +# Total waste of development time... +# +# This will build all the object files and then the archive .a file +# requires GCC, GNU make and a sense of humour. +# +# Tom St Denis +use strict; + +my $count = 0; +my $starttime = time; +my $rate = 0; +print "Scanning for source files...\n"; +foreach my $filename (glob "*.c") { + ++$count; +} +print "Source files to build: $count\nBuilding...\n"; +my $i = 0; +my $lines = 0; +my $filesbuilt = 0; +foreach my $filename (glob "*.c") { + printf("Building %3.2f%%, ", (++$i/$count)*100.0); + if ($i % 4 == 0) { print "/, "; } + if ($i % 4 == 1) { print "-, "; } + if ($i % 4 == 2) { print "\\, "; } + if ($i % 4 == 3) { print "|, "; } + if ($rate > 0) { + my $tleft = ($count - $i) / $rate; + my $tsec = $tleft%60; + my $tmin = ($tleft/60)%60; + my $thour = ($tleft/3600)%60; + printf("%2d:%02d:%02d left, ", $thour, $tmin, $tsec); + } + my $cnt = ($i/$count)*30.0; + my $x = 0; + print "["; + for (; $x < $cnt; $x++) { print "#"; } + for (; $x < 30; $x++) { print " "; } + print "]\r"; + my $tmp = $filename; + $tmp =~ s/\.c/".o"/ge; + if (open(SRC, "<$tmp")) { + close SRC; + } else { + !system("make $tmp > /dev/null 2>/dev/null") or die "\nERROR: Failed to make $tmp!!!\n"; + open( SRC, "<$filename" ) or die "Couldn't open $filename for reading: $!"; + ++$lines while (<SRC>); + close SRC or die "Error closing $filename after reading: $!"; + ++$filesbuilt; + } + + # update timer + if (time != $starttime) { + my $delay = time - $starttime; + $rate = $i/$delay; + } +} + +# finish building the library +printf("\nFinished building source (%d seconds, %3.2f files per second).\n", time - $starttime, $rate); +print "Compiled approximately $filesbuilt files and $lines lines of code.\n"; +print "Doing final make (building archive...)\n"; +!system("make > /dev/null 2>/dev/null") or die "\nERROR: Failed to perform last make command!!!\n"; +print "done.\n"; \ No newline at end of file
--- a/tommath.h Tue Jun 15 14:42:57 2004 +0000 +++ b/tommath.h Sun Dec 19 11:33:56 2004 +0000 @@ -21,6 +21,8 @@ #include <ctype.h> #include <limits.h> +#include <tommath_class.h> + #undef MIN #define MIN(x,y) ((x)<(y)?(x):(y)) #undef MAX @@ -39,6 +41,14 @@ #endif + +/* detect 64-bit mode if possible */ +#if defined(__x86_64__) + #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT)) + #define MP_64BIT + #endif +#endif + /* some default configurations. * * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits @@ -60,7 +70,7 @@ typedef signed long long long64; #endif - typedef ulong64 mp_digit; + typedef unsigned long mp_digit; typedef unsigned long mp_word __attribute__ ((mode(TI))); #define DIGIT_BIT 60 @@ -153,7 +163,7 @@ /* default precision */ #ifndef MP_PREC - #ifdef MP_LOW_MEM + #ifndef MP_LOW_MEM #define MP_PREC 64 /* default digits of precision */ #else #define MP_PREC 8 /* default digits of precision */ @@ -541,6 +551,7 @@ int mp_karatsuba_sqr(mp_int *a, mp_int *b); int mp_toom_sqr(mp_int *a, mp_int *b); int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c); +int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c); int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode); int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y);
--- a/tommath.src Tue Jun 15 14:42:57 2004 +0000 +++ b/tommath.src Sun Dec 19 11:33:56 2004 +0000 @@ -258,7 +258,7 @@ a mantissa of much larger precision than hardware alone can efficiently support. This approach could be useful where scientific applications must minimize the total output error over long calculations. -Another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$). +Yet another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$). In fact the library discussed within this text has already been used to form a polynomial basis library\footnote{See \url{http://poly.libtomcrypt.org} for more details.}. \subsection{Benefits of Multiple Precision Arithmetic} @@ -316,7 +316,7 @@ \section{Discussion and Notation} \subsection{Notation} -A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1} ... x_1 x_0)_{ \beta }$ and represent +A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1}, \ldots, x_1, x_0)_{ \beta }$ and represent the integer $x \equiv \sum_{i=0}^{n-1} x_i\beta^i$. The elements of the array $x$ are said to be the radix $\beta$ digits of the integer. For example, $x = (1,2,3)_{10}$ would represent the integer $1\cdot 10^2 + 2\cdot10^1 + 3\cdot10^0 = 123$. @@ -339,12 +339,11 @@ precision algorithm to solve the same problem. \subsection{Precision Notation} -For the purposes of this text a single precision variable must be able to represent integers in the range -$0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range -$0 \le x < q \beta^2$. The variable $\beta$ represents the radix of a single digit of a multiple precision integer and -must be of the form $q^p$ for $q, p \in \Z^+$. The extra radix-$q$ factor allows additions and subtractions to proceed -without truncation of the carry. Since all modern computers are binary, it is assumed that $q$ is two, for all intents -and purposes. +The variable $\beta$ represents the radix of a single digit of a multiple precision integer and +must be of the form $q^p$ for $q, p \in \Z^+$. A single precision variable must be able to represent integers in +the range $0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range +$0 \le x < q \beta^2$. The extra radix-$q$ factor allows additions and subtractions to proceed without truncation of the +carry. Since all modern computers are binary, it is assumed that $q$ is two. \index{mp\_digit} \index{mp\_word} Within the source code that will be presented for each algorithm, the data type \textbf{mp\_digit} will represent @@ -376,7 +375,7 @@ $5/2 = 2$ which will often be written as $\lfloor 5/2 \rfloor = 2$ for clarity. When an expression is written as a fraction a real value division is implied, for example ${5 \over 2} = 2.5$. -The norm of a multiple precision integer, for example, $\vert \vert x \vert \vert$ will be used to represent the number of digits in the representation +The norm of a multiple precision integer, for example $\vert \vert x \vert \vert$, will be used to represent the number of digits in the representation of the integer. For example, $\vert \vert 123 \vert \vert = 3$ and $\vert \vert 79452 \vert \vert = 5$. \subsection{Work Effort} @@ -569,7 +568,7 @@ highly modular. Being highly modular is a desirable property of any project as it often means the resulting product has a small footprint and updates are easy to perform. -Usually when I start a project I will begin with the header file. I define the data types I think I will need and +Usually when I start a project I will begin with the header files. I define the data types I think I will need and prototype the initial functions that are not dependent on other functions (within the library). After I implement these base functions I prototype more dependent functions and implement them. The process repeats until I implement all of the functions I require. For example, in the case of LibTomMath I implemented functions such as @@ -619,14 +618,26 @@ used within LibTomMath. \index{mp\_int} -\begin{verbatim} -typedef struct { - int used, alloc, sign; - mp_digit *dp; -} mp_int; -\end{verbatim} - -The mp\_int structure can be broken down as follows. +\begin{figure}[here] +\begin{center} +\begin{small} +%\begin{verbatim} +\begin{tabular}{|l|} +\hline +typedef struct \{ \\ +\hspace{3mm}int used, alloc, sign;\\ +\hspace{3mm}mp\_digit *dp;\\ +\} \textbf{mp\_int}; \\ +\hline +\end{tabular} +%\end{verbatim} +\end{small} +\caption{The mp\_int Structure} +\label{fig:mpint} +\end{center} +\end{figure} + +The mp\_int structure (fig. \ref{fig:mpint}) can be broken down as follows. \begin{enumerate} \item The \textbf{used} parameter denotes how many digits of the array \textbf{dp} contain the digits used to represent @@ -701,9 +712,10 @@ In the case of LibTomMath the only errors that are checked for are related to inappropriate inputs (division by zero for instance) and memory allocation errors. It will not check that the mp\_int passed to any function is valid nor will it check pointers for validity. Any function that can cause a runtime error will return an error code as an -\textbf{int} data type with one of the following values. +\textbf{int} data type with one of the following values (fig \ref{fig:errcodes}). \index{MP\_OKAY} \index{MP\_VAL} \index{MP\_MEM} +\begin{figure}[here] \begin{center} \begin{tabular}{|l|l|} \hline \textbf{Value} & \textbf{Meaning} \\ @@ -713,6 +725,9 @@ \hline \end{tabular} \end{center} +\caption{LibTomMath Error Codes} +\label{fig:errcodes} +\end{figure} When an error is detected within a function it should free any memory it allocated, often during the initialization of temporary mp\_ints, and return as soon as possible. The goal is to leave the system in the same state it was when the @@ -748,6 +763,7 @@ An mp\_int is said to be initialized if it is set to a valid, preferably default, state such that all of the members of the structure are set to valid values. The mp\_init algorithm will perform such an action. +\index{mp\_init} \begin{figure}[here] \begin{center} \begin{tabular}{l} @@ -770,17 +786,23 @@ \end{figure} \textbf{Algorithm mp\_init.} -The \textbf{MP\_PREC} name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.} -used to dictate the minimum precision of allocated mp\_int integers. Ideally, it is at least equal to $32$ since for most -purposes that will be more than enough. - -Memory for the default number of digits is allocated first. If the allocation fails the algorithm returns immediately -with the \textbf{MP\_MEM} error code. If the allocation succeeds the remaining members of the mp\_int structure -must be initialized to reflect the default initial state. - -The allocated digits are all set to zero (step three) to ensure they are in a known state. The \textbf{sign}, \textbf{used} -and \textbf{alloc} are subsequently initialized to represent the zero integer. By step seven the algorithm returns a success -code and the mp\_int $a$ has been successfully initialized to a valid state representing the integer zero. +The purpose of this function is to initialize an mp\_int structure so that the rest of the library can properly +manipulte it. It is assumed that the input may not have had any of its members previously initialized which is certainly +a valid assumption if the input resides on the stack. + +Before any of the members such as \textbf{sign}, \textbf{used} or \textbf{alloc} are initialized the memory for +the digits is allocated. If this fails the function returns before setting any of the other members. The \textbf{MP\_PREC} +name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.} +used to dictate the minimum precision of newly initialized mp\_int integers. Ideally, it is at least equal to the smallest +precision number you'll be working with. + +Allocating a block of digits at first instead of a single digit has the benefit of lowering the number of usually slow +heap operations later functions will have to perform in the future. If \textbf{MP\_PREC} is set correctly the slack +memory and the number of heap operations will be trivial. + +Once the allocation has been made the digits have to be set to zero as well as the \textbf{used}, \textbf{sign} and +\textbf{alloc} members initialized. This ensures that the mp\_int will always represent the default state of zero regardless +of the original condition of the input. \textbf{Remark.} This function introduces the idiosyncrasy that all iterative loops, commonly initiated with the ``for'' keyword, iterate incrementally @@ -796,19 +818,21 @@ is assumed that the caller has already allocated memory for the mp\_int structure, typically on the application stack. The call to mp\_init() is used only to initialize the members of the structure to a known default state. -Before any of the other members of the structure are initialized memory from the application heap is allocated with -the calloc() function (line @22,calloc@). The size of the allocated memory is large enough to hold \textbf{MP\_PREC} -mp\_digit variables. The calloc() function is used instead\footnote{calloc() will allocate memory in the same -manner as malloc() except that it also sets the contents to zero upon successfully allocating the memory.} of malloc() -since digits have to be set to zero for the function to finish correctly. The \textbf{OPT\_CAST} token is a macro -definition which will turn into a cast from void * to mp\_digit * for C++ compilers. It is not required for C compilers. - -After the memory has been successfully allocated the remainder of the members are initialized +Here we see (line @23,XMALLOC@) the memory allocation is performed first. This allows us to exit cleanly and quickly +if there is an error. If the allocation fails the routine will return \textbf{MP\_MEM} to the caller to indicate there +was a memory error. The function XMALLOC is what actually allocates the memory. Technically XMALLOC is not a function +but a macro defined in ``tommath.h``. By default, XMALLOC will evaluate to malloc() which is the C library's built--in +memory allocation routine. + +In order to assure the mp\_int is in a known state the digits must be set to zero. On most platforms this could have been +accomplished by using calloc() instead of malloc(). However, to correctly initialize a integer type to a given value in a +portable fashion you have to actually assign the value. The for loop (line @28,for@) performs this required +operation. + +After the memory has been successfully initialized the remainder of the members are initialized (lines @29,used@ through @31,sign@) to their respective default states. At this point the algorithm has succeeded and -a success code is returned to the calling function. - -If this function returns \textbf{MP\_OKAY} it is safe to assume the mp\_int structure has been properly initialized and -is safe to use with other functions within the library. +a success code is returned to the calling function. If this function returns \textbf{MP\_OKAY} it is safe to assume the +mp\_int structure has been properly initialized and is safe to use with other functions within the library. \subsection{Clearing an mp\_int} When an mp\_int is no longer required by the application, the memory that has been allocated for its digits must be @@ -819,7 +843,7 @@ \begin{tabular}{l} \hline Algorithm \textbf{mp\_clear}. \\ \textbf{Input}. An mp\_int $a$ \\ -\textbf{Output}. The memory for $a$ is freed for reuse. \\ +\textbf{Output}. The memory for $a$ shall be deallocated. \\ \hline \\ 1. If $a$ has been previously freed then return(\textit{MP\_OKAY}). \\ 2. for $n$ from 0 to $a.used - 1$ do \\ @@ -836,32 +860,31 @@ \end{figure} \textbf{Algorithm mp\_clear.} -This algorithm releases the memory allocated for an mp\_int back into the memory pool for reuse. It is designed -such that a given mp\_int structure can be cleared multiple times between initializations without attempting to -free the memory twice\footnote{In ISO C for example, calling free() twice on the same memory block causes undefinied -behaviour.}. - -The first step determines if the mp\_int structure has been marked as free already. If it has, the algorithm returns -success immediately as no further actions are required. Otherwise, the algorithm will proceed to put the structure -in a known empty and otherwise invalid state. First the digits of the mp\_int are set to zero. The memory that has been allocated for the -digits is then freed. The \textbf{used} and \textbf{alloc} counts are both set to zero and the \textbf{sign} set to -\textbf{MP\_ZPOS}. This known fixed state for cleared mp\_int structures will make debuging easier for the end -developer. That is, if they spot (via their debugger) an mp\_int they are using that is in this state it will be -obvious that they erroneously and prematurely cleared the mp\_int structure. - -Note that once an mp\_int has been cleared the mp\_int structure is no longer in a valid state for any other algorithm +This algorithm accomplishes two goals. First, it clears the digits and the other mp\_int members. This ensures that +if a developer accidentally re-uses a cleared structure it is less likely to cause problems. The second goal +is to free the allocated memory. + +The logic behind the algorithm is extended by marking cleared mp\_int structures so that subsequent calls to this +algorithm will not try to free the memory multiple times. Cleared mp\_ints are detectable by having a pre-defined invalid +digit pointer \textbf{dp} setting. + +Once an mp\_int has been cleared the mp\_int structure is no longer in a valid state for any other algorithm with the exception of algorithms mp\_init, mp\_init\_copy, mp\_init\_size and mp\_clear. EXAM,bn_mp_clear.c -The ``if'' statement (line @21,a->dp != NULL@) prevents the heap from being corrupted if a user double-frees an -mp\_int. This is because once the memory is freed the pointer is set to \textbf{NULL} (line @30,NULL@). - -Without the check, code that accidentally calls mp\_clear twice for a given mp\_int structure would try to free the memory -allocated for the digits twice. This may cause some C libraries to signal a fault. By setting the pointer to -\textbf{NULL} it helps debug code that may inadvertently free the mp\_int before it is truly not needed, because attempts -to reference digits should fail immediately. The allocated digits are set to zero before being freed (line @24,memset@). -This is ideal for cryptographic situations where the integer that the mp\_int represents might need to be kept a secret. +The algorithm only operates on the mp\_int if it hasn't been previously cleared. The if statement (line @23,a->dp != NULL@) +checks to see if the \textbf{dp} member is not \textbf{NULL}. If the mp\_int is a valid mp\_int then \textbf{dp} cannot be +\textbf{NULL} in which case the if statement will evaluate to true. + +The digits of the mp\_int are cleared by the for loop (line @25,for@) which assigns a zero to every digit. Similar to mp\_init() +the digits are assigned zero instead of using block memory operations (such as memset()) since this is more portable. + +The digits are deallocated off the heap via the XFREE macro. Similar to XMALLOC the XFREE macro actually evaluates to +a standard C library function. In this case the free() function. Since free() only deallocates the memory the pointer +still has to be reset to \textbf{NULL} manually (line @33,NULL@). + +Now that the digits have been cleared and deallocated the other members are set to their final values (lines @34,= 0@ and @35,ZPOS@). \section{Maintenance Algorithms} @@ -889,7 +912,7 @@ 1. if $a.alloc \ge b$ then return(\textit{MP\_OKAY}) \\ 2. $u \leftarrow b\mbox{ (mod }MP\_PREC\mbox{)}$ \\ 3. $v \leftarrow b + 2 \cdot MP\_PREC - u$ \\ -4. Re-Allocate the array of digits $a$ to size $v$ \\ +4. Re-allocate the array of digits $a$ to size $v$ \\ 5. If the allocation failed then return(\textit{MP\_MEM}). \\ 6. for n from a.alloc to $v - 1$ do \\ \hspace{+3mm}6.1 $a_n \leftarrow 0$ \\ @@ -914,15 +937,19 @@ EXAM,bn_mp_grow.c -The first step is to see if we actually need to perform a re-allocation at all (line @24,a->alloc < size@). If a reallocation -must occur the digit count is padded upwards to help prevent many trivial reallocations (line @28,size@). Next the reallocation is performed -and the return of realloc() is stored in a temporary pointer named $tmp$ (line @36,realloc@). The return is stored in a temporary -instead of $a.dp$ to prevent the code from losing the original pointer in case the reallocation fails. Had the return been stored -in $a.dp$ instead there would be no way to reclaim the heap originally used. - -If the reallocation fails the function will return \textbf{MP\_MEM} (line @39,return@), otherwise, the value of $tmp$ is assigned -to the pointer $a.dp$ and the function continues. A simple for loop from line @48,a->alloc@ to line @50,}@ will zero all digits -that were above the old \textbf{alloc} limit to make sure the integer is in a known state. +A quick optimization is to first determine if a memory re-allocation is required at all. The if statement (line @23,if@) checks +if the \textbf{alloc} member of the mp\_int is smaller than the requested digit count. If the count is not larger than \textbf{alloc} +the function skips the re-allocation part thus saving time. + +When a re-allocation is performed it is turned into an optimal request to save time in the future. The requested digit count is +padded upwards to 2nd multiple of \textbf{MP\_PREC} larger than \textbf{alloc} (line @25, size@). The XREALLOC function is used +to re-allocate the memory. As per the other functions XREALLOC is actually a macro which evaluates to realloc by default. The realloc +function leaves the base of the allocation intact which means the first \textbf{alloc} digits of the mp\_int are the same as before +the re-allocation. All that is left is to clear the newly allocated digits and return. + +Note that the re-allocation result is actually stored in a temporary pointer $tmp$. This is to allow this function to return +an error with a valid pointer. Earlier releases of the library stored the result of XREALLOC into the mp\_int $a$. That would +result in a memory leak if XREALLOC ever failed. \subsection{Initializing Variable Precision mp\_ints} Occasionally the number of digits required will be known in advance of an initialization, based on, for example, the size @@ -970,7 +997,7 @@ mp\_int is placed in a default state representing the integer zero. Otherwise, the error code \textbf{MP\_MEM} will be returned (line @27,return@). -The digits are allocated and set to zero at the same time with the calloc() function (line @25,calloc@). The +The digits are allocated and set to zero at the same time with the calloc() function (line @25,XCALLOC@). The \textbf{used} count is set to zero, the \textbf{alloc} count set to the padded digit count and the \textbf{sign} flag set to \textbf{MP\_ZPOS} to achieve a default valid mp\_int state (lines @29,used@, @30,alloc@ and @31,sign@). If the function returns succesfully then it is correct to assume that the mp\_int structure is in a valid state for the remainder of the
--- a/tommath.tex Tue Jun 15 14:42:57 2004 +0000 +++ b/tommath.tex Sun Dec 19 11:33:56 2004 +0000 @@ -258,7 +258,7 @@ a mantissa of much larger precision than hardware alone can efficiently support. This approach could be useful where scientific applications must minimize the total output error over long calculations. -Another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$). +Yet another use for large integers is within arithmetic on polynomials of large characteristic (i.e. $GF(p)[x]$ for large $p$). In fact the library discussed within this text has already been used to form a polynomial basis library\footnote{See \url{http://poly.libtomcrypt.org} for more details.}. \subsection{Benefits of Multiple Precision Arithmetic} @@ -316,7 +316,7 @@ \section{Discussion and Notation} \subsection{Notation} -A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1} ... x_1 x_0)_{ \beta }$ and represent +A multiple precision integer of $n$-digits shall be denoted as $x = (x_{n-1}, \ldots, x_1, x_0)_{ \beta }$ and represent the integer $x \equiv \sum_{i=0}^{n-1} x_i\beta^i$. The elements of the array $x$ are said to be the radix $\beta$ digits of the integer. For example, $x = (1,2,3)_{10}$ would represent the integer $1\cdot 10^2 + 2\cdot10^1 + 3\cdot10^0 = 123$. @@ -339,12 +339,11 @@ precision algorithm to solve the same problem. \subsection{Precision Notation} -For the purposes of this text a single precision variable must be able to represent integers in the range -$0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range -$0 \le x < q \beta^2$. The variable $\beta$ represents the radix of a single digit of a multiple precision integer and -must be of the form $q^p$ for $q, p \in \Z^+$. The extra radix-$q$ factor allows additions and subtractions to proceed -without truncation of the carry. Since all modern computers are binary, it is assumed that $q$ is two, for all intents -and purposes. +The variable $\beta$ represents the radix of a single digit of a multiple precision integer and +must be of the form $q^p$ for $q, p \in \Z^+$. A single precision variable must be able to represent integers in +the range $0 \le x < q \beta$ while a double precision variable must be able to represent integers in the range +$0 \le x < q \beta^2$. The extra radix-$q$ factor allows additions and subtractions to proceed without truncation of the +carry. Since all modern computers are binary, it is assumed that $q$ is two. \index{mp\_digit} \index{mp\_word} Within the source code that will be presented for each algorithm, the data type \textbf{mp\_digit} will represent @@ -376,7 +375,7 @@ $5/2 = 2$ which will often be written as $\lfloor 5/2 \rfloor = 2$ for clarity. When an expression is written as a fraction a real value division is implied, for example ${5 \over 2} = 2.5$. -The norm of a multiple precision integer, for example, $\vert \vert x \vert \vert$ will be used to represent the number of digits in the representation +The norm of a multiple precision integer, for example $\vert \vert x \vert \vert$, will be used to represent the number of digits in the representation of the integer. For example, $\vert \vert 123 \vert \vert = 3$ and $\vert \vert 79452 \vert \vert = 5$. \subsection{Work Effort} @@ -569,7 +568,7 @@ highly modular. Being highly modular is a desirable property of any project as it often means the resulting product has a small footprint and updates are easy to perform. -Usually when I start a project I will begin with the header file. I define the data types I think I will need and +Usually when I start a project I will begin with the header files. I define the data types I think I will need and prototype the initial functions that are not dependent on other functions (within the library). After I implement these base functions I prototype more dependent functions and implement them. The process repeats until I implement all of the functions I require. For example, in the case of LibTomMath I implemented functions such as @@ -625,14 +624,26 @@ used within LibTomMath. \index{mp\_int} -\begin{verbatim} -typedef struct { - int used, alloc, sign; - mp_digit *dp; -} mp_int; -\end{verbatim} - -The mp\_int structure can be broken down as follows. +\begin{figure}[here] +\begin{center} +\begin{small} +%\begin{verbatim} +\begin{tabular}{|l|} +\hline +typedef struct \{ \\ +\hspace{3mm}int used, alloc, sign;\\ +\hspace{3mm}mp\_digit *dp;\\ +\} \textbf{mp\_int}; \\ +\hline +\end{tabular} +%\end{verbatim} +\end{small} +\caption{The mp\_int Structure} +\label{fig:mpint} +\end{center} +\end{figure} + +The mp\_int structure (fig. \ref{fig:mpint}) can be broken down as follows. \begin{enumerate} \item The \textbf{used} parameter denotes how many digits of the array \textbf{dp} contain the digits used to represent @@ -707,9 +718,10 @@ In the case of LibTomMath the only errors that are checked for are related to inappropriate inputs (division by zero for instance) and memory allocation errors. It will not check that the mp\_int passed to any function is valid nor will it check pointers for validity. Any function that can cause a runtime error will return an error code as an -\textbf{int} data type with one of the following values. +\textbf{int} data type with one of the following values (fig \ref{fig:errcodes}). \index{MP\_OKAY} \index{MP\_VAL} \index{MP\_MEM} +\begin{figure}[here] \begin{center} \begin{tabular}{|l|l|} \hline \textbf{Value} & \textbf{Meaning} \\ @@ -719,6 +731,9 @@ \hline \end{tabular} \end{center} +\caption{LibTomMath Error Codes} +\label{fig:errcodes} +\end{figure} When an error is detected within a function it should free any memory it allocated, often during the initialization of temporary mp\_ints, and return as soon as possible. The goal is to leave the system in the same state it was when the @@ -754,6 +769,7 @@ An mp\_int is said to be initialized if it is set to a valid, preferably default, state such that all of the members of the structure are set to valid values. The mp\_init algorithm will perform such an action. +\index{mp\_init} \begin{figure}[here] \begin{center} \begin{tabular}{l} @@ -776,17 +792,23 @@ \end{figure} \textbf{Algorithm mp\_init.} -The \textbf{MP\_PREC} name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.} -used to dictate the minimum precision of allocated mp\_int integers. Ideally, it is at least equal to $32$ since for most -purposes that will be more than enough. - -Memory for the default number of digits is allocated first. If the allocation fails the algorithm returns immediately -with the \textbf{MP\_MEM} error code. If the allocation succeeds the remaining members of the mp\_int structure -must be initialized to reflect the default initial state. - -The allocated digits are all set to zero (step three) to ensure they are in a known state. The \textbf{sign}, \textbf{used} -and \textbf{alloc} are subsequently initialized to represent the zero integer. By step seven the algorithm returns a success -code and the mp\_int $a$ has been successfully initialized to a valid state representing the integer zero. +The purpose of this function is to initialize an mp\_int structure so that the rest of the library can properly +manipulte it. It is assumed that the input may not have had any of its members previously initialized which is certainly +a valid assumption if the input resides on the stack. + +Before any of the members such as \textbf{sign}, \textbf{used} or \textbf{alloc} are initialized the memory for +the digits is allocated. If this fails the function returns before setting any of the other members. The \textbf{MP\_PREC} +name represents a constant\footnote{Defined in the ``tommath.h'' header file within LibTomMath.} +used to dictate the minimum precision of newly initialized mp\_int integers. Ideally, it is at least equal to the smallest +precision number you'll be working with. + +Allocating a block of digits at first instead of a single digit has the benefit of lowering the number of usually slow +heap operations later functions will have to perform in the future. If \textbf{MP\_PREC} is set correctly the slack +memory and the number of heap operations will be trivial. + +Once the allocation has been made the digits have to be set to zero as well as the \textbf{used}, \textbf{sign} and +\textbf{alloc} members initialized. This ensures that the mp\_int will always represent the default state of zero regardless +of the original condition of the input. \textbf{Remark.} This function introduces the idiosyncrasy that all iterative loops, commonly initiated with the ``for'' keyword, iterate incrementally @@ -801,23 +823,31 @@ \vspace{-3mm} \begin{alltt} 016 -017 /* init a new bigint */ +017 /* init a new mp_int */ 018 int mp_init (mp_int * a) 019 \{ -020 /* allocate memory required and clear it */ -021 a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), MP_PREC); -022 if (a->dp == NULL) \{ -023 return MP_MEM; -024 \} -025 -026 /* set the used to zero, allocated digits to the default precision -027 * and sign to positive */ -028 a->used = 0; -029 a->alloc = MP_PREC; -030 a->sign = MP_ZPOS; -031 -032 return MP_OKAY; -033 \} +020 int i; +021 +022 /* allocate memory required and clear it */ +023 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * MP_PREC); +024 if (a->dp == NULL) \{ +025 return MP_MEM; +026 \} +027 +028 /* set the digits to zero */ +029 for (i = 0; i < MP_PREC; i++) \{ +030 a->dp[i] = 0; +031 \} +032 +033 /* set the used to zero, allocated digits to the default precision +034 * and sign to positive */ +035 a->used = 0; +036 a->alloc = MP_PREC; +037 a->sign = MP_ZPOS; +038 +039 return MP_OKAY; +040 \} +041 #endif \end{alltt} \end{small} @@ -825,19 +855,21 @@ is assumed that the caller has already allocated memory for the mp\_int structure, typically on the application stack. The call to mp\_init() is used only to initialize the members of the structure to a known default state. -Before any of the other members of the structure are initialized memory from the application heap is allocated with -the calloc() function (line @22,calloc@). The size of the allocated memory is large enough to hold \textbf{MP\_PREC} -mp\_digit variables. The calloc() function is used instead\footnote{calloc() will allocate memory in the same -manner as malloc() except that it also sets the contents to zero upon successfully allocating the memory.} of malloc() -since digits have to be set to zero for the function to finish correctly. The \textbf{OPT\_CAST} token is a macro -definition which will turn into a cast from void * to mp\_digit * for C++ compilers. It is not required for C compilers. - -After the memory has been successfully allocated the remainder of the members are initialized -(lines 28 through 30) to their respective default states. At this point the algorithm has succeeded and -a success code is returned to the calling function. - -If this function returns \textbf{MP\_OKAY} it is safe to assume the mp\_int structure has been properly initialized and -is safe to use with other functions within the library. +Here we see (line 23) the memory allocation is performed first. This allows us to exit cleanly and quickly +if there is an error. If the allocation fails the routine will return \textbf{MP\_MEM} to the caller to indicate there +was a memory error. The function XMALLOC is what actually allocates the memory. Technically XMALLOC is not a function +but a macro defined in ``tommath.h``. By default, XMALLOC will evaluate to malloc() which is the C library's built--in +memory allocation routine. + +In order to assure the mp\_int is in a known state the digits must be set to zero. On most platforms this could have been +accomplished by using calloc() instead of malloc(). However, to correctly initialize a integer type to a given value in a +portable fashion you have to actually assign the value. The for loop (line 29) performs this required +operation. + +After the memory has been successfully initialized the remainder of the members are initialized +(lines 33 through 34) to their respective default states. At this point the algorithm has succeeded and +a success code is returned to the calling function. If this function returns \textbf{MP\_OKAY} it is safe to assume the +mp\_int structure has been properly initialized and is safe to use with other functions within the library. \subsection{Clearing an mp\_int} When an mp\_int is no longer required by the application, the memory that has been allocated for its digits must be @@ -848,7 +880,7 @@ \begin{tabular}{l} \hline Algorithm \textbf{mp\_clear}. \\ \textbf{Input}. An mp\_int $a$ \\ -\textbf{Output}. The memory for $a$ is freed for reuse. \\ +\textbf{Output}. The memory for $a$ shall be deallocated. \\ \hline \\ 1. If $a$ has been previously freed then return(\textit{MP\_OKAY}). \\ 2. for $n$ from 0 to $a.used - 1$ do \\ @@ -865,20 +897,15 @@ \end{figure} \textbf{Algorithm mp\_clear.} -This algorithm releases the memory allocated for an mp\_int back into the memory pool for reuse. It is designed -such that a given mp\_int structure can be cleared multiple times between initializations without attempting to -free the memory twice\footnote{In ISO C for example, calling free() twice on the same memory block causes undefinied -behaviour.}. - -The first step determines if the mp\_int structure has been marked as free already. If it has, the algorithm returns -success immediately as no further actions are required. Otherwise, the algorithm will proceed to put the structure -in a known empty and otherwise invalid state. First the digits of the mp\_int are set to zero. The memory that has been allocated for the -digits is then freed. The \textbf{used} and \textbf{alloc} counts are both set to zero and the \textbf{sign} set to -\textbf{MP\_ZPOS}. This known fixed state for cleared mp\_int structures will make debuging easier for the end -developer. That is, if they spot (via their debugger) an mp\_int they are using that is in this state it will be -obvious that they erroneously and prematurely cleared the mp\_int structure. - -Note that once an mp\_int has been cleared the mp\_int structure is no longer in a valid state for any other algorithm +This algorithm accomplishes two goals. First, it clears the digits and the other mp\_int members. This ensures that +if a developer accidentally re-uses a cleared structure it is less likely to cause problems. The second goal +is to free the allocated memory. + +The logic behind the algorithm is extended by marking cleared mp\_int structures so that subsequent calls to this +algorithm will not try to free the memory multiple times. Cleared mp\_ints are detectable by having a pre-defined invalid +digit pointer \textbf{dp} setting. + +Once an mp\_int has been cleared the mp\_int structure is no longer in a valid state for any other algorithm with the exception of algorithms mp\_init, mp\_init\_copy, mp\_init\_size and mp\_clear. \vspace{+3mm}\begin{small} @@ -890,31 +917,40 @@ 018 void 019 mp_clear (mp_int * a) 020 \{ -021 /* only do anything if a hasn't been freed previously */ -022 if (a->dp != NULL) \{ -023 /* first zero the digits */ -024 memset (a->dp, 0, sizeof (mp_digit) * a->used); -025 -026 /* free ram */ -027 XFREE(a->dp); -028 -029 /* reset members to make debugging easier */ -030 a->dp = NULL; -031 a->alloc = a->used = 0; -032 a->sign = MP_ZPOS; -033 \} -034 \} +021 int i; +022 +023 /* only do anything if a hasn't been freed previously */ +024 if (a->dp != NULL) \{ +025 /* first zero the digits */ +026 for (i = 0; i < a->used; i++) \{ +027 a->dp[i] = 0; +028 \} +029 +030 /* free ram */ +031 XFREE(a->dp); +032 +033 /* reset members to make debugging easier */ +034 a->dp = NULL; +035 a->alloc = a->used = 0; +036 a->sign = MP_ZPOS; +037 \} +038 \} +039 #endif \end{alltt} \end{small} -The ``if'' statement (line 22) prevents the heap from being corrupted if a user double-frees an -mp\_int. This is because once the memory is freed the pointer is set to \textbf{NULL} (line 30). - -Without the check, code that accidentally calls mp\_clear twice for a given mp\_int structure would try to free the memory -allocated for the digits twice. This may cause some C libraries to signal a fault. By setting the pointer to -\textbf{NULL} it helps debug code that may inadvertently free the mp\_int before it is truly not needed, because attempts -to reference digits should fail immediately. The allocated digits are set to zero before being freed (line 24). -This is ideal for cryptographic situations where the integer that the mp\_int represents might need to be kept a secret. +The algorithm only operates on the mp\_int if it hasn't been previously cleared. The if statement (line 24) +checks to see if the \textbf{dp} member is not \textbf{NULL}. If the mp\_int is a valid mp\_int then \textbf{dp} cannot be +\textbf{NULL} in which case the if statement will evaluate to true. + +The digits of the mp\_int are cleared by the for loop (line 26) which assigns a zero to every digit. Similar to mp\_init() +the digits are assigned zero instead of using block memory operations (such as memset()) since this is more portable. + +The digits are deallocated off the heap via the XFREE macro. Similar to XMALLOC the XFREE macro actually evaluates to +a standard C library function. In this case the free() function. Since free() only deallocates the memory the pointer +still has to be reset to \textbf{NULL} manually (line 34). + +Now that the digits have been cleared and deallocated the other members are set to their final values (lines 35 and 36). \section{Maintenance Algorithms} @@ -942,7 +978,7 @@ 1. if $a.alloc \ge b$ then return(\textit{MP\_OKAY}) \\ 2. $u \leftarrow b\mbox{ (mod }MP\_PREC\mbox{)}$ \\ 3. $v \leftarrow b + 2 \cdot MP\_PREC - u$ \\ -4. Re-Allocate the array of digits $a$ to size $v$ \\ +4. Re-allocate the array of digits $a$ to size $v$ \\ 5. If the allocation failed then return(\textit{MP\_MEM}). \\ 6. for n from a.alloc to $v - 1$ do \\ \hspace{+3mm}6.1 $a_n \leftarrow 0$ \\ @@ -1005,18 +1041,23 @@ 049 \} 050 return MP_OKAY; 051 \} +052 #endif \end{alltt} \end{small} -The first step is to see if we actually need to perform a re-allocation at all (line 24). If a reallocation -must occur the digit count is padded upwards to help prevent many trivial reallocations (line 26). Next the reallocation is performed -and the return of realloc() is stored in a temporary pointer named $tmp$ (line 36). The return is stored in a temporary -instead of $a.dp$ to prevent the code from losing the original pointer in case the reallocation fails. Had the return been stored -in $a.dp$ instead there would be no way to reclaim the heap originally used. - -If the reallocation fails the function will return \textbf{MP\_MEM} (line 37), otherwise, the value of $tmp$ is assigned -to the pointer $a.dp$ and the function continues. A simple for loop from line 46 to line 51 will zero all digits -that were above the old \textbf{alloc} limit to make sure the integer is in a known state. +A quick optimization is to first determine if a memory re-allocation is required at all. The if statement (line 23) checks +if the \textbf{alloc} member of the mp\_int is smaller than the requested digit count. If the count is not larger than \textbf{alloc} +the function skips the re-allocation part thus saving time. + +When a re-allocation is performed it is turned into an optimal request to save time in the future. The requested digit count is +padded upwards to 2nd multiple of \textbf{MP\_PREC} larger than \textbf{alloc} (line 26). The XREALLOC function is used +to re-allocate the memory. As per the other functions XREALLOC is actually a macro which evaluates to realloc by default. The realloc +function leaves the base of the allocation intact which means the first \textbf{alloc} digits of the mp\_int are the same as before +the re-allocation. All that is left is to clear the newly allocated digits and return. + +Note that the re-allocation result is actually stored in a temporary pointer $tmp$. This is to allow this function to return +an error with a valid pointer. Earlier releases of the library stored the result of XREALLOC into the mp\_int $a$. That would +result in a memory leak if XREALLOC ever failed. \subsection{Initializing Variable Precision mp\_ints} Occasionally the number of digits required will be known in advance of an initialization, based on, for example, the size @@ -1065,31 +1106,41 @@ 017 /* init an mp_init for a given size */ 018 int mp_init_size (mp_int * a, int size) 019 \{ -020 /* pad size so there are always extra digits */ -021 size += (MP_PREC * 2) - (size % MP_PREC); -022 -023 /* alloc mem */ -024 a->dp = OPT_CAST(mp_digit) XCALLOC (sizeof (mp_digit), size); -025 if (a->dp == NULL) \{ -026 return MP_MEM; -027 \} -028 a->used = 0; -029 a->alloc = size; -030 a->sign = MP_ZPOS; -031 -032 return MP_OKAY; -033 \} +020 int x; +021 +022 /* pad size so there are always extra digits */ +023 size += (MP_PREC * 2) - (size % MP_PREC); +024 +025 /* alloc mem */ +026 a->dp = OPT_CAST(mp_digit) XMALLOC (sizeof (mp_digit) * size); +027 if (a->dp == NULL) \{ +028 return MP_MEM; +029 \} +030 +031 /* set the members */ +032 a->used = 0; +033 a->alloc = size; +034 a->sign = MP_ZPOS; +035 +036 /* zero the digits */ +037 for (x = 0; x < size; x++) \{ +038 a->dp[x] = 0; +039 \} +040 +041 return MP_OKAY; +042 \} +043 #endif \end{alltt} \end{small} -The number of digits $b$ requested is padded (line 21) by first augmenting it to the next multiple of +The number of digits $b$ requested is padded (line 23) by first augmenting it to the next multiple of \textbf{MP\_PREC} and then adding \textbf{MP\_PREC} to the result. If the memory can be successfully allocated the mp\_int is placed in a default state representing the integer zero. Otherwise, the error code \textbf{MP\_MEM} will be -returned (line 26). - -The digits are allocated and set to zero at the same time with the calloc() function (line @25,calloc@). The +returned (line 28). + +The digits are allocated and set to zero at the same time with the calloc() function (line @25,XCALLOC@). The \textbf{used} count is set to zero, the \textbf{alloc} count set to the padded digit count and the \textbf{sign} flag set -to \textbf{MP\_ZPOS} to achieve a default valid mp\_int state (lines 28, 29 and 30). If the function +to \textbf{MP\_ZPOS} to achieve a default valid mp\_int state (lines 32, 33 and 34). If the function returns succesfully then it is correct to assume that the mp\_int structure is in a valid state for the remainder of the functions to work with. @@ -1165,6 +1216,7 @@ 051 return res; /* Assumed ok, if error flagged above. */ 052 \} 053 +054 #endif \end{alltt} \end{small} @@ -1249,6 +1301,7 @@ 036 a->sign = MP_ZPOS; 037 \} 038 \} +039 #endif \end{alltt} \end{small} @@ -1385,6 +1438,7 @@ 060 b->sign = a->sign; 061 return MP_OKAY; 062 \} +063 #endif \end{alltt} \end{small} @@ -1498,6 +1552,7 @@ 024 \} 025 return mp_copy (b, a); 026 \} +027 #endif \end{alltt} \end{small} @@ -1542,6 +1597,7 @@ 022 a->used = 0; 023 memset (a->dp, 0, sizeof (mp_digit) * a->alloc); 024 \} +025 #endif \end{alltt} \end{small} @@ -1602,6 +1658,7 @@ 035 036 return MP_OKAY; 037 \} +038 #endif \end{alltt} \end{small} @@ -1653,6 +1710,7 @@ 026 \} 027 return MP_OKAY; 028 \} +029 #endif \end{alltt} \end{small} @@ -1695,6 +1753,7 @@ 021 a->dp[0] = b & MP_MASK; 022 a->used = (a->dp[0] != 0) ? 1 : 0; 023 \} +024 #endif \end{alltt} \end{small} @@ -1771,6 +1830,7 @@ 040 mp_clamp (a); 041 return MP_OKAY; 042 \} +043 #endif \end{alltt} \end{small} @@ -1872,6 +1932,7 @@ 047 \} 048 return MP_EQ; 049 \} +050 #endif \end{alltt} \end{small} @@ -1935,6 +1996,7 @@ 035 return mp_cmp_mag(a, b); 036 \} 037 \} +038 #endif \end{alltt} \end{small} @@ -2152,6 +2214,7 @@ 101 mp_clamp (c); 102 return MP_OKAY; 103 \} +104 #endif \end{alltt} \end{small} @@ -2320,6 +2383,7 @@ 081 return MP_OKAY; 082 \} 083 +084 #endif \end{alltt} \end{small} @@ -2451,6 +2515,7 @@ 045 return res; 046 \} 047 +048 #endif \end{alltt} \end{small} @@ -2562,6 +2627,7 @@ 051 return res; 052 \} 053 +054 #endif \end{alltt} \end{small} @@ -2695,6 +2761,7 @@ 074 b->sign = a->sign; 075 return MP_OKAY; 076 \} +077 #endif \end{alltt} \end{small} @@ -2794,6 +2861,7 @@ 060 mp_clamp (b); 061 return MP_OKAY; 062 \} +063 #endif \end{alltt} \end{small} @@ -2913,6 +2981,7 @@ 059 \} 060 return MP_OKAY; 061 \} +062 #endif \end{alltt} \end{small} @@ -3022,6 +3091,7 @@ 064 /* remove excess digits */ 065 a->used -= b; 066 \} +067 #endif \end{alltt} \end{small} @@ -3154,6 +3224,7 @@ 077 mp_clamp (c); 078 return MP_OKAY; 079 \} +080 #endif \end{alltt} \end{small} @@ -3281,6 +3352,7 @@ 089 mp_clear (&t); 090 return MP_OKAY; 091 \} +092 #endif \end{alltt} \end{small} @@ -3370,6 +3442,7 @@ 047 mp_clamp (c); 048 return MP_OKAY; 049 \} +050 #endif \end{alltt} \end{small} @@ -3603,6 +3676,7 @@ 083 mp_clear (&t); 084 return MP_OKAY; 085 \} +086 #endif \end{alltt} \end{small} @@ -3806,109 +3880,82 @@ 033 int 034 fast_s_mp_mul_digs (mp_int * a, mp_int * b, mp_int * c, int digs) 035 \{ -036 int olduse, res, pa, ix; -037 mp_word W[MP_WARRAY]; -038 -039 /* grow the destination as required */ -040 if (c->alloc < digs) \{ -041 if ((res = mp_grow (c, digs)) != MP_OKAY) \{ -042 return res; -043 \} -044 \} -045 -046 /* clear temp buf (the columns) */ -047 memset (W, 0, sizeof (mp_word) * digs); -048 -049 /* calculate the columns */ -050 pa = a->used; -051 for (ix = 0; ix < pa; ix++) \{ -052 /* this multiplier has been modified to allow you to -053 * control how many digits of output are produced. -054 * So at most we want to make upto "digs" digits of output. -055 * -056 * this adds products to distinct columns (at ix+iy) of W -057 * note that each step through the loop is not dependent on -058 * the previous which means the compiler can easily unroll -059 * the loop without scheduling problems -060 */ -061 \{ -062 register mp_digit tmpx, *tmpy; -063 register mp_word *_W; -064 register int iy, pb; -065 -066 /* alias for the the word on the left e.g. A[ix] * A[iy] */ -067 tmpx = a->dp[ix]; -068 -069 /* alias for the right side */ -070 tmpy = b->dp; -071 -072 /* alias for the columns, each step through the loop adds a new -073 term to each column -074 */ -075 _W = W + ix; -076 -077 /* the number of digits is limited by their placement. E.g. -078 we avoid multiplying digits that will end up above the # of -079 digits of precision requested -080 */ -081 pb = MIN (b->used, digs - ix); -082 -083 for (iy = 0; iy < pb; iy++) \{ -084 *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++); -085 \} -086 \} -087 -088 \} -089 -090 /* setup dest */ -091 olduse = c->used; -092 c->used = digs; +036 int olduse, res, pa, ix, iz; +037 mp_digit W[MP_WARRAY]; +038 register mp_word _W; +039 +040 /* grow the destination as required */ +041 if (c->alloc < digs) \{ +042 if ((res = mp_grow (c, digs)) != MP_OKAY) \{ +043 return res; +044 \} +045 \} +046 +047 /* number of output digits to produce */ +048 pa = MIN(digs, a->used + b->used); +049 +050 /* clear the carry */ +051 _W = 0; +052 for (ix = 0; ix <= pa; ix++) \{ +053 int tx, ty; +054 int iy; +055 mp_digit *tmpx, *tmpy; +056 +057 /* get offsets into the two bignums */ +058 ty = MIN(b->used-1, ix); +059 tx = ix - ty; +060 +061 /* setup temp aliases */ +062 tmpx = a->dp + tx; +063 tmpy = b->dp + ty; +064 +065 /* this is the number of times the loop will iterrate, essentially its + +066 while (tx++ < a->used && ty-- >= 0) \{ ... \} +067 */ +068 iy = MIN(a->used-tx, ty+1); +069 +070 /* execute loop */ +071 for (iz = 0; iz < iy; ++iz) \{ +072 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); +073 \} +074 +075 /* store term */ +076 W[ix] = ((mp_digit)_W) & MP_MASK; +077 +078 /* make next carry */ +079 _W = _W >> ((mp_word)DIGIT_BIT); +080 \} +081 +082 /* setup dest */ +083 olduse = c->used; +084 c->used = digs; +085 +086 \{ +087 register mp_digit *tmpc; +088 tmpc = c->dp; +089 for (ix = 0; ix < digs; ix++) \{ +090 /* now extract the previous digit [below the carry] */ +091 *tmpc++ = W[ix]; +092 \} 093 -094 \{ -095 register mp_digit *tmpc; -096 -097 /* At this point W[] contains the sums of each column. To get the -098 * correct result we must take the extra bits from each column and -099 * carry them down -100 * -101 * Note that while this adds extra code to the multiplier it -102 * saves time since the carry propagation is removed from the -103 * above nested loop.This has the effect of reducing the work -104 * from N*(N+N*c)==N**2 + c*N**2 to N**2 + N*c where c is the -105 * cost of the shifting. On very small numbers this is slower -106 * but on most cryptographic size numbers it is faster. -107 * -108 * In this particular implementation we feed the carries from -109 * behind which means when the loop terminates we still have one -110 * last digit to copy -111 */ -112 tmpc = c->dp; -113 for (ix = 1; ix < digs; ix++) \{ -114 /* forward the carry from the previous temp */ -115 W[ix] += (W[ix - 1] >> ((mp_word) DIGIT_BIT)); -116 -117 /* now extract the previous digit [below the carry] */ -118 *tmpc++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); -119 \} -120 /* fetch the last digit */ -121 *tmpc++ = (mp_digit) (W[digs - 1] & ((mp_word) MP_MASK)); -122 -123 /* clear unused digits [that existed in the old copy of c] */ -124 for (; ix < olduse; ix++) \{ -125 *tmpc++ = 0; -126 \} -127 \} -128 mp_clamp (c); -129 return MP_OKAY; -130 \} +094 /* clear unused digits [that existed in the old copy of c] */ +095 for (; ix < olduse; ix++) \{ +096 *tmpc++ = 0; +097 \} +098 \} +099 mp_clamp (c); +100 return MP_OKAY; +101 \} +102 #endif \end{alltt} \end{small} -The memset on line 47 clears the initial $\hat W$ array to zero in a single step. Like the slower baseline multiplication -implementation a series of aliases (\textit{lines 67, 70 and 75}) are used to simplify the inner $O(n^2)$ loop. +The memset on line @47,memset@ clears the initial $\hat W$ array to zero in a single step. Like the slower baseline multiplication +implementation a series of aliases (\textit{lines 62, 63 and 76}) are used to simplify the inner $O(n^2)$ loop. In this case a new alias $\_\hat W$ has been added which refers to the double precision columns offset by $ix$ in each pass. -The inner loop on lines 83, 84 and 85 is where the algorithm will spend the majority of the time, which is why it has been +The inner loop on lines 89, 79 and 80 is where the algorithm will spend the majority of the time, which is why it has been stripped to the bones of any extra baggage\footnote{Hence the pointer aliases.}. On x86 processors the multiplication and additions amount to at the very least five instructions (\textit{two loads, two additions, one multiply}) while on the ARMv4 processors they amount to only three (\textit{one load, one store, one multiply-add}). For both of the x86 and ARMv4 processors the GCC compiler performs a good job at unrolling the loop @@ -4168,92 +4215,90 @@ 076 goto X0Y0; 077 078 /* now shift the digits */ -079 x0.sign = x1.sign = a->sign; -080 y0.sign = y1.sign = b->sign; -081 -082 x0.used = y0.used = B; -083 x1.used = a->used - B; -084 y1.used = b->used - B; -085 -086 \{ -087 register int x; -088 register mp_digit *tmpa, *tmpb, *tmpx, *tmpy; -089 -090 /* we copy the digits directly instead of using higher level functions -091 * since we also need to shift the digits -092 */ -093 tmpa = a->dp; -094 tmpb = b->dp; -095 -096 tmpx = x0.dp; -097 tmpy = y0.dp; -098 for (x = 0; x < B; x++) \{ -099 *tmpx++ = *tmpa++; -100 *tmpy++ = *tmpb++; -101 \} -102 -103 tmpx = x1.dp; -104 for (x = B; x < a->used; x++) \{ -105 *tmpx++ = *tmpa++; -106 \} -107 -108 tmpy = y1.dp; -109 for (x = B; x < b->used; x++) \{ -110 *tmpy++ = *tmpb++; -111 \} -112 \} -113 -114 /* only need to clamp the lower words since by definition the -115 * upper words x1/y1 must have a known number of digits -116 */ -117 mp_clamp (&x0); -118 mp_clamp (&y0); -119 -120 /* now calc the products x0y0 and x1y1 */ -121 /* after this x0 is no longer required, free temp [x0==t2]! */ -122 if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY) -123 goto X1Y1; /* x0y0 = x0*y0 */ -124 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) -125 goto X1Y1; /* x1y1 = x1*y1 */ -126 -127 /* now calc x1-x0 and y1-y0 */ -128 if (mp_sub (&x1, &x0, &t1) != MP_OKAY) -129 goto X1Y1; /* t1 = x1 - x0 */ -130 if (mp_sub (&y1, &y0, &x0) != MP_OKAY) -131 goto X1Y1; /* t2 = y1 - y0 */ -132 if (mp_mul (&t1, &x0, &t1) != MP_OKAY) -133 goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */ -134 -135 /* add x0y0 */ -136 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) -137 goto X1Y1; /* t2 = x0y0 + x1y1 */ -138 if (mp_sub (&x0, &t1, &t1) != MP_OKAY) -139 goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */ -140 -141 /* shift by B */ -142 if (mp_lshd (&t1, B) != MP_OKAY) -143 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */ -144 if (mp_lshd (&x1y1, B * 2) != MP_OKAY) -145 goto X1Y1; /* x1y1 = x1y1 << 2*B */ -146 -147 if (mp_add (&x0y0, &t1, &t1) != MP_OKAY) -148 goto X1Y1; /* t1 = x0y0 + t1 */ -149 if (mp_add (&t1, &x1y1, c) != MP_OKAY) -150 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */ +079 x0.used = y0.used = B; +080 x1.used = a->used - B; +081 y1.used = b->used - B; +082 +083 \{ +084 register int x; +085 register mp_digit *tmpa, *tmpb, *tmpx, *tmpy; +086 +087 /* we copy the digits directly instead of using higher level functions +088 * since we also need to shift the digits +089 */ +090 tmpa = a->dp; +091 tmpb = b->dp; +092 +093 tmpx = x0.dp; +094 tmpy = y0.dp; +095 for (x = 0; x < B; x++) \{ +096 *tmpx++ = *tmpa++; +097 *tmpy++ = *tmpb++; +098 \} +099 +100 tmpx = x1.dp; +101 for (x = B; x < a->used; x++) \{ +102 *tmpx++ = *tmpa++; +103 \} +104 +105 tmpy = y1.dp; +106 for (x = B; x < b->used; x++) \{ +107 *tmpy++ = *tmpb++; +108 \} +109 \} +110 +111 /* only need to clamp the lower words since by definition the +112 * upper words x1/y1 must have a known number of digits +113 */ +114 mp_clamp (&x0); +115 mp_clamp (&y0); +116 +117 /* now calc the products x0y0 and x1y1 */ +118 /* after this x0 is no longer required, free temp [x0==t2]! */ +119 if (mp_mul (&x0, &y0, &x0y0) != MP_OKAY) +120 goto X1Y1; /* x0y0 = x0*y0 */ +121 if (mp_mul (&x1, &y1, &x1y1) != MP_OKAY) +122 goto X1Y1; /* x1y1 = x1*y1 */ +123 +124 /* now calc x1-x0 and y1-y0 */ +125 if (mp_sub (&x1, &x0, &t1) != MP_OKAY) +126 goto X1Y1; /* t1 = x1 - x0 */ +127 if (mp_sub (&y1, &y0, &x0) != MP_OKAY) +128 goto X1Y1; /* t2 = y1 - y0 */ +129 if (mp_mul (&t1, &x0, &t1) != MP_OKAY) +130 goto X1Y1; /* t1 = (x1 - x0) * (y1 - y0) */ +131 +132 /* add x0y0 */ +133 if (mp_add (&x0y0, &x1y1, &x0) != MP_OKAY) +134 goto X1Y1; /* t2 = x0y0 + x1y1 */ +135 if (mp_sub (&x0, &t1, &t1) != MP_OKAY) +136 goto X1Y1; /* t1 = x0y0 + x1y1 - (x1-x0)*(y1-y0) */ +137 +138 /* shift by B */ +139 if (mp_lshd (&t1, B) != MP_OKAY) +140 goto X1Y1; /* t1 = (x0y0 + x1y1 - (x1-x0)*(y1-y0))<<B */ +141 if (mp_lshd (&x1y1, B * 2) != MP_OKAY) +142 goto X1Y1; /* x1y1 = x1y1 << 2*B */ +143 +144 if (mp_add (&x0y0, &t1, &t1) != MP_OKAY) +145 goto X1Y1; /* t1 = x0y0 + t1 */ +146 if (mp_add (&t1, &x1y1, c) != MP_OKAY) +147 goto X1Y1; /* t1 = x0y0 + t1 + x1y1 */ +148 +149 /* Algorithm succeeded set the return code to MP_OKAY */ +150 err = MP_OKAY; 151 -152 /* Algorithm succeeded set the return code to MP_OKAY */ -153 err = MP_OKAY; -154 -155 X1Y1:mp_clear (&x1y1); -156 X0Y0:mp_clear (&x0y0); -157 T1:mp_clear (&t1); -158 Y1:mp_clear (&y1); -159 Y0:mp_clear (&y0); -160 X1:mp_clear (&x1); -161 X0:mp_clear (&x0); -162 ERR: -163 return err; -164 \} +152 X1Y1:mp_clear (&x1y1); +153 X0Y0:mp_clear (&x0y0); +154 T1:mp_clear (&t1); +155 Y1:mp_clear (&y1); +156 Y0:mp_clear (&y0); +157 X1:mp_clear (&x1); +158 X0:mp_clear (&x0); +159 ERR: +160 return err; +161 \} +162 #endif \end{alltt} \end{small} @@ -4269,13 +4314,13 @@ The first algebraic portion of the algorithm is to split the two inputs into their halves. However, instead of using mp\_mod\_2d and mp\_rshd to extract the halves, the respective code has been placed inline within the body of the function. To initialize the halves, the \textbf{used} and -\textbf{sign} members are copied first. The first for loop on line 98 copies the lower halves. Since they are both the same magnitude it -is simpler to calculate both lower halves in a single loop. The for loop on lines 104 and 109 calculate the upper halves $x1$ and +\textbf{sign} members are copied first. The first for loop on line 101 copies the lower halves. Since they are both the same magnitude it +is simpler to calculate both lower halves in a single loop. The for loop on lines 106 and 106 calculate the upper halves $x1$ and $y1$ respectively. By inlining the calculation of the halves, the Karatsuba multiplier has a slightly lower overhead and can be used for smaller magnitude inputs. -When line 153 is reached, the algorithm has completed succesfully. The ``error status'' variable $err$ is set to \textbf{MP\_OKAY} so that +When line 150 is reached, the algorithm has completed succesfully. The ``error status'' variable $err$ is set to \textbf{MP\_OKAY} so that the same code that handles errors can be used to clear the temporary variables and return. \subsection{Toom-Cook $3$-Way Multiplication} @@ -4394,262 +4439,269 @@ \vspace{-3mm} \begin{alltt} 016 -017 /* multiplication using the Toom-Cook 3-way algorithm */ -018 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) -019 \{ -020 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; -021 int res, B; -022 -023 /* init temps */ -024 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, -025 &a0, &a1, &a2, &b0, &b1, -026 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) \{ -027 return res; -028 \} -029 -030 /* B */ -031 B = MIN(a->used, b->used) / 3; -032 -033 /* a = a2 * B**2 + a1 * B + a0 */ -034 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) \{ -035 goto ERR; -036 \} -037 -038 if ((res = mp_copy(a, &a1)) != MP_OKAY) \{ -039 goto ERR; -040 \} -041 mp_rshd(&a1, B); -042 mp_mod_2d(&a1, DIGIT_BIT * B, &a1); -043 -044 if ((res = mp_copy(a, &a2)) != MP_OKAY) \{ -045 goto ERR; -046 \} -047 mp_rshd(&a2, B*2); -048 -049 /* b = b2 * B**2 + b1 * B + b0 */ -050 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) \{ -051 goto ERR; -052 \} -053 -054 if ((res = mp_copy(b, &b1)) != MP_OKAY) \{ -055 goto ERR; -056 \} -057 mp_rshd(&b1, B); -058 mp_mod_2d(&b1, DIGIT_BIT * B, &b1); -059 -060 if ((res = mp_copy(b, &b2)) != MP_OKAY) \{ -061 goto ERR; -062 \} -063 mp_rshd(&b2, B*2); -064 -065 /* w0 = a0*b0 */ -066 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) \{ -067 goto ERR; -068 \} +017 /* multiplication using the Toom-Cook 3-way algorithm +018 * +019 * Much more complicated than Karatsuba but has a lower asymptotic running t + ime of +020 * O(N**1.464). This algorithm is only particularly useful on VERY large +021 * inputs (we're talking 1000s of digits here...). +022 */ +023 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c) +024 \{ +025 mp_int w0, w1, w2, w3, w4, tmp1, tmp2, a0, a1, a2, b0, b1, b2; +026 int res, B; +027 +028 /* init temps */ +029 if ((res = mp_init_multi(&w0, &w1, &w2, &w3, &w4, +030 &a0, &a1, &a2, &b0, &b1, +031 &b2, &tmp1, &tmp2, NULL)) != MP_OKAY) \{ +032 return res; +033 \} +034 +035 /* B */ +036 B = MIN(a->used, b->used) / 3; +037 +038 /* a = a2 * B**2 + a1 * B + a0 */ +039 if ((res = mp_mod_2d(a, DIGIT_BIT * B, &a0)) != MP_OKAY) \{ +040 goto ERR; +041 \} +042 +043 if ((res = mp_copy(a, &a1)) != MP_OKAY) \{ +044 goto ERR; +045 \} +046 mp_rshd(&a1, B); +047 mp_mod_2d(&a1, DIGIT_BIT * B, &a1); +048 +049 if ((res = mp_copy(a, &a2)) != MP_OKAY) \{ +050 goto ERR; +051 \} +052 mp_rshd(&a2, B*2); +053 +054 /* b = b2 * B**2 + b1 * B + b0 */ +055 if ((res = mp_mod_2d(b, DIGIT_BIT * B, &b0)) != MP_OKAY) \{ +056 goto ERR; +057 \} +058 +059 if ((res = mp_copy(b, &b1)) != MP_OKAY) \{ +060 goto ERR; +061 \} +062 mp_rshd(&b1, B); +063 mp_mod_2d(&b1, DIGIT_BIT * B, &b1); +064 +065 if ((res = mp_copy(b, &b2)) != MP_OKAY) \{ +066 goto ERR; +067 \} +068 mp_rshd(&b2, B*2); 069 -070 /* w4 = a2 * b2 */ -071 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) \{ +070 /* w0 = a0*b0 */ +071 if ((res = mp_mul(&a0, &b0, &w0)) != MP_OKAY) \{ 072 goto ERR; 073 \} 074 -075 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */ -076 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) \{ +075 /* w4 = a2 * b2 */ +076 if ((res = mp_mul(&a2, &b2, &w4)) != MP_OKAY) \{ 077 goto ERR; 078 \} -079 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{ -080 goto ERR; -081 \} -082 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{ -083 goto ERR; -084 \} -085 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) \{ -086 goto ERR; -087 \} -088 -089 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) \{ -090 goto ERR; -091 \} -092 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{ -093 goto ERR; -094 \} -095 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{ -096 goto ERR; -097 \} -098 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) \{ -099 goto ERR; -100 \} -101 -102 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) \{ -103 goto ERR; -104 \} -105 -106 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */ -107 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) \{ +079 +080 /* w1 = (a2 + 2(a1 + 2a0))(b2 + 2(b1 + 2b0)) */ +081 if ((res = mp_mul_2(&a0, &tmp1)) != MP_OKAY) \{ +082 goto ERR; +083 \} +084 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{ +085 goto ERR; +086 \} +087 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{ +088 goto ERR; +089 \} +090 if ((res = mp_add(&tmp1, &a2, &tmp1)) != MP_OKAY) \{ +091 goto ERR; +092 \} +093 +094 if ((res = mp_mul_2(&b0, &tmp2)) != MP_OKAY) \{ +095 goto ERR; +096 \} +097 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{ +098 goto ERR; +099 \} +100 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{ +101 goto ERR; +102 \} +103 if ((res = mp_add(&tmp2, &b2, &tmp2)) != MP_OKAY) \{ +104 goto ERR; +105 \} +106 +107 if ((res = mp_mul(&tmp1, &tmp2, &w1)) != MP_OKAY) \{ 108 goto ERR; 109 \} -110 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{ -111 goto ERR; -112 \} -113 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{ -114 goto ERR; -115 \} -116 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{ -117 goto ERR; -118 \} -119 -120 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) \{ -121 goto ERR; -122 \} -123 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{ -124 goto ERR; -125 \} -126 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{ -127 goto ERR; -128 \} -129 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{ -130 goto ERR; -131 \} -132 -133 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) \{ -134 goto ERR; -135 \} -136 -137 -138 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */ -139 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) \{ -140 goto ERR; -141 \} -142 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{ -143 goto ERR; -144 \} -145 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) \{ -146 goto ERR; -147 \} -148 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{ -149 goto ERR; -150 \} -151 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) \{ -152 goto ERR; -153 \} -154 -155 /* now solve the matrix -156 -157 0 0 0 0 1 -158 1 2 4 8 16 -159 1 1 1 1 1 -160 16 8 4 2 1 -161 1 0 0 0 0 -162 -163 using 12 subtractions, 4 shifts, -164 2 small divisions and 1 small multiplication -165 */ -166 -167 /* r1 - r4 */ -168 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) \{ -169 goto ERR; -170 \} -171 /* r3 - r0 */ -172 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) \{ -173 goto ERR; -174 \} -175 /* r1/2 */ -176 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) \{ -177 goto ERR; -178 \} -179 /* r3/2 */ -180 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) \{ -181 goto ERR; -182 \} -183 /* r2 - r0 - r4 */ -184 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) \{ -185 goto ERR; -186 \} -187 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) \{ -188 goto ERR; -189 \} -190 /* r1 - r2 */ -191 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{ -192 goto ERR; -193 \} -194 /* r3 - r2 */ -195 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{ -196 goto ERR; -197 \} -198 /* r1 - 8r0 */ -199 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) \{ -200 goto ERR; -201 \} -202 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) \{ -203 goto ERR; -204 \} -205 /* r3 - 8r4 */ -206 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) \{ -207 goto ERR; -208 \} -209 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) \{ -210 goto ERR; -211 \} -212 /* 3r2 - r1 - r3 */ -213 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) \{ -214 goto ERR; -215 \} -216 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) \{ -217 goto ERR; -218 \} -219 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) \{ -220 goto ERR; -221 \} -222 /* r1 - r2 */ -223 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{ -224 goto ERR; -225 \} -226 /* r3 - r2 */ -227 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{ -228 goto ERR; -229 \} -230 /* r1/3 */ -231 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) \{ -232 goto ERR; -233 \} -234 /* r3/3 */ -235 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) \{ -236 goto ERR; -237 \} -238 -239 /* at this point shift W[n] by B*n */ -240 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) \{ +110 +111 /* w3 = (a0 + 2(a1 + 2a2))(b0 + 2(b1 + 2b2)) */ +112 if ((res = mp_mul_2(&a2, &tmp1)) != MP_OKAY) \{ +113 goto ERR; +114 \} +115 if ((res = mp_add(&tmp1, &a1, &tmp1)) != MP_OKAY) \{ +116 goto ERR; +117 \} +118 if ((res = mp_mul_2(&tmp1, &tmp1)) != MP_OKAY) \{ +119 goto ERR; +120 \} +121 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{ +122 goto ERR; +123 \} +124 +125 if ((res = mp_mul_2(&b2, &tmp2)) != MP_OKAY) \{ +126 goto ERR; +127 \} +128 if ((res = mp_add(&tmp2, &b1, &tmp2)) != MP_OKAY) \{ +129 goto ERR; +130 \} +131 if ((res = mp_mul_2(&tmp2, &tmp2)) != MP_OKAY) \{ +132 goto ERR; +133 \} +134 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{ +135 goto ERR; +136 \} +137 +138 if ((res = mp_mul(&tmp1, &tmp2, &w3)) != MP_OKAY) \{ +139 goto ERR; +140 \} +141 +142 +143 /* w2 = (a2 + a1 + a0)(b2 + b1 + b0) */ +144 if ((res = mp_add(&a2, &a1, &tmp1)) != MP_OKAY) \{ +145 goto ERR; +146 \} +147 if ((res = mp_add(&tmp1, &a0, &tmp1)) != MP_OKAY) \{ +148 goto ERR; +149 \} +150 if ((res = mp_add(&b2, &b1, &tmp2)) != MP_OKAY) \{ +151 goto ERR; +152 \} +153 if ((res = mp_add(&tmp2, &b0, &tmp2)) != MP_OKAY) \{ +154 goto ERR; +155 \} +156 if ((res = mp_mul(&tmp1, &tmp2, &w2)) != MP_OKAY) \{ +157 goto ERR; +158 \} +159 +160 /* now solve the matrix +161 +162 0 0 0 0 1 +163 1 2 4 8 16 +164 1 1 1 1 1 +165 16 8 4 2 1 +166 1 0 0 0 0 +167 +168 using 12 subtractions, 4 shifts, +169 2 small divisions and 1 small multiplication +170 */ +171 +172 /* r1 - r4 */ +173 if ((res = mp_sub(&w1, &w4, &w1)) != MP_OKAY) \{ +174 goto ERR; +175 \} +176 /* r3 - r0 */ +177 if ((res = mp_sub(&w3, &w0, &w3)) != MP_OKAY) \{ +178 goto ERR; +179 \} +180 /* r1/2 */ +181 if ((res = mp_div_2(&w1, &w1)) != MP_OKAY) \{ +182 goto ERR; +183 \} +184 /* r3/2 */ +185 if ((res = mp_div_2(&w3, &w3)) != MP_OKAY) \{ +186 goto ERR; +187 \} +188 /* r2 - r0 - r4 */ +189 if ((res = mp_sub(&w2, &w0, &w2)) != MP_OKAY) \{ +190 goto ERR; +191 \} +192 if ((res = mp_sub(&w2, &w4, &w2)) != MP_OKAY) \{ +193 goto ERR; +194 \} +195 /* r1 - r2 */ +196 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{ +197 goto ERR; +198 \} +199 /* r3 - r2 */ +200 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{ +201 goto ERR; +202 \} +203 /* r1 - 8r0 */ +204 if ((res = mp_mul_2d(&w0, 3, &tmp1)) != MP_OKAY) \{ +205 goto ERR; +206 \} +207 if ((res = mp_sub(&w1, &tmp1, &w1)) != MP_OKAY) \{ +208 goto ERR; +209 \} +210 /* r3 - 8r4 */ +211 if ((res = mp_mul_2d(&w4, 3, &tmp1)) != MP_OKAY) \{ +212 goto ERR; +213 \} +214 if ((res = mp_sub(&w3, &tmp1, &w3)) != MP_OKAY) \{ +215 goto ERR; +216 \} +217 /* 3r2 - r1 - r3 */ +218 if ((res = mp_mul_d(&w2, 3, &w2)) != MP_OKAY) \{ +219 goto ERR; +220 \} +221 if ((res = mp_sub(&w2, &w1, &w2)) != MP_OKAY) \{ +222 goto ERR; +223 \} +224 if ((res = mp_sub(&w2, &w3, &w2)) != MP_OKAY) \{ +225 goto ERR; +226 \} +227 /* r1 - r2 */ +228 if ((res = mp_sub(&w1, &w2, &w1)) != MP_OKAY) \{ +229 goto ERR; +230 \} +231 /* r3 - r2 */ +232 if ((res = mp_sub(&w3, &w2, &w3)) != MP_OKAY) \{ +233 goto ERR; +234 \} +235 /* r1/3 */ +236 if ((res = mp_div_3(&w1, &w1, NULL)) != MP_OKAY) \{ +237 goto ERR; +238 \} +239 /* r3/3 */ +240 if ((res = mp_div_3(&w3, &w3, NULL)) != MP_OKAY) \{ 241 goto ERR; 242 \} -243 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) \{ -244 goto ERR; -245 \} -246 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) \{ -247 goto ERR; -248 \} -249 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) \{ -250 goto ERR; -251 \} -252 -253 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) \{ -254 goto ERR; -255 \} -256 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) \{ -257 goto ERR; -258 \} -259 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) \{ -260 goto ERR; -261 \} -262 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) \{ -263 goto ERR; -264 \} -265 -266 ERR: -267 mp_clear_multi(&w0, &w1, &w2, &w3, &w4, -268 &a0, &a1, &a2, &b0, &b1, -269 &b2, &tmp1, &tmp2, NULL); -270 return res; -271 \} -272 +243 +244 /* at this point shift W[n] by B*n */ +245 if ((res = mp_lshd(&w1, 1*B)) != MP_OKAY) \{ +246 goto ERR; +247 \} +248 if ((res = mp_lshd(&w2, 2*B)) != MP_OKAY) \{ +249 goto ERR; +250 \} +251 if ((res = mp_lshd(&w3, 3*B)) != MP_OKAY) \{ +252 goto ERR; +253 \} +254 if ((res = mp_lshd(&w4, 4*B)) != MP_OKAY) \{ +255 goto ERR; +256 \} +257 +258 if ((res = mp_add(&w0, &w1, c)) != MP_OKAY) \{ +259 goto ERR; +260 \} +261 if ((res = mp_add(&w2, &w3, &tmp1)) != MP_OKAY) \{ +262 goto ERR; +263 \} +264 if ((res = mp_add(&w4, &tmp1, &tmp1)) != MP_OKAY) \{ +265 goto ERR; +266 \} +267 if ((res = mp_add(&tmp1, c, c)) != MP_OKAY) \{ +268 goto ERR; +269 \} +270 +271 ERR: +272 mp_clear_multi(&w0, &w1, &w2, &w3, &w4, +273 &a0, &a1, &a2, &b0, &b1, +274 &b2, &tmp1, &tmp2, NULL); +275 return res; +276 \} +277 +278 #endif \end{alltt} \end{small} @@ -4707,36 +4759,49 @@ 021 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; 022 023 /* use Toom-Cook? */ -024 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) \{ -025 res = mp_toom_mul(a, b, c); -026 /* use Karatsuba? */ -027 \} else if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) \{ -028 res = mp_karatsuba_mul (a, b, c); -029 \} else \{ -030 /* can we use the fast multiplier? -031 * -032 * The fast multiplier can be used if the output will -033 * have less than MP_WARRAY digits and the number of -034 * digits won't affect carry propagation -035 */ -036 int digs = a->used + b->used + 1; -037 -038 if ((digs < MP_WARRAY) && -039 MIN(a->used, b->used) <= -040 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{ -041 res = fast_s_mp_mul_digs (a, b, c, digs); -042 \} else \{ -043 res = s_mp_mul (a, b, c); -044 \} -045 \} -046 c->sign = neg; -047 return res; -048 \} +024 #ifdef BN_MP_TOOM_MUL_C +025 if (MIN (a->used, b->used) >= TOOM_MUL_CUTOFF) \{ +026 res = mp_toom_mul(a, b, c); +027 \} else +028 #endif +029 #ifdef BN_MP_KARATSUBA_MUL_C +030 /* use Karatsuba? */ +031 if (MIN (a->used, b->used) >= KARATSUBA_MUL_CUTOFF) \{ +032 res = mp_karatsuba_mul (a, b, c); +033 \} else +034 #endif +035 \{ +036 /* can we use the fast multiplier? +037 * +038 * The fast multiplier can be used if the output will +039 * have less than MP_WARRAY digits and the number of +040 * digits won't affect carry propagation +041 */ +042 int digs = a->used + b->used + 1; +043 +044 #ifdef BN_FAST_S_MP_MUL_DIGS_C +045 if ((digs < MP_WARRAY) && +046 MIN(a->used, b->used) <= +047 (1 << ((CHAR_BIT * sizeof (mp_word)) - (2 * DIGIT_BIT)))) \{ +048 res = fast_s_mp_mul_digs (a, b, c, digs); +049 \} else +050 #endif +051 #ifdef BN_S_MP_MUL_DIGS_C +052 res = s_mp_mul (a, b, c); /* uses s_mp_mul_digs */ +053 #else +054 res = MP_VAL; +055 #endif +056 +057 \} +058 c->sign = (c->used > 0) ? neg : MP_ZPOS; +059 return res; +060 \} +061 #endif \end{alltt} \end{small} The implementation is rather simplistic and is not particularly noteworthy. Line 23 computes the sign of the result using the ``?'' -operator from the C programming language. Line 40 computes $\delta$ using the fact that $1 << k$ is equal to $2^k$. +operator from the C programming language. Line 47 computes $\delta$ using the fact that $1 << k$ is equal to $2^k$. \section{Squaring} \label{sec:basesquare} @@ -4901,6 +4966,7 @@ 077 mp_clear (&t); 078 return MP_OKAY; 079 \} +080 #endif \end{alltt} \end{small} @@ -5003,112 +5069,105 @@ 031 * Based on Algorithm 14.16 on pp.597 of HAC. 032 * 033 */ -034 int fast_s_mp_sqr (mp_int * a, mp_int * b) -035 \{ -036 int olduse, newused, res, ix, pa; -037 mp_word W2[MP_WARRAY], W[MP_WARRAY]; -038 -039 /* calculate size of product and allocate as required */ -040 pa = a->used; -041 newused = pa + pa + 1; -042 if (b->alloc < newused) \{ -043 if ((res = mp_grow (b, newused)) != MP_OKAY) \{ -044 return res; -045 \} -046 \} -047 -048 /* zero temp buffer (columns) -049 * Note that there are two buffers. Since squaring requires -050 * a outer and inner product and the inner product requires -051 * computing a product and doubling it (a relatively expensive -052 * op to perform n**2 times if you don't have to) the inner and -053 * outer products are computed in different buffers. This way -054 * the inner product can be doubled using n doublings instead of -055 * n**2 -056 */ -057 memset (W, 0, newused * sizeof (mp_word)); -058 memset (W2, 0, newused * sizeof (mp_word)); +034 /* the jist of squaring... +035 +036 you do like mult except the offset of the tmpx [one that starts closer to ze + ro] +037 can't equal the offset of tmpy. So basically you set up iy like before then + you min it with +038 (ty-tx) so that it never happens. You double all those you add in the inner + loop +039 +040 After that loop you do the squares and add them in. +041 +042 Remove W2 and don't memset W +043 +044 */ +045 +046 int fast_s_mp_sqr (mp_int * a, mp_int * b) +047 \{ +048 int olduse, res, pa, ix, iz; +049 mp_digit W[MP_WARRAY], *tmpx; +050 mp_word W1; +051 +052 /* grow the destination as required */ +053 pa = a->used + a->used; +054 if (b->alloc < pa) \{ +055 if ((res = mp_grow (b, pa)) != MP_OKAY) \{ +056 return res; +057 \} +058 \} 059 -060 /* This computes the inner product. To simplify the inner N**2 loop -061 * the multiplication by two is done afterwards in the N loop. -062 */ -063 for (ix = 0; ix < pa; ix++) \{ -064 /* compute the outer product -065 * -066 * Note that every outer product is computed -067 * for a particular column only once which means that -068 * there is no need todo a double precision addition -069 * into the W2[] array. -070 */ -071 W2[ix + ix] = ((mp_word)a->dp[ix]) * ((mp_word)a->dp[ix]); -072 -073 \{ -074 register mp_digit tmpx, *tmpy; -075 register mp_word *_W; -076 register int iy; +060 /* number of output digits to produce */ +061 W1 = 0; +062 for (ix = 0; ix <= pa; ix++) \{ +063 int tx, ty, iy; +064 mp_word _W; +065 mp_digit *tmpy; +066 +067 /* clear counter */ +068 _W = 0; +069 +070 /* get offsets into the two bignums */ +071 ty = MIN(a->used-1, ix); +072 tx = ix - ty; +073 +074 /* setup temp aliases */ +075 tmpx = a->dp + tx; +076 tmpy = a->dp + ty; 077 -078 /* copy of left side */ -079 tmpx = a->dp[ix]; -080 -081 /* alias for right side */ -082 tmpy = a->dp + (ix + 1); -083 -084 /* the column to store the result in */ -085 _W = W + (ix + ix + 1); -086 -087 /* inner products */ -088 for (iy = ix + 1; iy < pa; iy++) \{ -089 *_W++ += ((mp_word)tmpx) * ((mp_word)*tmpy++); -090 \} -091 \} -092 \} +078 /* this is the number of times the loop will iterrate, essentially its + +079 while (tx++ < a->used && ty-- >= 0) \{ ... \} +080 */ +081 iy = MIN(a->used-tx, ty+1); +082 +083 /* now for squaring tx can never equal ty +084 * we halve the distance since they approach at a rate of 2x +085 * and we have to round because odd cases need to be executed +086 */ +087 iy = MIN(iy, (ty-tx+1)>>1); +088 +089 /* execute loop */ +090 for (iz = 0; iz < iy; iz++) \{ +091 _W += ((mp_word)*tmpx++)*((mp_word)*tmpy--); +092 \} 093 -094 /* setup dest */ -095 olduse = b->used; -096 b->used = newused; -097 -098 /* now compute digits -099 * -100 * We have to double the inner product sums, add in the -101 * outer product sums, propagate carries and convert -102 * to single precision. -103 */ -104 \{ -105 register mp_digit *tmpb; -106 -107 /* double first value, since the inner products are -108 * half of what they should be -109 */ -110 W[0] += W[0] + W2[0]; -111 -112 tmpb = b->dp; -113 for (ix = 1; ix < newused; ix++) \{ -114 /* double/add next digit */ -115 W[ix] += W[ix] + W2[ix]; -116 -117 /* propagate carry forwards [from the previous digit] */ -118 W[ix] = W[ix] + (W[ix - 1] >> ((mp_word) DIGIT_BIT)); +094 /* double the inner product and add carry */ +095 _W = _W + _W + W1; +096 +097 /* even columns have the square term in them */ +098 if ((ix&1) == 0) \{ +099 _W += ((mp_word)a->dp[ix>>1])*((mp_word)a->dp[ix>>1]); +100 \} +101 +102 /* store it */ +103 W[ix] = _W; +104 +105 /* make next carry */ +106 W1 = _W >> ((mp_word)DIGIT_BIT); +107 \} +108 +109 /* setup dest */ +110 olduse = b->used; +111 b->used = a->used+a->used; +112 +113 \{ +114 mp_digit *tmpb; +115 tmpb = b->dp; +116 for (ix = 0; ix < pa; ix++) \{ +117 *tmpb++ = W[ix] & MP_MASK; +118 \} 119 -120 /* store the current digit now that the carry isn't -121 * needed -122 */ -123 *tmpb++ = (mp_digit) (W[ix - 1] & ((mp_word) MP_MASK)); -124 \} -125 /* set the last value. Note even if the carry is zero -126 * this is required since the next step will not zero -127 * it if b originally had a value at b->dp[2*a.used] -128 */ -129 *tmpb++ = (mp_digit) (W[(newused) - 1] & ((mp_word) MP_MASK)); -130 -131 /* clear high digits of b if there were any originally */ -132 for (; ix < olduse; ix++) \{ -133 *tmpb++ = 0; -134 \} -135 \} -136 -137 mp_clamp (b); -138 return MP_OKAY; -139 \} +120 /* clear unused digits [that existed in the old copy of c] */ +121 for (; ix < olduse; ix++) \{ +122 *tmpb++ = 0; +123 \} +124 \} +125 mp_clamp (b); +126 return MP_OKAY; +127 \} +128 #endif \end{alltt} \end{small} @@ -5221,7 +5280,7 @@ 017 /* Karatsuba squaring, computes b = a*a using three 018 * half size squarings 019 * -020 * See comments of mp_karatsuba_mul for details. It +020 * See comments of karatsuba_mul for details. It 021 * is essentially the same algorithm but merely 022 * tuned to perform recursive squarings. 023 */ @@ -5317,6 +5376,7 @@ 113 ERR: 114 return err; 115 \} +116 #endif \end{alltt} \end{small} @@ -5383,25 +5443,37 @@ 020 \{ 021 int res; 022 -023 /* use Toom-Cook? */ -024 if (a->used >= TOOM_SQR_CUTOFF) \{ -025 res = mp_toom_sqr(a, b); -026 /* Karatsuba? */ -027 \} else if (a->used >= KARATSUBA_SQR_CUTOFF) \{ -028 res = mp_karatsuba_sqr (a, b); -029 \} else \{ -030 /* can we use the fast comba multiplier? */ -031 if ((a->used * 2 + 1) < MP_WARRAY && -032 a->used < -033 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) \{ -034 res = fast_s_mp_sqr (a, b); -035 \} else \{ -036 res = s_mp_sqr (a, b); -037 \} -038 \} -039 b->sign = MP_ZPOS; -040 return res; -041 \} +023 #ifdef BN_MP_TOOM_SQR_C +024 /* use Toom-Cook? */ +025 if (a->used >= TOOM_SQR_CUTOFF) \{ +026 res = mp_toom_sqr(a, b); +027 /* Karatsuba? */ +028 \} else +029 #endif +030 #ifdef BN_MP_KARATSUBA_SQR_C +031 if (a->used >= KARATSUBA_SQR_CUTOFF) \{ +032 res = mp_karatsuba_sqr (a, b); +033 \} else +034 #endif +035 \{ +036 #ifdef BN_FAST_S_MP_SQR_C +037 /* can we use the fast comba multiplier? */ +038 if ((a->used * 2 + 1) < MP_WARRAY && +039 a->used < +040 (1 << (sizeof(mp_word) * CHAR_BIT - 2*DIGIT_BIT - 1))) \{ +041 res = fast_s_mp_sqr (a, b); +042 \} else +043 #endif +044 #ifdef BN_S_MP_SQR_C +045 res = s_mp_sqr (a, b); +046 #else +047 res = MP_VAL; +048 #endif +049 \} +050 b->sign = MP_ZPOS; +051 return res; +052 \} +053 #endif \end{alltt} \end{small} @@ -5675,50 +5747,62 @@ 038 goto CLEANUP; 039 \} 040 \} else \{ -041 if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{ -042 goto CLEANUP; -043 \} -044 \} -045 -046 /* q3 = q2 / b**(k+1) */ -047 mp_rshd (&q, um + 1); -048 -049 /* x = x mod b**(k+1), quick (no division) */ -050 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) \{ -051 goto CLEANUP; -052 \} -053 -054 /* q = q * m mod b**(k+1), quick (no division) */ -055 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) \{ -056 goto CLEANUP; -057 \} -058 -059 /* x = x - q */ -060 if ((res = mp_sub (x, &q, x)) != MP_OKAY) \{ -061 goto CLEANUP; -062 \} -063 -064 /* If x < 0, add b**(k+1) to it */ -065 if (mp_cmp_d (x, 0) == MP_LT) \{ -066 mp_set (&q, 1); -067 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) -068 goto CLEANUP; -069 if ((res = mp_add (x, &q, x)) != MP_OKAY) -070 goto CLEANUP; -071 \} -072 -073 /* Back off if it's too big */ -074 while (mp_cmp (x, m) != MP_LT) \{ -075 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) \{ -076 goto CLEANUP; -077 \} -078 \} -079 -080 CLEANUP: -081 mp_clear (&q); -082 -083 return res; -084 \} +041 #ifdef BN_S_MP_MUL_HIGH_DIGS_C +042 if ((res = s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{ +043 goto CLEANUP; +044 \} +045 #elif defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) +046 if ((res = fast_s_mp_mul_high_digs (&q, mu, &q, um - 1)) != MP_OKAY) \{ +047 goto CLEANUP; +048 \} +049 #else +050 \{ +051 res = MP_VAL; +052 goto CLEANUP; +053 \} +054 #endif +055 \} +056 +057 /* q3 = q2 / b**(k+1) */ +058 mp_rshd (&q, um + 1); +059 +060 /* x = x mod b**(k+1), quick (no division) */ +061 if ((res = mp_mod_2d (x, DIGIT_BIT * (um + 1), x)) != MP_OKAY) \{ +062 goto CLEANUP; +063 \} +064 +065 /* q = q * m mod b**(k+1), quick (no division) */ +066 if ((res = s_mp_mul_digs (&q, m, &q, um + 1)) != MP_OKAY) \{ +067 goto CLEANUP; +068 \} +069 +070 /* x = x - q */ +071 if ((res = mp_sub (x, &q, x)) != MP_OKAY) \{ +072 goto CLEANUP; +073 \} +074 +075 /* If x < 0, add b**(k+1) to it */ +076 if (mp_cmp_d (x, 0) == MP_LT) \{ +077 mp_set (&q, 1); +078 if ((res = mp_lshd (&q, um + 1)) != MP_OKAY) +079 goto CLEANUP; +080 if ((res = mp_add (x, &q, x)) != MP_OKAY) +081 goto CLEANUP; +082 \} +083 +084 /* Back off if it's too big */ +085 while (mp_cmp (x, m) != MP_LT) \{ +086 if ((res = s_mp_sub (x, m, x)) != MP_OKAY) \{ +087 goto CLEANUP; +088 \} +089 \} +090 +091 CLEANUP: +092 mp_clear (&q); +093 +094 return res; +095 \} +096 #endif \end{alltt} \end{small} @@ -5761,16 +5845,16 @@ 017 /* pre-calculate the value required for Barrett reduction 018 * For a given modulus "b" it calulates the value required in "a" 019 */ -020 int -021 mp_reduce_setup (mp_int * a, mp_int * b) -022 \{ -023 int res; -024 -025 if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) \{ -026 return res; -027 \} -028 return mp_div (a, b, a, NULL); -029 \} +020 int mp_reduce_setup (mp_int * a, mp_int * b) +021 \{ +022 int res; +023 +024 if ((res = mp_2expt (a, b->used * 2 * DIGIT_BIT)) != MP_OKAY) \{ +025 return res; +026 \} +027 return mp_div (a, b, a, NULL); +028 \} +029 #endif \end{alltt} \end{small} @@ -6038,7 +6122,7 @@ 023 024 /* can the fast reduction [comba] method be used? 025 * -026 * Note that unlike in mp_mul you're safely allowed *less* +026 * Note that unlike in mul you're safely allowed *less* 027 * than the available columns [255 per default] since carries 028 * are fixed up in the inner loop. 029 */ @@ -6061,7 +6145,7 @@ 046 /* mu = ai * rho mod b 047 * 048 * The value of rho must be precalculated via -049 * bn_mp_montgomery_setup() such that +049 * montgomery_setup() such that 050 * it equals -1/n0 mod b this allows the 051 * following inner loop to reduce the 052 * input one digit at a time @@ -6125,6 +6209,7 @@ 110 111 return MP_OKAY; 112 \} +113 #endif \end{alltt} \end{small} @@ -6220,7 +6305,7 @@ 016 017 /* computes xR**-1 == x (mod N) via Montgomery Reduction 018 * -019 * This is an optimized implementation of mp_montgomery_reduce +019 * This is an optimized implementation of montgomery_reduce 020 * which uses the comba method to quickly calculate the columns of the 021 * reduction. 022 * @@ -6369,6 +6454,7 @@ 165 \} 166 return MP_OKAY; 167 \} +168 #endif \end{alltt} \end{small} @@ -6450,10 +6536,11 @@ 047 #endif 048 049 /* rho = -1/m mod b */ -050 *rho = (((mp_digit) 1 << ((mp_digit) DIGIT_BIT)) - x) & MP_MASK; +050 *rho = (((mp_word)1 << ((mp_word) DIGIT_BIT)) - x) & MP_MASK; 051 052 return MP_OKAY; 053 \} +054 #endif \end{alltt} \end{small} @@ -6719,6 +6806,7 @@ 086 \} 087 return MP_OKAY; 088 \} +089 #endif \end{alltt} \end{small} @@ -6773,6 +6861,7 @@ 024 ((mp_word)a->dp[0])); 025 \} 026 +027 #endif \end{alltt} \end{small} @@ -6830,6 +6919,7 @@ 035 return 1; 036 \} 037 +038 #endif \end{alltt} \end{small} @@ -6914,6 +7004,7 @@ 054 return res; 055 \} 056 +057 #endif \end{alltt} \end{small} @@ -6983,6 +7074,7 @@ 040 mp_clear(&tmp); 041 return MP_OKAY; 042 \} +043 #endif \end{alltt} \end{small} @@ -7031,32 +7123,34 @@ 017 /* determines if mp_reduce_2k can be used */ 018 int mp_reduce_is_2k(mp_int *a) 019 \{ -020 int ix, iy, iz, iw; -021 -022 if (a->used == 0) \{ -023 return 0; -024 \} else if (a->used == 1) \{ -025 return 1; -026 \} else if (a->used > 1) \{ -027 iy = mp_count_bits(a); -028 iz = 1; -029 iw = 1; -030 -031 /* Test every bit from the second digit up, must be 1 */ -032 for (ix = DIGIT_BIT; ix < iy; ix++) \{ -033 if ((a->dp[iw] & iz) == 0) \{ -034 return 0; -035 \} -036 iz <<= 1; -037 if (iz > (int)MP_MASK) \{ -038 ++iw; -039 iz = 1; -040 \} -041 \} -042 \} -043 return 1; -044 \} -045 +020 int ix, iy, iw; +021 mp_digit iz; +022 +023 if (a->used == 0) \{ +024 return 0; +025 \} else if (a->used == 1) \{ +026 return 1; +027 \} else if (a->used > 1) \{ +028 iy = mp_count_bits(a); +029 iz = 1; +030 iw = 1; +031 +032 /* Test every bit from the second digit up, must be 1 */ +033 for (ix = DIGIT_BIT; ix < iy; ix++) \{ +034 if ((a->dp[iw] & iz) == 0) \{ +035 return 0; +036 \} +037 iz <<= 1; +038 if (iz > (mp_digit)MP_MASK) \{ +039 ++iw; +040 iz = 1; +041 \} +042 \} +043 \} +044 return 1; +045 \} +046 +047 #endif \end{alltt} \end{small} @@ -7265,6 +7359,7 @@ 049 mp_clear (&g); 050 return MP_OKAY; 051 \} +052 #endif \end{alltt} \end{small} @@ -7470,51 +7565,72 @@ 031 032 /* if exponent X is negative we have to recurse */ 033 if (X->sign == MP_NEG) \{ -034 mp_int tmpG, tmpX; -035 int err; -036 -037 /* first compute 1/G mod P */ -038 if ((err = mp_init(&tmpG)) != MP_OKAY) \{ -039 return err; -040 \} -041 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) \{ -042 mp_clear(&tmpG); -043 return err; -044 \} -045 -046 /* now get |X| */ -047 if ((err = mp_init(&tmpX)) != MP_OKAY) \{ -048 mp_clear(&tmpG); -049 return err; -050 \} -051 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) \{ -052 mp_clear_multi(&tmpG, &tmpX, NULL); -053 return err; -054 \} -055 -056 /* and now compute (1/G)**|X| instead of G**X [X < 0] */ -057 err = mp_exptmod(&tmpG, &tmpX, P, Y); -058 mp_clear_multi(&tmpG, &tmpX, NULL); -059 return err; -060 \} -061 -062 /* is it a DR modulus? */ -063 dr = mp_dr_is_modulus(P); -064 -065 /* if not, is it a uDR modulus? */ -066 if (dr == 0) \{ -067 dr = mp_reduce_is_2k(P) << 1; -068 \} -069 -070 /* if the modulus is odd or dr != 0 use the fast method */ -071 if (mp_isodd (P) == 1 || dr != 0) \{ -072 return mp_exptmod_fast (G, X, P, Y, dr); -073 \} else \{ -074 /* otherwise use the generic Barrett reduction technique */ -075 return s_mp_exptmod (G, X, P, Y); -076 \} -077 \} -078 +034 #ifdef BN_MP_INVMOD_C +035 mp_int tmpG, tmpX; +036 int err; +037 +038 /* first compute 1/G mod P */ +039 if ((err = mp_init(&tmpG)) != MP_OKAY) \{ +040 return err; +041 \} +042 if ((err = mp_invmod(G, P, &tmpG)) != MP_OKAY) \{ +043 mp_clear(&tmpG); +044 return err; +045 \} +046 +047 /* now get |X| */ +048 if ((err = mp_init(&tmpX)) != MP_OKAY) \{ +049 mp_clear(&tmpG); +050 return err; +051 \} +052 if ((err = mp_abs(X, &tmpX)) != MP_OKAY) \{ +053 mp_clear_multi(&tmpG, &tmpX, NULL); +054 return err; +055 \} +056 +057 /* and now compute (1/G)**|X| instead of G**X [X < 0] */ +058 err = mp_exptmod(&tmpG, &tmpX, P, Y); +059 mp_clear_multi(&tmpG, &tmpX, NULL); +060 return err; +061 #else +062 /* no invmod */ +063 return MP_VAL +064 #endif +065 \} +066 +067 #ifdef BN_MP_DR_IS_MODULUS_C +068 /* is it a DR modulus? */ +069 dr = mp_dr_is_modulus(P); +070 #else +071 dr = 0; +072 #endif +073 +074 #ifdef BN_MP_REDUCE_IS_2K_C +075 /* if not, is it a uDR modulus? */ +076 if (dr == 0) \{ +077 dr = mp_reduce_is_2k(P) << 1; +078 \} +079 #endif +080 +081 /* if the modulus is odd or dr != 0 use the fast method */ +082 #ifdef BN_MP_EXPTMOD_FAST_C +083 if (mp_isodd (P) == 1 || dr != 0) \{ +084 return mp_exptmod_fast (G, X, P, Y, dr); +085 \} else \{ +086 #endif +087 #ifdef BN_S_MP_EXPTMOD_C +088 /* otherwise use the generic Barrett reduction technique */ +089 return s_mp_exptmod (G, X, P, Y); +090 #else +091 /* no exptmod for evens */ +092 return MP_VAL; +093 #endif +094 #ifdef BN_MP_EXPTMOD_FAST_C +095 \} +096 #endif +097 \} +098 +099 #endif \end{alltt} \end{small} @@ -7523,8 +7639,8 @@ the modular inverse of $G$ and $tmpX$ is assigned the absolute value of $X$. The algorithm will recuse with these new values with a positive exponent. -If the exponent is positive the algorithm resumes the exponentiation. Line 63 determines if the modulus is of the restricted Diminished Radix -form. If it is not line 67 attempts to determine if it is of a unrestricted Diminished Radix form. The integer $dr$ will take on one +If the exponent is positive the algorithm resumes the exponentiation. Line 69 determines if the modulus is of the restricted Diminished Radix +form. If it is not line 77 attempts to determine if it is of a unrestricted Diminished Radix form. The integer $dr$ will take on one of three values. \begin{enumerate} @@ -7533,7 +7649,7 @@ \item $dr = 2$ means that the modulus is of unrestricted Diminished Radix form. \end{enumerate} -Line 70 determines if the fast modular exponentiation algorithm can be used. It is allowed if $dr \ne 0$ or if the modulus is odd. Otherwise, +Line 67 determines if the fast modular exponentiation algorithm can be used. It is allowed if $dr \ne 0$ or if the modulus is odd. Otherwise, the slower s\_mp\_exptmod algorithm is used which uses Barrett reduction. \subsection{Barrett Modular Exponentiation} @@ -7913,6 +8029,7 @@ 232 \} 233 return err; 234 \} +235 #endif \end{alltt} \end{small} @@ -7981,10 +8098,11 @@ 036 a->used = b / DIGIT_BIT + 1; 037 038 /* put the single bit in its place */ -039 a->dp[b / DIGIT_BIT] = 1 << (b % DIGIT_BIT); +039 a->dp[b / DIGIT_BIT] = ((mp_digit)1) << (b % DIGIT_BIT); 040 041 return MP_OKAY; 042 \} +043 #endif \end{alltt} \end{small} @@ -8234,201 +8352,277 @@ \vspace{-3mm} \begin{alltt} 016 -017 /* integer signed division. -018 * c*b + d == a [e.g. a/b, c=quotient, d=remainder] -019 * HAC pp.598 Algorithm 14.20 -020 * -021 * Note that the description in HAC is horribly -022 * incomplete. For example, it doesn't consider -023 * the case where digits are removed from 'x' in -024 * the inner loop. It also doesn't consider the -025 * case that y has fewer than three digits, etc.. -026 * -027 * The overall algorithm is as described as -028 * 14.20 from HAC but fixed to treat these cases. -029 */ -030 int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d) -031 \{ -032 mp_int q, x, y, t1, t2; -033 int res, n, t, i, norm, neg; -034 -035 /* is divisor zero ? */ -036 if (mp_iszero (b) == 1) \{ -037 return MP_VAL; -038 \} -039 -040 /* if a < b then q=0, r = a */ -041 if (mp_cmp_mag (a, b) == MP_LT) \{ -042 if (d != NULL) \{ -043 res = mp_copy (a, d); -044 \} else \{ -045 res = MP_OKAY; -046 \} -047 if (c != NULL) \{ -048 mp_zero (c); -049 \} -050 return res; -051 \} -052 -053 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) \{ -054 return res; -055 \} -056 q.used = a->used + 2; +017 #ifdef BN_MP_DIV_SMALL +018 +019 /* slower bit-bang division... also smaller */ +020 int mp_div(mp_int * a, mp_int * b, mp_int * c, mp_int * d) +021 \{ +022 mp_int ta, tb, tq, q; +023 int res, n, n2; +024 +025 /* is divisor zero ? */ +026 if (mp_iszero (b) == 1) \{ +027 return MP_VAL; +028 \} +029 +030 /* if a < b then q=0, r = a */ +031 if (mp_cmp_mag (a, b) == MP_LT) \{ +032 if (d != NULL) \{ +033 res = mp_copy (a, d); +034 \} else \{ +035 res = MP_OKAY; +036 \} +037 if (c != NULL) \{ +038 mp_zero (c); +039 \} +040 return res; +041 \} +042 +043 /* init our temps */ +044 if ((res = mp_init_multi(&ta, &tb, &tq, &q, NULL) != MP_OKAY)) \{ +045 return res; +046 \} +047 +048 +049 mp_set(&tq, 1); +050 n = mp_count_bits(a) - mp_count_bits(b); +051 if (((res = mp_copy(a, &ta)) != MP_OKAY) || +052 ((res = mp_copy(b, &tb)) != MP_OKAY) || +053 ((res = mp_mul_2d(&tb, n, &tb)) != MP_OKAY) || +054 ((res = mp_mul_2d(&tq, n, &tq)) != MP_OKAY)) \{ +055 goto __ERR; +056 \} 057 -058 if ((res = mp_init (&t1)) != MP_OKAY) \{ -059 goto __Q; -060 \} -061 -062 if ((res = mp_init (&t2)) != MP_OKAY) \{ -063 goto __T1; -064 \} -065 -066 if ((res = mp_init_copy (&x, a)) != MP_OKAY) \{ -067 goto __T2; -068 \} -069 -070 if ((res = mp_init_copy (&y, b)) != MP_OKAY) \{ -071 goto __X; -072 \} -073 -074 /* fix the sign */ -075 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; -076 x.sign = y.sign = MP_ZPOS; -077 -078 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */ -079 norm = mp_count_bits(&y) % DIGIT_BIT; -080 if (norm < (int)(DIGIT_BIT-1)) \{ -081 norm = (DIGIT_BIT-1) - norm; -082 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) \{ -083 goto __Y; -084 \} -085 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) \{ -086 goto __Y; -087 \} -088 \} else \{ -089 norm = 0; -090 \} -091 -092 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */ -093 n = x.used - 1; -094 t = y.used - 1; -095 -096 /* while (x >= y*b**n-t) do \{ q[n-t] += 1; x -= y*b**\{n-t\} \} */ -097 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) \{ /* y = y*b**\{n-t\} */ -098 goto __Y; -099 \} -100 -101 while (mp_cmp (&x, &y) != MP_LT) \{ -102 ++(q.dp[n - t]); -103 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) \{ -104 goto __Y; -105 \} -106 \} -107 -108 /* reset y by shifting it back down */ -109 mp_rshd (&y, n - t); -110 -111 /* step 3. for i from n down to (t + 1) */ -112 for (i = n; i >= (t + 1); i--) \{ -113 if (i > x.used) \{ -114 continue; -115 \} -116 -117 /* step 3.1 if xi == yt then set q\{i-t-1\} to b-1, -118 * otherwise set q\{i-t-1\} to (xi*b + x\{i-1\})/yt */ -119 if (x.dp[i] == y.dp[t]) \{ -120 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1); -121 \} else \{ -122 mp_word tmp; -123 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT); -124 tmp |= ((mp_word) x.dp[i - 1]); -125 tmp /= ((mp_word) y.dp[t]); -126 if (tmp > (mp_word) MP_MASK) -127 tmp = MP_MASK; -128 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK)); -129 \} -130 -131 /* while (q\{i-t-1\} * (yt * b + y\{t-1\})) > -132 xi * b**2 + xi-1 * b + xi-2 -133 -134 do q\{i-t-1\} -= 1; -135 */ -136 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK; -137 do \{ -138 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK; -139 -140 /* find left hand */ -141 mp_zero (&t1); -142 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1]; -143 t1.dp[1] = y.dp[t]; -144 t1.used = 2; -145 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) \{ -146 goto __Y; -147 \} -148 -149 /* find right hand */ -150 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2]; -151 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1]; -152 t2.dp[2] = x.dp[i]; -153 t2.used = 3; -154 \} while (mp_cmp_mag(&t1, &t2) == MP_GT); -155 -156 /* step 3.3 x = x - q\{i-t-1\} * y * b**\{i-t-1\} */ -157 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) \{ -158 goto __Y; -159 \} -160 -161 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{ -162 goto __Y; -163 \} -164 -165 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) \{ -166 goto __Y; -167 \} -168 -169 /* if x < 0 then \{ x = x + y*b**\{i-t-1\}; q\{i-t-1\} -= 1; \} */ -170 if (x.sign == MP_NEG) \{ -171 if ((res = mp_copy (&y, &t1)) != MP_OKAY) \{ -172 goto __Y; -173 \} -174 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{ -175 goto __Y; -176 \} -177 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) \{ -178 goto __Y; -179 \} -180 -181 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK; -182 \} -183 \} -184 -185 /* now q is the quotient and x is the remainder -186 * [which we have to normalize] -187 */ -188 -189 /* get sign before writing to c */ -190 x.sign = a->sign; -191 -192 if (c != NULL) \{ -193 mp_clamp (&q); -194 mp_exch (&q, c); -195 c->sign = neg; -196 \} -197 -198 if (d != NULL) \{ -199 mp_div_2d (&x, norm, &x, NULL); -200 mp_exch (&x, d); -201 \} +058 while (n-- >= 0) \{ +059 if (mp_cmp(&tb, &ta) != MP_GT) \{ +060 if (((res = mp_sub(&ta, &tb, &ta)) != MP_OKAY) || +061 ((res = mp_add(&q, &tq, &q)) != MP_OKAY)) \{ +062 goto __ERR; +063 \} +064 \} +065 if (((res = mp_div_2d(&tb, 1, &tb, NULL)) != MP_OKAY) || +066 ((res = mp_div_2d(&tq, 1, &tq, NULL)) != MP_OKAY)) \{ +067 goto __ERR; +068 \} +069 \} +070 +071 /* now q == quotient and ta == remainder */ +072 n = a->sign; +073 n2 = (a->sign == b->sign ? MP_ZPOS : MP_NEG); +074 if (c != NULL) \{ +075 mp_exch(c, &q); +076 c->sign = n2; +077 \} +078 if (d != NULL) \{ +079 mp_exch(d, &ta); +080 d->sign = n; +081 \} +082 __ERR: +083 mp_clear_multi(&ta, &tb, &tq, &q, NULL); +084 return res; +085 \} +086 +087 #else +088 +089 /* integer signed division. +090 * c*b + d == a [e.g. a/b, c=quotient, d=remainder] +091 * HAC pp.598 Algorithm 14.20 +092 * +093 * Note that the description in HAC is horribly +094 * incomplete. For example, it doesn't consider +095 * the case where digits are removed from 'x' in +096 * the inner loop. It also doesn't consider the +097 * case that y has fewer than three digits, etc.. +098 * +099 * The overall algorithm is as described as +100 * 14.20 from HAC but fixed to treat these cases. +101 */ +102 int mp_div (mp_int * a, mp_int * b, mp_int * c, mp_int * d) +103 \{ +104 mp_int q, x, y, t1, t2; +105 int res, n, t, i, norm, neg; +106 +107 /* is divisor zero ? */ +108 if (mp_iszero (b) == 1) \{ +109 return MP_VAL; +110 \} +111 +112 /* if a < b then q=0, r = a */ +113 if (mp_cmp_mag (a, b) == MP_LT) \{ +114 if (d != NULL) \{ +115 res = mp_copy (a, d); +116 \} else \{ +117 res = MP_OKAY; +118 \} +119 if (c != NULL) \{ +120 mp_zero (c); +121 \} +122 return res; +123 \} +124 +125 if ((res = mp_init_size (&q, a->used + 2)) != MP_OKAY) \{ +126 return res; +127 \} +128 q.used = a->used + 2; +129 +130 if ((res = mp_init (&t1)) != MP_OKAY) \{ +131 goto __Q; +132 \} +133 +134 if ((res = mp_init (&t2)) != MP_OKAY) \{ +135 goto __T1; +136 \} +137 +138 if ((res = mp_init_copy (&x, a)) != MP_OKAY) \{ +139 goto __T2; +140 \} +141 +142 if ((res = mp_init_copy (&y, b)) != MP_OKAY) \{ +143 goto __X; +144 \} +145 +146 /* fix the sign */ +147 neg = (a->sign == b->sign) ? MP_ZPOS : MP_NEG; +148 x.sign = y.sign = MP_ZPOS; +149 +150 /* normalize both x and y, ensure that y >= b/2, [b == 2**DIGIT_BIT] */ +151 norm = mp_count_bits(&y) % DIGIT_BIT; +152 if (norm < (int)(DIGIT_BIT-1)) \{ +153 norm = (DIGIT_BIT-1) - norm; +154 if ((res = mp_mul_2d (&x, norm, &x)) != MP_OKAY) \{ +155 goto __Y; +156 \} +157 if ((res = mp_mul_2d (&y, norm, &y)) != MP_OKAY) \{ +158 goto __Y; +159 \} +160 \} else \{ +161 norm = 0; +162 \} +163 +164 /* note hac does 0 based, so if used==5 then its 0,1,2,3,4, e.g. use 4 */ +165 n = x.used - 1; +166 t = y.used - 1; +167 +168 /* while (x >= y*b**n-t) do \{ q[n-t] += 1; x -= y*b**\{n-t\} \} */ +169 if ((res = mp_lshd (&y, n - t)) != MP_OKAY) \{ /* y = y*b**\{n-t\} */ +170 goto __Y; +171 \} +172 +173 while (mp_cmp (&x, &y) != MP_LT) \{ +174 ++(q.dp[n - t]); +175 if ((res = mp_sub (&x, &y, &x)) != MP_OKAY) \{ +176 goto __Y; +177 \} +178 \} +179 +180 /* reset y by shifting it back down */ +181 mp_rshd (&y, n - t); +182 +183 /* step 3. for i from n down to (t + 1) */ +184 for (i = n; i >= (t + 1); i--) \{ +185 if (i > x.used) \{ +186 continue; +187 \} +188 +189 /* step 3.1 if xi == yt then set q\{i-t-1\} to b-1, +190 * otherwise set q\{i-t-1\} to (xi*b + x\{i-1\})/yt */ +191 if (x.dp[i] == y.dp[t]) \{ +192 q.dp[i - t - 1] = ((((mp_digit)1) << DIGIT_BIT) - 1); +193 \} else \{ +194 mp_word tmp; +195 tmp = ((mp_word) x.dp[i]) << ((mp_word) DIGIT_BIT); +196 tmp |= ((mp_word) x.dp[i - 1]); +197 tmp /= ((mp_word) y.dp[t]); +198 if (tmp > (mp_word) MP_MASK) +199 tmp = MP_MASK; +200 q.dp[i - t - 1] = (mp_digit) (tmp & (mp_word) (MP_MASK)); +201 \} 202 -203 res = MP_OKAY; -204 -205 __Y:mp_clear (&y); -206 __X:mp_clear (&x); -207 __T2:mp_clear (&t2); -208 __T1:mp_clear (&t1); -209 __Q:mp_clear (&q); -210 return res; -211 \} +203 /* while (q\{i-t-1\} * (yt * b + y\{t-1\})) > +204 xi * b**2 + xi-1 * b + xi-2 +205 +206 do q\{i-t-1\} -= 1; +207 */ +208 q.dp[i - t - 1] = (q.dp[i - t - 1] + 1) & MP_MASK; +209 do \{ +210 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1) & MP_MASK; +211 +212 /* find left hand */ +213 mp_zero (&t1); +214 t1.dp[0] = (t - 1 < 0) ? 0 : y.dp[t - 1]; +215 t1.dp[1] = y.dp[t]; +216 t1.used = 2; +217 if ((res = mp_mul_d (&t1, q.dp[i - t - 1], &t1)) != MP_OKAY) \{ +218 goto __Y; +219 \} +220 +221 /* find right hand */ +222 t2.dp[0] = (i - 2 < 0) ? 0 : x.dp[i - 2]; +223 t2.dp[1] = (i - 1 < 0) ? 0 : x.dp[i - 1]; +224 t2.dp[2] = x.dp[i]; +225 t2.used = 3; +226 \} while (mp_cmp_mag(&t1, &t2) == MP_GT); +227 +228 /* step 3.3 x = x - q\{i-t-1\} * y * b**\{i-t-1\} */ +229 if ((res = mp_mul_d (&y, q.dp[i - t - 1], &t1)) != MP_OKAY) \{ +230 goto __Y; +231 \} +232 +233 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{ +234 goto __Y; +235 \} +236 +237 if ((res = mp_sub (&x, &t1, &x)) != MP_OKAY) \{ +238 goto __Y; +239 \} +240 +241 /* if x < 0 then \{ x = x + y*b**\{i-t-1\}; q\{i-t-1\} -= 1; \} */ +242 if (x.sign == MP_NEG) \{ +243 if ((res = mp_copy (&y, &t1)) != MP_OKAY) \{ +244 goto __Y; +245 \} +246 if ((res = mp_lshd (&t1, i - t - 1)) != MP_OKAY) \{ +247 goto __Y; +248 \} +249 if ((res = mp_add (&x, &t1, &x)) != MP_OKAY) \{ +250 goto __Y; +251 \} +252 +253 q.dp[i - t - 1] = (q.dp[i - t - 1] - 1UL) & MP_MASK; +254 \} +255 \} +256 +257 /* now q is the quotient and x is the remainder +258 * [which we have to normalize] +259 */ +260 +261 /* get sign before writing to c */ +262 x.sign = x.used == 0 ? MP_ZPOS : a->sign; +263 +264 if (c != NULL) \{ +265 mp_clamp (&q); +266 mp_exch (&q, c); +267 c->sign = neg; +268 \} +269 +270 if (d != NULL) \{ +271 mp_div_2d (&x, norm, &x, NULL); +272 mp_exch (&x, d); +273 \} +274 +275 res = MP_OKAY; +276 +277 __Y:mp_clear (&y); +278 __X:mp_clear (&x); +279 __T2:mp_clear (&t2); +280 __T1:mp_clear (&t1); +281 __Q:mp_clear (&q); +282 return res; +283 \} +284 +285 #endif +286 +287 #endif \end{alltt} \end{small} @@ -8440,23 +8634,23 @@ mp_div(&a, &b, &c, NULL); /* c = [a/b] */ \end{verbatim} -Lines 36 and 42 handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor -respectively. After the two trivial cases all of the temporary variables are initialized. Line 75 determines the sign of +Lines 37 and 44 handle the two trivial cases of inputs which are division by zero and dividend smaller than the divisor +respectively. After the two trivial cases all of the temporary variables are initialized. Line 105 determines the sign of the quotient and line 76 ensures that both $x$ and $y$ are positive. -The number of bits in the leading digit is calculated on line 80. Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits +The number of bits in the leading digit is calculated on line 105. Implictly an mp\_int with $r$ digits will require $lg(\beta)(r-1) + k$ bits of precision which when reduced modulo $lg(\beta)$ produces the value of $k$. In this case $k$ is the number of bits in the leading digit which is exactly what is required. For the algorithm to operate $k$ must equal $lg(\beta) - 1$ and when it does not the inputs must be normalized by shifting them to the left by $lg(\beta) - 1 - k$ bits. Throughout the variables $n$ and $t$ will represent the highest digit of $x$ and $y$ respectively. These are first used to produce the -leading digit of the quotient. The loop beginning on line 112 will produce the remainder of the quotient digits. - -The conditional ``continue'' on line 113 is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the +leading digit of the quotient. The loop beginning on line 183 will produce the remainder of the quotient digits. + +The conditional ``continue'' on line 114 is used to prevent the algorithm from reading past the leading edge of $x$ which can occur when the algorithm eliminates multiple non-zero digits in a single iteration. This ensures that $x_i$ is always non-zero since by definition the digits above the $i$'th position $x$ must be zero in order for the quotient to be precise\footnote{Precise as far as integer division is concerned.}. -Lines 142, 143 and 150 through 152 manually construct the high accuracy estimations by setting the digits of the two mp\_int +Lines 130, 130 and 134 through 134 manually construct the high accuracy estimations by setting the digits of the two mp\_int variables directly. \section{Single Digit Helpers} @@ -8582,6 +8776,7 @@ 101 return MP_OKAY; 102 \} 103 +104 #endif \end{alltt} \end{small} @@ -8689,6 +8884,7 @@ 070 071 return MP_OKAY; 072 \} +073 #endif \end{alltt} \end{small} @@ -8785,7 +8981,7 @@ 054 /* power of two ? */ 055 if (s_is_power_of_two(b, &ix) == 1) \{ 056 if (d != NULL) \{ -057 *d = a->dp[0] & ((1<<ix) - 1); +057 *d = a->dp[0] & ((((mp_digit)1)<<ix) - 1); 058 \} 059 if (c != NULL) \{ 060 return mp_div_2d(a, ix, c, NULL); @@ -8793,44 +8989,47 @@ 062 return MP_OKAY; 063 \} 064 -065 /* three? */ -066 if (b == 3) \{ -067 return mp_div_3(a, c, d); -068 \} -069 -070 /* no easy answer [c'est la vie]. Just division */ -071 if ((res = mp_init_size(&q, a->used)) != MP_OKAY) \{ -072 return res; -073 \} -074 -075 q.used = a->used; -076 q.sign = a->sign; -077 w = 0; -078 for (ix = a->used - 1; ix >= 0; ix--) \{ -079 w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]); -080 -081 if (w >= b) \{ -082 t = (mp_digit)(w / b); -083 w -= ((mp_word)t) * ((mp_word)b); -084 \} else \{ -085 t = 0; -086 \} -087 q.dp[ix] = (mp_digit)t; -088 \} -089 -090 if (d != NULL) \{ -091 *d = (mp_digit)w; -092 \} -093 -094 if (c != NULL) \{ -095 mp_clamp(&q); -096 mp_exch(&q, c); -097 \} -098 mp_clear(&q); -099 -100 return res; -101 \} -102 +065 #ifdef BN_MP_DIV_3_C +066 /* three? */ +067 if (b == 3) \{ +068 return mp_div_3(a, c, d); +069 \} +070 #endif +071 +072 /* no easy answer [c'est la vie]. Just division */ +073 if ((res = mp_init_size(&q, a->used)) != MP_OKAY) \{ +074 return res; +075 \} +076 +077 q.used = a->used; +078 q.sign = a->sign; +079 w = 0; +080 for (ix = a->used - 1; ix >= 0; ix--) \{ +081 w = (w << ((mp_word)DIGIT_BIT)) | ((mp_word)a->dp[ix]); +082 +083 if (w >= b) \{ +084 t = (mp_digit)(w / b); +085 w -= ((mp_word)t) * ((mp_word)b); +086 \} else \{ +087 t = 0; +088 \} +089 q.dp[ix] = (mp_digit)t; +090 \} +091 +092 if (d != NULL) \{ +093 *d = (mp_digit)w; +094 \} +095 +096 if (c != NULL) \{ +097 mp_clamp(&q); +098 mp_exch(&q, c); +099 \} +100 mp_clear(&q); +101 +102 return res; +103 \} +104 +105 #endif \end{alltt} \end{small} @@ -9016,6 +9215,7 @@ 124 __T1:mp_clear (&t1); 125 return res; 126 \} +127 #endif \end{alltt} \end{small} @@ -9091,6 +9291,7 @@ 047 048 return MP_OKAY; 049 \} +050 #endif \end{alltt} \end{small} @@ -9234,6 +9435,7 @@ 074 \} 075 return MP_OKAY; 076 \} +077 #endif \end{alltt} \end{small} @@ -9352,6 +9554,7 @@ 067 return MP_OKAY; 068 \} 069 +070 #endif \end{alltt} \end{small} @@ -9631,6 +9834,7 @@ 105 __U:mp_clear (&v); 106 return res; 107 \} +108 #endif \end{alltt} \end{small} @@ -9725,6 +9929,7 @@ 052 mp_clear_multi (&t1, &t2, NULL); 053 return res; 054 \} +055 #endif \end{alltt} \end{small} @@ -9966,6 +10171,7 @@ 097 __A1:mp_clear (&a1); 098 return res; 099 \} +100 #endif \end{alltt} \end{small} @@ -10095,161 +10301,25 @@ 017 /* hac 14.61, pp608 */ 018 int mp_invmod (mp_int * a, mp_int * b, mp_int * c) 019 \{ -020 mp_int x, y, u, v, A, B, C, D; -021 int res; -022 -023 /* b cannot be negative */ -024 if (b->sign == MP_NEG || mp_iszero(b) == 1) \{ -025 return MP_VAL; -026 \} -027 -028 /* if the modulus is odd we can use a faster routine instead */ -029 if (mp_isodd (b) == 1) \{ -030 return fast_mp_invmod (a, b, c); -031 \} -032 -033 /* init temps */ -034 if ((res = mp_init_multi(&x, &y, &u, &v, -035 &A, &B, &C, &D, NULL)) != MP_OKAY) \{ -036 return res; -037 \} -038 -039 /* x = a, y = b */ -040 if ((res = mp_copy (a, &x)) != MP_OKAY) \{ -041 goto __ERR; -042 \} -043 if ((res = mp_copy (b, &y)) != MP_OKAY) \{ -044 goto __ERR; -045 \} -046 -047 /* 2. [modified] if x,y are both even then return an error! */ -048 if (mp_iseven (&x) == 1 && mp_iseven (&y) == 1) \{ -049 res = MP_VAL; -050 goto __ERR; -051 \} -052 -053 /* 3. u=x, v=y, A=1, B=0, C=0,D=1 */ -054 if ((res = mp_copy (&x, &u)) != MP_OKAY) \{ -055 goto __ERR; -056 \} -057 if ((res = mp_copy (&y, &v)) != MP_OKAY) \{ -058 goto __ERR; -059 \} -060 mp_set (&A, 1); -061 mp_set (&D, 1); -062 -063 top: -064 /* 4. while u is even do */ -065 while (mp_iseven (&u) == 1) \{ -066 /* 4.1 u = u/2 */ -067 if ((res = mp_div_2 (&u, &u)) != MP_OKAY) \{ -068 goto __ERR; -069 \} -070 /* 4.2 if A or B is odd then */ -071 if (mp_isodd (&A) == 1 || mp_isodd (&B) == 1) \{ -072 /* A = (A+y)/2, B = (B-x)/2 */ -073 if ((res = mp_add (&A, &y, &A)) != MP_OKAY) \{ -074 goto __ERR; -075 \} -076 if ((res = mp_sub (&B, &x, &B)) != MP_OKAY) \{ -077 goto __ERR; -078 \} -079 \} -080 /* A = A/2, B = B/2 */ -081 if ((res = mp_div_2 (&A, &A)) != MP_OKAY) \{ -082 goto __ERR; -083 \} -084 if ((res = mp_div_2 (&B, &B)) != MP_OKAY) \{ -085 goto __ERR; -086 \} -087 \} -088 -089 /* 5. while v is even do */ -090 while (mp_iseven (&v) == 1) \{ -091 /* 5.1 v = v/2 */ -092 if ((res = mp_div_2 (&v, &v)) != MP_OKAY) \{ -093 goto __ERR; -094 \} -095 /* 5.2 if C or D is odd then */ -096 if (mp_isodd (&C) == 1 || mp_isodd (&D) == 1) \{ -097 /* C = (C+y)/2, D = (D-x)/2 */ -098 if ((res = mp_add (&C, &y, &C)) != MP_OKAY) \{ -099 goto __ERR; -100 \} -101 if ((res = mp_sub (&D, &x, &D)) != MP_OKAY) \{ -102 goto __ERR; -103 \} -104 \} -105 /* C = C/2, D = D/2 */ -106 if ((res = mp_div_2 (&C, &C)) != MP_OKAY) \{ -107 goto __ERR; -108 \} -109 if ((res = mp_div_2 (&D, &D)) != MP_OKAY) \{ -110 goto __ERR; -111 \} -112 \} -113 -114 /* 6. if u >= v then */ -115 if (mp_cmp (&u, &v) != MP_LT) \{ -116 /* u = u - v, A = A - C, B = B - D */ -117 if ((res = mp_sub (&u, &v, &u)) != MP_OKAY) \{ -118 goto __ERR; -119 \} -120 -121 if ((res = mp_sub (&A, &C, &A)) != MP_OKAY) \{ -122 goto __ERR; -123 \} -124 -125 if ((res = mp_sub (&B, &D, &B)) != MP_OKAY) \{ -126 goto __ERR; -127 \} -128 \} else \{ -129 /* v - v - u, C = C - A, D = D - B */ -130 if ((res = mp_sub (&v, &u, &v)) != MP_OKAY) \{ -131 goto __ERR; -132 \} -133 -134 if ((res = mp_sub (&C, &A, &C)) != MP_OKAY) \{ -135 goto __ERR; -136 \} -137 -138 if ((res = mp_sub (&D, &B, &D)) != MP_OKAY) \{ -139 goto __ERR; -140 \} -141 \} -142 -143 /* if not zero goto step 4 */ -144 if (mp_iszero (&u) == 0) -145 goto top; -146 -147 /* now a = C, b = D, gcd == g*v */ -148 -149 /* if v != 1 then there is no inverse */ -150 if (mp_cmp_d (&v, 1) != MP_EQ) \{ -151 res = MP_VAL; -152 goto __ERR; -153 \} -154 -155 /* if its too low */ -156 while (mp_cmp_d(&C, 0) == MP_LT) \{ -157 if ((res = mp_add(&C, b, &C)) != MP_OKAY) \{ -158 goto __ERR; -159 \} -160 \} -161 -162 /* too big */ -163 while (mp_cmp_mag(&C, b) != MP_LT) \{ -164 if ((res = mp_sub(&C, b, &C)) != MP_OKAY) \{ -165 goto __ERR; -166 \} -167 \} -168 -169 /* C is now the inverse */ -170 mp_exch (&C, c); -171 res = MP_OKAY; -172 __ERR:mp_clear_multi (&x, &y, &u, &v, &A, &B, &C, &D, NULL); -173 return res; -174 \} +020 /* b cannot be negative */ +021 if (b->sign == MP_NEG || mp_iszero(b) == 1) \{ +022 return MP_VAL; +023 \} +024 +025 #ifdef BN_FAST_MP_INVMOD_C +026 /* if the modulus is odd we can use a faster routine instead */ +027 if (mp_isodd (b) == 1) \{ +028 return fast_mp_invmod (a, b, c); +029 \} +030 #endif +031 +032 #ifdef BN_MP_INVMOD_SLOW_C +033 return mp_invmod_slow(a, b, c); +034 #endif +035 +036 return MP_VAL; +037 \} +038 #endif \end{alltt} \end{small} @@ -10350,6 +10420,7 @@ 042 043 return MP_OKAY; 044 \} +045 #endif \end{alltt} \end{small} @@ -10400,6 +10471,7 @@ 053 0x062B, 0x062F, 0x063D, 0x0641, 0x0647, 0x0649, 0x064D, 0x0653 054 #endif 055 \}; +056 #endif \end{alltt} \end{small} @@ -10487,6 +10559,7 @@ 054 __T:mp_clear (&t); 055 return err; 056 \} +057 #endif \end{alltt} \end{small} @@ -10621,6 +10694,7 @@ 095 __N1:mp_clear (&n1); 096 return err; 097 \} +098 #endif \end{alltt} \end{small}
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/tommath_class.h Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,951 @@ +#if !(defined(LTM1) && defined(LTM2) && defined(LTM3)) +#if defined(LTM2) +#define LTM3 +#endif +#if defined(LTM1) +#define LTM2 +#endif +#define LTM1 + +#if defined(LTM_ALL) +#define BN_ERROR_C +#define BN_FAST_MP_INVMOD_C +#define BN_FAST_MP_MONTGOMERY_REDUCE_C +#define BN_FAST_S_MP_MUL_DIGS_C +#define BN_FAST_S_MP_MUL_HIGH_DIGS_C +#define BN_FAST_S_MP_SQR_C +#define BN_MP_2EXPT_C +#define BN_MP_ABS_C +#define BN_MP_ADD_C +#define BN_MP_ADD_D_C +#define BN_MP_ADDMOD_C +#define BN_MP_AND_C +#define BN_MP_CLAMP_C +#define BN_MP_CLEAR_C +#define BN_MP_CLEAR_MULTI_C +#define BN_MP_CMP_C +#define BN_MP_CMP_D_C +#define BN_MP_CMP_MAG_C +#define BN_MP_CNT_LSB_C +#define BN_MP_COPY_C +#define BN_MP_COUNT_BITS_C +#define BN_MP_DIV_C +#define BN_MP_DIV_2_C +#define BN_MP_DIV_2D_C +#define BN_MP_DIV_3_C +#define BN_MP_DIV_D_C +#define BN_MP_DR_IS_MODULUS_C +#define BN_MP_DR_REDUCE_C +#define BN_MP_DR_SETUP_C +#define BN_MP_EXCH_C +#define BN_MP_EXPT_D_C +#define BN_MP_EXPTMOD_C +#define BN_MP_EXPTMOD_FAST_C +#define BN_MP_EXTEUCLID_C +#define BN_MP_FREAD_C +#define BN_MP_FWRITE_C +#define BN_MP_GCD_C +#define BN_MP_GET_INT_C +#define BN_MP_GROW_C +#define BN_MP_INIT_C +#define BN_MP_INIT_COPY_C +#define BN_MP_INIT_MULTI_C +#define BN_MP_INIT_SET_C +#define BN_MP_INIT_SET_INT_C +#define BN_MP_INIT_SIZE_C +#define BN_MP_INVMOD_C +#define BN_MP_INVMOD_SLOW_C +#define BN_MP_IS_SQUARE_C +#define BN_MP_JACOBI_C +#define BN_MP_KARATSUBA_MUL_C +#define BN_MP_KARATSUBA_SQR_C +#define BN_MP_LCM_C +#define BN_MP_LSHD_C +#define BN_MP_MOD_C +#define BN_MP_MOD_2D_C +#define BN_MP_MOD_D_C +#define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C +#define BN_MP_MONTGOMERY_REDUCE_C +#define BN_MP_MONTGOMERY_SETUP_C +#define BN_MP_MUL_C +#define BN_MP_MUL_2_C +#define BN_MP_MUL_2D_C +#define BN_MP_MUL_D_C +#define BN_MP_MULMOD_C +#define BN_MP_N_ROOT_C +#define BN_MP_NEG_C +#define BN_MP_OR_C +#define BN_MP_PRIME_FERMAT_C +#define BN_MP_PRIME_IS_DIVISIBLE_C +#define BN_MP_PRIME_IS_PRIME_C +#define BN_MP_PRIME_MILLER_RABIN_C +#define BN_MP_PRIME_NEXT_PRIME_C +#define BN_MP_PRIME_RABIN_MILLER_TRIALS_C +#define BN_MP_PRIME_RANDOM_EX_C +#define BN_MP_RADIX_SIZE_C +#define BN_MP_RADIX_SMAP_C +#define BN_MP_RAND_C +#define BN_MP_READ_RADIX_C +#define BN_MP_READ_SIGNED_BIN_C +#define BN_MP_READ_UNSIGNED_BIN_C +#define BN_MP_REDUCE_C +#define BN_MP_REDUCE_2K_C +#define BN_MP_REDUCE_2K_SETUP_C +#define BN_MP_REDUCE_IS_2K_C +#define BN_MP_REDUCE_SETUP_C +#define BN_MP_RSHD_C +#define BN_MP_SET_C +#define BN_MP_SET_INT_C +#define BN_MP_SHRINK_C +#define BN_MP_SIGNED_BIN_SIZE_C +#define BN_MP_SQR_C +#define BN_MP_SQRMOD_C +#define BN_MP_SQRT_C +#define BN_MP_SUB_C +#define BN_MP_SUB_D_C +#define BN_MP_SUBMOD_C +#define BN_MP_TO_SIGNED_BIN_C +#define BN_MP_TO_UNSIGNED_BIN_C +#define BN_MP_TOOM_MUL_C +#define BN_MP_TOOM_SQR_C +#define BN_MP_TORADIX_C +#define BN_MP_TORADIX_N_C +#define BN_MP_UNSIGNED_BIN_SIZE_C +#define BN_MP_XOR_C +#define BN_MP_ZERO_C +#define BN_PRIME_TAB_C +#define BN_REVERSE_C +#define BN_S_MP_ADD_C +#define BN_S_MP_EXPTMOD_C +#define BN_S_MP_MUL_DIGS_C +#define BN_S_MP_MUL_HIGH_DIGS_C +#define BN_S_MP_SQR_C +#define BN_S_MP_SUB_C +#define BNCORE_C +#endif + +#if defined(BN_ERROR_C) + #define BN_MP_ERROR_TO_STRING_C +#endif + +#if defined(BN_FAST_MP_INVMOD_C) + #define BN_MP_ISEVEN_C + #define BN_MP_INIT_MULTI_C + #define BN_MP_COPY_C + #define BN_MP_ABS_C + #define BN_MP_SET_C + #define BN_MP_DIV_2_C + #define BN_MP_ISODD_C + #define BN_MP_SUB_C + #define BN_MP_CMP_C + #define BN_MP_ISZERO_C + #define BN_MP_CMP_D_C + #define BN_MP_ADD_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_MULTI_C +#endif + +#if defined(BN_FAST_MP_MONTGOMERY_REDUCE_C) + #define BN_MP_GROW_C + #define BN_MP_RSHD_C + #define BN_MP_CLAMP_C + #define BN_MP_CMP_MAG_C + #define BN_S_MP_SUB_C +#endif + +#if defined(BN_FAST_S_MP_MUL_DIGS_C) + #define BN_MP_GROW_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_FAST_S_MP_MUL_HIGH_DIGS_C) + #define BN_MP_GROW_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_FAST_S_MP_SQR_C) + #define BN_MP_GROW_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_MP_2EXPT_C) + #define BN_MP_ZERO_C + #define BN_MP_GROW_C +#endif + +#if defined(BN_MP_ABS_C) + #define BN_MP_COPY_C +#endif + +#if defined(BN_MP_ADD_C) + #define BN_S_MP_ADD_C + #define BN_MP_CMP_MAG_C + #define BN_S_MP_SUB_C +#endif + +#if defined(BN_MP_ADD_D_C) + #define BN_MP_GROW_C + #define BN_MP_SUB_D_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_MP_ADDMOD_C) + #define BN_MP_INIT_C + #define BN_MP_ADD_C + #define BN_MP_CLEAR_C + #define BN_MP_MOD_C +#endif + +#if defined(BN_MP_AND_C) + #define BN_MP_INIT_COPY_C + #define BN_MP_CLAMP_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_CLAMP_C) +#endif + +#if defined(BN_MP_CLEAR_C) +#endif + +#if defined(BN_MP_CLEAR_MULTI_C) + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_CMP_C) + #define BN_MP_CMP_MAG_C +#endif + +#if defined(BN_MP_CMP_D_C) +#endif + +#if defined(BN_MP_CMP_MAG_C) +#endif + +#if defined(BN_MP_CNT_LSB_C) + #define BN_MP_ISZERO_C +#endif + +#if defined(BN_MP_COPY_C) + #define BN_MP_GROW_C +#endif + +#if defined(BN_MP_COUNT_BITS_C) +#endif + +#if defined(BN_MP_DIV_C) + #define BN_MP_ISZERO_C + #define BN_MP_CMP_MAG_C + #define BN_MP_COPY_C + #define BN_MP_ZERO_C + #define BN_MP_INIT_MULTI_C + #define BN_MP_SET_C + #define BN_MP_COUNT_BITS_C + #define BN_MP_MUL_2D_C + #define BN_MP_CMP_C + #define BN_MP_SUB_C + #define BN_MP_ADD_C + #define BN_MP_DIV_2D_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_MULTI_C + #define BN_MP_INIT_SIZE_C + #define BN_MP_INIT_C + #define BN_MP_INIT_COPY_C + #define BN_MP_LSHD_C + #define BN_MP_RSHD_C + #define BN_MP_MUL_D_C + #define BN_MP_CLAMP_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_DIV_2_C) + #define BN_MP_GROW_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_MP_DIV_2D_C) + #define BN_MP_COPY_C + #define BN_MP_ZERO_C + #define BN_MP_INIT_C + #define BN_MP_MOD_2D_C + #define BN_MP_CLEAR_C + #define BN_MP_RSHD_C + #define BN_MP_CLAMP_C + #define BN_MP_EXCH_C +#endif + +#if defined(BN_MP_DIV_3_C) + #define BN_MP_INIT_SIZE_C + #define BN_MP_CLAMP_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_DIV_D_C) + #define BN_MP_ISZERO_C + #define BN_MP_COPY_C + #define BN_MP_DIV_2D_C + #define BN_MP_DIV_3_C + #define BN_MP_INIT_SIZE_C + #define BN_MP_CLAMP_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_DR_IS_MODULUS_C) +#endif + +#if defined(BN_MP_DR_REDUCE_C) + #define BN_MP_GROW_C + #define BN_MP_CLAMP_C + #define BN_MP_CMP_MAG_C + #define BN_S_MP_SUB_C +#endif + +#if defined(BN_MP_DR_SETUP_C) +#endif + +#if defined(BN_MP_EXCH_C) +#endif + +#if defined(BN_MP_EXPT_D_C) + #define BN_MP_INIT_COPY_C + #define BN_MP_SET_C + #define BN_MP_SQR_C + #define BN_MP_CLEAR_C + #define BN_MP_MUL_C +#endif + +#if defined(BN_MP_EXPTMOD_C) + #define BN_MP_INIT_C + #define BN_MP_INVMOD_C + #define BN_MP_CLEAR_C + #define BN_MP_ABS_C + #define BN_MP_CLEAR_MULTI_C + #define BN_MP_DR_IS_MODULUS_C + #define BN_MP_REDUCE_IS_2K_C + #define BN_MP_ISODD_C + #define BN_MP_EXPTMOD_FAST_C + #define BN_S_MP_EXPTMOD_C +#endif + +#if defined(BN_MP_EXPTMOD_FAST_C) + #define BN_MP_COUNT_BITS_C + #define BN_MP_INIT_C + #define BN_MP_CLEAR_C + #define BN_MP_MONTGOMERY_SETUP_C + #define BN_FAST_MP_MONTGOMERY_REDUCE_C + #define BN_MP_MONTGOMERY_REDUCE_C + #define BN_MP_DR_SETUP_C + #define BN_MP_DR_REDUCE_C + #define BN_MP_REDUCE_2K_SETUP_C + #define BN_MP_REDUCE_2K_C + #define BN_MP_MONTGOMERY_CALC_NORMALIZATION_C + #define BN_MP_MULMOD_C + #define BN_MP_SET_C + #define BN_MP_MOD_C + #define BN_MP_COPY_C + #define BN_MP_SQR_C + #define BN_MP_MUL_C + #define BN_MP_EXCH_C +#endif + +#if defined(BN_MP_EXTEUCLID_C) + #define BN_MP_INIT_MULTI_C + #define BN_MP_SET_C + #define BN_MP_COPY_C + #define BN_MP_ISZERO_C + #define BN_MP_DIV_C + #define BN_MP_MUL_C + #define BN_MP_SUB_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_MULTI_C +#endif + +#if defined(BN_MP_FREAD_C) + #define BN_MP_ZERO_C + #define BN_MP_S_RMAP_C + #define BN_MP_MUL_D_C + #define BN_MP_ADD_D_C + #define BN_MP_CMP_D_C +#endif + +#if defined(BN_MP_FWRITE_C) + #define BN_MP_RADIX_SIZE_C + #define BN_MP_TORADIX_C +#endif + +#if defined(BN_MP_GCD_C) + #define BN_MP_ISZERO_C + #define BN_MP_ABS_C + #define BN_MP_ZERO_C + #define BN_MP_INIT_COPY_C + #define BN_MP_CNT_LSB_C + #define BN_MP_DIV_2D_C + #define BN_MP_CMP_MAG_C + #define BN_MP_EXCH_C + #define BN_S_MP_SUB_C + #define BN_MP_MUL_2D_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_GET_INT_C) +#endif + +#if defined(BN_MP_GROW_C) +#endif + +#if defined(BN_MP_INIT_C) +#endif + +#if defined(BN_MP_INIT_COPY_C) + #define BN_MP_COPY_C +#endif + +#if defined(BN_MP_INIT_MULTI_C) + #define BN_MP_ERR_C + #define BN_MP_INIT_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_INIT_SET_C) + #define BN_MP_INIT_C + #define BN_MP_SET_C +#endif + +#if defined(BN_MP_INIT_SET_INT_C) + #define BN_MP_INIT_C + #define BN_MP_SET_INT_C +#endif + +#if defined(BN_MP_INIT_SIZE_C) + #define BN_MP_INIT_C +#endif + +#if defined(BN_MP_INVMOD_C) + #define BN_MP_ISZERO_C + #define BN_MP_ISODD_C + #define BN_FAST_MP_INVMOD_C + #define BN_MP_INVMOD_SLOW_C +#endif + +#if defined(BN_MP_INVMOD_SLOW_C) + #define BN_MP_ISZERO_C + #define BN_MP_INIT_MULTI_C + #define BN_MP_COPY_C + #define BN_MP_ISEVEN_C + #define BN_MP_SET_C + #define BN_MP_DIV_2_C + #define BN_MP_ISODD_C + #define BN_MP_ADD_C + #define BN_MP_SUB_C + #define BN_MP_CMP_C + #define BN_MP_CMP_D_C + #define BN_MP_CMP_MAG_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_MULTI_C +#endif + +#if defined(BN_MP_IS_SQUARE_C) + #define BN_MP_MOD_D_C + #define BN_MP_INIT_SET_INT_C + #define BN_MP_MOD_C + #define BN_MP_GET_INT_C + #define BN_MP_SQRT_C + #define BN_MP_SQR_C + #define BN_MP_CMP_MAG_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_JACOBI_C) + #define BN_MP_CMP_D_C + #define BN_MP_ISZERO_C + #define BN_MP_INIT_COPY_C + #define BN_MP_CNT_LSB_C + #define BN_MP_DIV_2D_C + #define BN_MP_MOD_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_KARATSUBA_MUL_C) + #define BN_MP_MUL_C + #define BN_MP_INIT_SIZE_C + #define BN_MP_CLAMP_C + #define BN_MP_SUB_C + #define BN_MP_ADD_C + #define BN_MP_LSHD_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_KARATSUBA_SQR_C) + #define BN_MP_INIT_SIZE_C + #define BN_MP_CLAMP_C + #define BN_MP_SQR_C + #define BN_MP_SUB_C + #define BN_S_MP_ADD_C + #define BN_MP_LSHD_C + #define BN_MP_ADD_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_LCM_C) + #define BN_MP_INIT_MULTI_C + #define BN_MP_GCD_C + #define BN_MP_CMP_MAG_C + #define BN_MP_DIV_C + #define BN_MP_MUL_C + #define BN_MP_CLEAR_MULTI_C +#endif + +#if defined(BN_MP_LSHD_C) + #define BN_MP_GROW_C + #define BN_MP_RSHD_C +#endif + +#if defined(BN_MP_MOD_C) + #define BN_MP_INIT_C + #define BN_MP_DIV_C + #define BN_MP_CLEAR_C + #define BN_MP_ADD_C + #define BN_MP_EXCH_C +#endif + +#if defined(BN_MP_MOD_2D_C) + #define BN_MP_ZERO_C + #define BN_MP_COPY_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_MP_MOD_D_C) + #define BN_MP_DIV_D_C +#endif + +#if defined(BN_MP_MONTGOMERY_CALC_NORMALIZATION_C) + #define BN_MP_COUNT_BITS_C + #define BN_MP_2EXPT_C + #define BN_MP_SET_C + #define BN_MP_MUL_2_C + #define BN_MP_CMP_MAG_C + #define BN_S_MP_SUB_C +#endif + +#if defined(BN_MP_MONTGOMERY_REDUCE_C) + #define BN_FAST_MP_MONTGOMERY_REDUCE_C + #define BN_MP_GROW_C + #define BN_MP_CLAMP_C + #define BN_MP_RSHD_C + #define BN_MP_CMP_MAG_C + #define BN_S_MP_SUB_C +#endif + +#if defined(BN_MP_MONTGOMERY_SETUP_C) +#endif + +#if defined(BN_MP_MUL_C) + #define BN_MP_TOOM_MUL_C + #define BN_MP_KARATSUBA_MUL_C + #define BN_FAST_S_MP_MUL_DIGS_C + #define BN_S_MP_MUL_C + #define BN_S_MP_MUL_DIGS_C +#endif + +#if defined(BN_MP_MUL_2_C) + #define BN_MP_GROW_C +#endif + +#if defined(BN_MP_MUL_2D_C) + #define BN_MP_COPY_C + #define BN_MP_GROW_C + #define BN_MP_LSHD_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_MP_MUL_D_C) + #define BN_MP_GROW_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_MP_MULMOD_C) + #define BN_MP_INIT_C + #define BN_MP_MUL_C + #define BN_MP_CLEAR_C + #define BN_MP_MOD_C +#endif + +#if defined(BN_MP_N_ROOT_C) + #define BN_MP_INIT_C + #define BN_MP_SET_C + #define BN_MP_COPY_C + #define BN_MP_EXPT_D_C + #define BN_MP_MUL_C + #define BN_MP_SUB_C + #define BN_MP_MUL_D_C + #define BN_MP_DIV_C + #define BN_MP_CMP_C + #define BN_MP_SUB_D_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_NEG_C) + #define BN_MP_COPY_C + #define BN_MP_ISZERO_C +#endif + +#if defined(BN_MP_OR_C) + #define BN_MP_INIT_COPY_C + #define BN_MP_CLAMP_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_PRIME_FERMAT_C) + #define BN_MP_CMP_D_C + #define BN_MP_INIT_C + #define BN_MP_EXPTMOD_C + #define BN_MP_CMP_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_PRIME_IS_DIVISIBLE_C) + #define BN_MP_MOD_D_C +#endif + +#if defined(BN_MP_PRIME_IS_PRIME_C) + #define BN_MP_CMP_D_C + #define BN_MP_PRIME_IS_DIVISIBLE_C + #define BN_MP_INIT_C + #define BN_MP_SET_C + #define BN_MP_PRIME_MILLER_RABIN_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_PRIME_MILLER_RABIN_C) + #define BN_MP_CMP_D_C + #define BN_MP_INIT_COPY_C + #define BN_MP_SUB_D_C + #define BN_MP_CNT_LSB_C + #define BN_MP_DIV_2D_C + #define BN_MP_EXPTMOD_C + #define BN_MP_CMP_C + #define BN_MP_SQRMOD_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_PRIME_NEXT_PRIME_C) + #define BN_MP_CMP_D_C + #define BN_MP_SET_C + #define BN_MP_SUB_D_C + #define BN_MP_ISEVEN_C + #define BN_MP_MOD_D_C + #define BN_MP_INIT_C + #define BN_MP_ADD_D_C + #define BN_MP_PRIME_MILLER_RABIN_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_PRIME_RABIN_MILLER_TRIALS_C) +#endif + +#if defined(BN_MP_PRIME_RANDOM_EX_C) + #define BN_MP_READ_UNSIGNED_BIN_C + #define BN_MP_PRIME_IS_PRIME_C + #define BN_MP_SUB_D_C + #define BN_MP_DIV_2_C + #define BN_MP_MUL_2_C + #define BN_MP_ADD_D_C +#endif + +#if defined(BN_MP_RADIX_SIZE_C) + #define BN_MP_COUNT_BITS_C + #define BN_MP_INIT_COPY_C + #define BN_MP_ISZERO_C + #define BN_MP_DIV_D_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_RADIX_SMAP_C) + #define BN_MP_S_RMAP_C +#endif + +#if defined(BN_MP_RAND_C) + #define BN_MP_ZERO_C + #define BN_MP_ADD_D_C + #define BN_MP_LSHD_C +#endif + +#if defined(BN_MP_READ_RADIX_C) + #define BN_MP_ZERO_C + #define BN_MP_S_RMAP_C + #define BN_MP_MUL_D_C + #define BN_MP_ADD_D_C + #define BN_MP_ISZERO_C +#endif + +#if defined(BN_MP_READ_SIGNED_BIN_C) + #define BN_MP_READ_UNSIGNED_BIN_C +#endif + +#if defined(BN_MP_READ_UNSIGNED_BIN_C) + #define BN_MP_GROW_C + #define BN_MP_ZERO_C + #define BN_MP_MUL_2D_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_MP_REDUCE_C) + #define BN_MP_REDUCE_SETUP_C + #define BN_MP_INIT_COPY_C + #define BN_MP_RSHD_C + #define BN_MP_MUL_C + #define BN_S_MP_MUL_HIGH_DIGS_C + #define BN_FAST_S_MP_MUL_HIGH_DIGS_C + #define BN_MP_MOD_2D_C + #define BN_S_MP_MUL_DIGS_C + #define BN_MP_SUB_C + #define BN_MP_CMP_D_C + #define BN_MP_SET_C + #define BN_MP_LSHD_C + #define BN_MP_ADD_C + #define BN_MP_CMP_C + #define BN_S_MP_SUB_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_REDUCE_2K_C) + #define BN_MP_INIT_C + #define BN_MP_COUNT_BITS_C + #define BN_MP_DIV_2D_C + #define BN_MP_MUL_D_C + #define BN_S_MP_ADD_C + #define BN_MP_CMP_MAG_C + #define BN_S_MP_SUB_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_REDUCE_2K_SETUP_C) + #define BN_MP_INIT_C + #define BN_MP_COUNT_BITS_C + #define BN_MP_2EXPT_C + #define BN_MP_CLEAR_C + #define BN_S_MP_SUB_C +#endif + +#if defined(BN_MP_REDUCE_IS_2K_C) + #define BN_MP_REDUCE_2K_C + #define BN_MP_COUNT_BITS_C +#endif + +#if defined(BN_MP_REDUCE_SETUP_C) + #define BN_MP_2EXPT_C + #define BN_MP_DIV_C +#endif + +#if defined(BN_MP_RSHD_C) + #define BN_MP_ZERO_C +#endif + +#if defined(BN_MP_SET_C) + #define BN_MP_ZERO_C +#endif + +#if defined(BN_MP_SET_INT_C) + #define BN_MP_ZERO_C + #define BN_MP_MUL_2D_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_MP_SHRINK_C) +#endif + +#if defined(BN_MP_SIGNED_BIN_SIZE_C) + #define BN_MP_UNSIGNED_BIN_SIZE_C +#endif + +#if defined(BN_MP_SQR_C) + #define BN_MP_TOOM_SQR_C + #define BN_MP_KARATSUBA_SQR_C + #define BN_FAST_S_MP_SQR_C + #define BN_S_MP_SQR_C +#endif + +#if defined(BN_MP_SQRMOD_C) + #define BN_MP_INIT_C + #define BN_MP_SQR_C + #define BN_MP_CLEAR_C + #define BN_MP_MOD_C +#endif + +#if defined(BN_MP_SQRT_C) + #define BN_MP_N_ROOT_C + #define BN_MP_ISZERO_C + #define BN_MP_ZERO_C + #define BN_MP_INIT_COPY_C + #define BN_MP_RSHD_C + #define BN_MP_DIV_C + #define BN_MP_ADD_C + #define BN_MP_DIV_2_C + #define BN_MP_CMP_MAG_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_SUB_C) + #define BN_S_MP_ADD_C + #define BN_MP_CMP_MAG_C + #define BN_S_MP_SUB_C +#endif + +#if defined(BN_MP_SUB_D_C) + #define BN_MP_GROW_C + #define BN_MP_ADD_D_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_MP_SUBMOD_C) + #define BN_MP_INIT_C + #define BN_MP_SUB_C + #define BN_MP_CLEAR_C + #define BN_MP_MOD_C +#endif + +#if defined(BN_MP_TO_SIGNED_BIN_C) + #define BN_MP_TO_UNSIGNED_BIN_C +#endif + +#if defined(BN_MP_TO_UNSIGNED_BIN_C) + #define BN_MP_INIT_COPY_C + #define BN_MP_ISZERO_C + #define BN_MP_DIV_2D_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_TOOM_MUL_C) + #define BN_MP_INIT_MULTI_C + #define BN_MP_MOD_2D_C + #define BN_MP_COPY_C + #define BN_MP_RSHD_C + #define BN_MP_MUL_C + #define BN_MP_MUL_2_C + #define BN_MP_ADD_C + #define BN_MP_SUB_C + #define BN_MP_DIV_2_C + #define BN_MP_MUL_2D_C + #define BN_MP_MUL_D_C + #define BN_MP_DIV_3_C + #define BN_MP_LSHD_C + #define BN_MP_CLEAR_MULTI_C +#endif + +#if defined(BN_MP_TOOM_SQR_C) + #define BN_MP_INIT_MULTI_C + #define BN_MP_MOD_2D_C + #define BN_MP_COPY_C + #define BN_MP_RSHD_C + #define BN_MP_SQR_C + #define BN_MP_MUL_2_C + #define BN_MP_ADD_C + #define BN_MP_SUB_C + #define BN_MP_DIV_2_C + #define BN_MP_MUL_2D_C + #define BN_MP_MUL_D_C + #define BN_MP_DIV_3_C + #define BN_MP_LSHD_C + #define BN_MP_CLEAR_MULTI_C +#endif + +#if defined(BN_MP_TORADIX_C) + #define BN_MP_ISZERO_C + #define BN_MP_INIT_COPY_C + #define BN_MP_DIV_D_C + #define BN_MP_CLEAR_C + #define BN_MP_S_RMAP_C +#endif + +#if defined(BN_MP_TORADIX_N_C) + #define BN_MP_ISZERO_C + #define BN_MP_INIT_COPY_C + #define BN_MP_DIV_D_C + #define BN_MP_CLEAR_C + #define BN_MP_S_RMAP_C +#endif + +#if defined(BN_MP_UNSIGNED_BIN_SIZE_C) + #define BN_MP_COUNT_BITS_C +#endif + +#if defined(BN_MP_XOR_C) + #define BN_MP_INIT_COPY_C + #define BN_MP_CLAMP_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_MP_ZERO_C) +#endif + +#if defined(BN_PRIME_TAB_C) +#endif + +#if defined(BN_REVERSE_C) +#endif + +#if defined(BN_S_MP_ADD_C) + #define BN_MP_GROW_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BN_S_MP_EXPTMOD_C) + #define BN_MP_COUNT_BITS_C + #define BN_MP_INIT_C + #define BN_MP_CLEAR_C + #define BN_MP_REDUCE_SETUP_C + #define BN_MP_MOD_C + #define BN_MP_COPY_C + #define BN_MP_SQR_C + #define BN_MP_REDUCE_C + #define BN_MP_MUL_C + #define BN_MP_SET_C + #define BN_MP_EXCH_C +#endif + +#if defined(BN_S_MP_MUL_DIGS_C) + #define BN_FAST_S_MP_MUL_DIGS_C + #define BN_MP_INIT_SIZE_C + #define BN_MP_CLAMP_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_S_MP_MUL_HIGH_DIGS_C) + #define BN_FAST_S_MP_MUL_HIGH_DIGS_C + #define BN_MP_INIT_SIZE_C + #define BN_MP_CLAMP_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_S_MP_SQR_C) + #define BN_MP_INIT_SIZE_C + #define BN_MP_CLAMP_C + #define BN_MP_EXCH_C + #define BN_MP_CLEAR_C +#endif + +#if defined(BN_S_MP_SUB_C) + #define BN_MP_GROW_C + #define BN_MP_CLAMP_C +#endif + +#if defined(BNCORE_C) +#endif + +#ifdef LTM3 +#define LTM_LAST +#endif +#include <tommath_superclass.h> +#include <tommath_class.h> +#else +#define LTM_LAST +#endif
--- /dev/null Thu Jan 01 00:00:00 1970 +0000 +++ b/tommath_superclass.h Sun Dec 19 11:33:56 2004 +0000 @@ -0,0 +1,72 @@ +/* super class file for PK algos */ + +/* default ... include all MPI */ +#define LTM_ALL + +/* RSA only (does not support DH/DSA/ECC) */ +// #define SC_RSA_1 + +/* For reference.... On an Athlon64 optimizing for speed... + + LTM's mpi.o with all functions [striped] is 142KiB in size. + +*/ + +/* Works for RSA only, mpi.o is 68KiB */ +#ifdef SC_RSA_1 + #define BN_MP_SHRINK_C + #define BN_MP_LCM_C + #define BN_MP_PRIME_RANDOM_EX_C + #define BN_MP_INVMOD_C + #define BN_MP_GCD_C + #define BN_MP_MOD_C + #define BN_MP_MULMOD_C + #define BN_MP_ADDMOD_C + #define BN_MP_EXPTMOD_C + #define BN_MP_SET_INT_C + #define BN_MP_INIT_MULTI_C + #define BN_MP_CLEAR_MULTI_C + #define BN_MP_UNSIGNED_BIN_SIZE_C + #define BN_MP_TO_UNSIGNED_BIN_C + #define BN_MP_MOD_D_C + #define BN_MP_PRIME_RABIN_MILLER_TRIALS_C + #define BN_REVERSE_C + #define BN_PRIME_TAB_C + + /* other modifiers */ + #define BN_MP_DIV_SMALL /* Slower division, not critical */ + + /* here we are on the last pass so we turn things off. The functions classes are still there + * but we remove them specifically from the build. This also invokes tweaks in functions + * like removing support for even moduli, etc... + */ +#ifdef LTM_LAST + #undef BN_MP_TOOM_MUL_C + #undef BN_MP_TOOM_SQR_C + #undef BN_MP_KARATSUBA_MUL_C + #undef BN_MP_KARATSUBA_SQR_C + #undef BN_MP_REDUCE_C + #undef BN_MP_REDUCE_SETUP_C + #undef BN_MP_DR_IS_MODULUS_C + #undef BN_MP_DR_SETUP_C + #undef BN_MP_DR_REDUCE_C + #undef BN_MP_REDUCE_IS_2K_C + #undef BN_MP_REDUCE_2K_SETUP_C + #undef BN_MP_REDUCE_2K_C + #undef BN_S_MP_EXPTMOD_C + #undef BN_MP_DIV_3_C + #undef BN_S_MP_MUL_HIGH_DIGS_C + #undef BN_FAST_S_MP_MUL_HIGH_DIGS_C + #undef BN_FAST_MP_INVMOD_C + + /* To safely undefine these you have to make sure your RSA key won't exceed the Comba threshold + * which is roughly 255 digits [7140 bits for 32-bit machines, 15300 bits for 64-bit machines] + * which means roughly speaking you can handle upto 2536-bit RSA keys with these defined without + * trouble. + */ + #undef BN_S_MP_MUL_DIGS_C + #undef BN_S_MP_SQR_C + #undef BN_MP_MONTGOMERY_REDUCE_C +#endif + +#endif