Mercurial > dropbear
diff mpi.c @ 143:5d99163f7e32 libtomcrypt-orig
import of libtomcrypt 0.99
| author | Matt Johnston <matt@ucc.asn.au> |
|---|---|
| date | Sun, 19 Dec 2004 11:34:45 +0000 |
| parents | 6362d3854bb4 |
| children |
line wrap: on
line diff
--- a/mpi.c Tue Jun 15 14:07:21 2004 +0000 +++ b/mpi.c Sun Dec 19 11:34:45 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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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) { @@ -407,48 +415,39 @@ } } - /* 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 */ @@ -457,32 +456,11 @@ { 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 <ltc_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 <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> - -/* init a new bigint */ +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_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 <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> - -/* multiplication using the Toom-Cook 3-way algorithm */ +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 <ltc_tommath.h> +#include <ltc_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 @@ -8372,43 +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 <ltc_tommath.h> +#include <ltc_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 Northwood /GCC v3.3.3 / 59/ 81/profiled build - Intel P4 Northwood /GCC v3.3.3 / 59/ 80/profiled_single build - Intel P4 Northwood /ICC v8.0 / 57/ 70/profiled build - Intel P4 Northwood /ICC v8.0 / 54/ 76/profiled_single build - AMD Athlon XP /GCC v3.2 / 109/ 127/ + Intel P4 Northwood /GCC v3.4.1 / 88/ 128/LTM 0.32 ;-) */ -int KARATSUBA_MUL_CUTOFF = 57, /* Min. number of digits before Karatsuba multiplication is used. */ - KARATSUBA_SQR_CUTOFF = 70, /* 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 */