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comparison src/headers/ltc_tommath.h @ 191:1c15b283127b libtomcrypt-orig

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Import of libtomcrypt 1.02 with manual path rename rearrangement etc
author Matt Johnston <matt@ucc.asn.au>
date Fri, 06 May 2005 13:23:02 +0000
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children 39d5d58461d6
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143:5d99163f7e32 191:1c15b283127b
1 /* LibTomMath, multiple-precision integer library -- Tom St Denis
2 *
3 * LibTomMath is a library that provides multiple-precision
4 * integer arithmetic as well as number theoretic functionality.
5 *
6 * The library was designed directly after the MPI library by
7 * Michael Fromberger but has been written from scratch with
8 * additional optimizations in place.
9 *
10 * The library is free for all purposes without any express
11 * guarantee it works.
12 *
13 * Tom St Denis, [email protected], http://math.libtomcrypt.org
14 */
15 #ifndef BN_H_
16 #define BN_H_
17
18 #include <stdio.h>
19 #include <string.h>
20 #include <stdlib.h>
21 #include <ctype.h>
22 #include <limits.h>
23
24 #include <tommath_class.h>
25
26 #undef MIN
27 #define MIN(x,y) ((x)<(y)?(x):(y))
28 #undef MAX
29 #define MAX(x,y) ((x)>(y)?(x):(y))
30
31 #ifdef __cplusplus
32 extern "C" {
33
34 /* C++ compilers don't like assigning void * to mp_digit * */
35 #define OPT_CAST(x) (x *)
36
37 #else
38
39 /* C on the other hand doesn't care */
40 #define OPT_CAST(x)
41
42 #endif
43
44
45 /* detect 64-bit mode if possible */
46 #if defined(__x86_64__)
47 #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
48 #define MP_64BIT
49 #endif
50 #endif
51
52 /* some default configurations.
53 *
54 * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
55 * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
56 *
57 * At the very least a mp_digit must be able to hold 7 bits
58 * [any size beyond that is ok provided it doesn't overflow the data type]
59 */
60 #ifdef MP_8BIT
61 typedef unsigned char mp_digit;
62 typedef unsigned short mp_word;
63 #elif defined(MP_16BIT)
64 typedef unsigned short mp_digit;
65 typedef unsigned long mp_word;
66 #elif defined(MP_64BIT)
67 /* for GCC only on supported platforms */
68 #ifndef CRYPT
69 typedef unsigned long long ulong64;
70 typedef signed long long long64;
71 #endif
72
73 typedef unsigned long mp_digit;
74 typedef unsigned long mp_word __attribute__ ((mode(TI)));
75
76 #define DIGIT_BIT 60
77 #else
78 /* this is the default case, 28-bit digits */
79
80 /* this is to make porting into LibTomCrypt easier :-) */
81 #ifndef CRYPT
82 #if defined(_MSC_VER) || defined(__BORLANDC__)
83 typedef unsigned __int64 ulong64;
84 typedef signed __int64 long64;
85 #else
86 typedef unsigned long long ulong64;
87 typedef signed long long long64;
88 #endif
89 #endif
90
91 typedef unsigned long mp_digit;
92 typedef ulong64 mp_word;
93
94 #ifdef MP_31BIT
95 /* this is an extension that uses 31-bit digits */
96 #define DIGIT_BIT 31
97 #else
98 /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
99 #define DIGIT_BIT 28
100 #define MP_28BIT
101 #endif
102 #endif
103
104 /* define heap macros */
105 #ifndef CRYPT
106 /* default to libc stuff */
107 #ifndef XMALLOC
108 #define XMALLOC malloc
109 #define XFREE free
110 #define XREALLOC realloc
111 #define XCALLOC calloc
112 #else
113 /* prototypes for our heap functions */
114 extern void *XMALLOC(size_t n);
115 extern void *XREALLOC(void *p, size_t n);
116 extern void *XCALLOC(size_t n, size_t s);
117 extern void XFREE(void *p);
118 #endif
119 #endif
120
121
122 /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
123 #ifndef DIGIT_BIT
124 #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */
125 #endif
126
127 #define MP_DIGIT_BIT DIGIT_BIT
128 #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
129 #define MP_DIGIT_MAX MP_MASK
130
131 /* equalities */
132 #define MP_LT -1 /* less than */
133 #define MP_EQ 0 /* equal to */
134 #define MP_GT 1 /* greater than */
135
136 #define MP_ZPOS 0 /* positive integer */
137 #define MP_NEG 1 /* negative */
138
139 #define MP_OKAY 0 /* ok result */
140 #define MP_MEM -2 /* out of mem */
141 #define MP_VAL -3 /* invalid input */
142 #define MP_RANGE MP_VAL
143
144 #define MP_YES 1 /* yes response */
145 #define MP_NO 0 /* no response */
146
147 /* Primality generation flags */
148 #define LTM_PRIME_BBS 0x0001 /* BBS style prime */
149 #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */
150 #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */
151
152 typedef int mp_err;
153
154 /* you'll have to tune these... */
155 extern int KARATSUBA_MUL_CUTOFF,
156 KARATSUBA_SQR_CUTOFF,
157 TOOM_MUL_CUTOFF,
158 TOOM_SQR_CUTOFF;
159
160 /* define this to use lower memory usage routines (exptmods mostly) */
161 /* #define MP_LOW_MEM */
162
163 /* default precision */
164 #ifndef MP_PREC
165 #ifndef MP_LOW_MEM
166 #define MP_PREC 64 /* default digits of precision */
167 #else
168 #define MP_PREC 8 /* default digits of precision */
169 #endif
170 #endif
171
172 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
173 #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
174
175 /* the infamous mp_int structure */
176 typedef struct {
177 int used, alloc, sign;
178 mp_digit *dp;
179 } mp_int;
180
181 /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
182 typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
183
184
185 #define USED(m) ((m)->used)
186 #define DIGIT(m,k) ((m)->dp[(k)])
187 #define SIGN(m) ((m)->sign)
188
189 /* error code to char* string */
190 char *mp_error_to_string(int code);
191
192 /* ---> init and deinit bignum functions <--- */
193 /* init a bignum */
194 int mp_init(mp_int *a);
195
196 /* free a bignum */
197 void mp_clear(mp_int *a);
198
199 /* init a null terminated series of arguments */
200 int mp_init_multi(mp_int *mp, ...);
201
202 /* clear a null terminated series of arguments */
203 void mp_clear_multi(mp_int *mp, ...);
204
205 /* exchange two ints */
206 void mp_exch(mp_int *a, mp_int *b);
207
208 /* shrink ram required for a bignum */
209 int mp_shrink(mp_int *a);
210
211 /* grow an int to a given size */
212 int mp_grow(mp_int *a, int size);
213
214 /* init to a given number of digits */
215 int mp_init_size(mp_int *a, int size);
216
217 /* ---> Basic Manipulations <--- */
218 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
219 #define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
220 #define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
221
222 /* set to zero */
223 void mp_zero(mp_int *a);
224
225 /* set to a digit */
226 void mp_set(mp_int *a, mp_digit b);
227
228 /* set a 32-bit const */
229 int mp_set_int(mp_int *a, unsigned long b);
230
231 /* get a 32-bit value */
232 unsigned long mp_get_int(mp_int * a);
233
234 /* initialize and set a digit */
235 int mp_init_set (mp_int * a, mp_digit b);
236
237 /* initialize and set 32-bit value */
238 int mp_init_set_int (mp_int * a, unsigned long b);
239
240 /* copy, b = a */
241 int mp_copy(mp_int *a, mp_int *b);
242
243 /* inits and copies, a = b */
244 int mp_init_copy(mp_int *a, mp_int *b);
245
246 /* trim unused digits */
247 void mp_clamp(mp_int *a);
248
249 /* ---> digit manipulation <--- */
250
251 /* right shift by "b" digits */
252 void mp_rshd(mp_int *a, int b);
253
254 /* left shift by "b" digits */
255 int mp_lshd(mp_int *a, int b);
256
257 /* c = a / 2**b */
258 int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d);
259
260 /* b = a/2 */
261 int mp_div_2(mp_int *a, mp_int *b);
262
263 /* c = a * 2**b */
264 int mp_mul_2d(mp_int *a, int b, mp_int *c);
265
266 /* b = a*2 */
267 int mp_mul_2(mp_int *a, mp_int *b);
268
269 /* c = a mod 2**d */
270 int mp_mod_2d(mp_int *a, int b, mp_int *c);
271
272 /* computes a = 2**b */
273 int mp_2expt(mp_int *a, int b);
274
275 /* Counts the number of lsbs which are zero before the first zero bit */
276 int mp_cnt_lsb(mp_int *a);
277
278 /* I Love Earth! */
279
280 /* makes a pseudo-random int of a given size */
281 int mp_rand(mp_int *a, int digits);
282
283 /* ---> binary operations <--- */
284 /* c = a XOR b */
285 int mp_xor(mp_int *a, mp_int *b, mp_int *c);
286
287 /* c = a OR b */
288 int mp_or(mp_int *a, mp_int *b, mp_int *c);
289
290 /* c = a AND b */
291 int mp_and(mp_int *a, mp_int *b, mp_int *c);
292
293 /* ---> Basic arithmetic <--- */
294
295 /* b = -a */
296 int mp_neg(mp_int *a, mp_int *b);
297
298 /* b = |a| */
299 int mp_abs(mp_int *a, mp_int *b);
300
301 /* compare a to b */
302 int mp_cmp(mp_int *a, mp_int *b);
303
304 /* compare |a| to |b| */
305 int mp_cmp_mag(mp_int *a, mp_int *b);
306
307 /* c = a + b */
308 int mp_add(mp_int *a, mp_int *b, mp_int *c);
309
310 /* c = a - b */
311 int mp_sub(mp_int *a, mp_int *b, mp_int *c);
312
313 /* c = a * b */
314 int mp_mul(mp_int *a, mp_int *b, mp_int *c);
315
316 /* b = a*a */
317 int mp_sqr(mp_int *a, mp_int *b);
318
319 /* a/b => cb + d == a */
320 int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
321
322 /* c = a mod b, 0 <= c < b */
323 int mp_mod(mp_int *a, mp_int *b, mp_int *c);
324
325 /* ---> single digit functions <--- */
326
327 /* compare against a single digit */
328 int mp_cmp_d(mp_int *a, mp_digit b);
329
330 /* c = a + b */
331 int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
332
333 /* c = a - b */
334 int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
335
336 /* c = a * b */
337 int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
338
339 /* a/b => cb + d == a */
340 int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
341
342 /* a/3 => 3c + d == a */
343 int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
344
345 /* c = a**b */
346 int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
347
348 /* c = a mod b, 0 <= c < b */
349 int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
350
351 /* ---> number theory <--- */
352
353 /* d = a + b (mod c) */
354 int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
355
356 /* d = a - b (mod c) */
357 int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
358
359 /* d = a * b (mod c) */
360 int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
361
362 /* c = a * a (mod b) */
363 int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);
364
365 /* c = 1/a (mod b) */
366 int mp_invmod(mp_int *a, mp_int *b, mp_int *c);
367
368 /* c = (a, b) */
369 int mp_gcd(mp_int *a, mp_int *b, mp_int *c);
370
371 /* produces value such that U1*a + U2*b = U3 */
372 int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
373
374 /* c = [a, b] or (a*b)/(a, b) */
375 int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
376
377 /* finds one of the b'th root of a, such that |c|**b <= |a|
378 *
379 * returns error if a < 0 and b is even
380 */
381 int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
382
383 /* special sqrt algo */
384 int mp_sqrt(mp_int *arg, mp_int *ret);
385
386 /* is number a square? */
387 int mp_is_square(mp_int *arg, int *ret);
388
389 /* computes the jacobi c = (a | n) (or Legendre if b is prime) */
390 int mp_jacobi(mp_int *a, mp_int *n, int *c);
391
392 /* used to setup the Barrett reduction for a given modulus b */
393 int mp_reduce_setup(mp_int *a, mp_int *b);
394
395 /* Barrett Reduction, computes a (mod b) with a precomputed value c
396 *
397 * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
398 * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
399 */
400 int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
401
402 /* setups the montgomery reduction */
403 int mp_montgomery_setup(mp_int *a, mp_digit *mp);
404
405 /* computes a = B**n mod b without division or multiplication useful for
406 * normalizing numbers in a Montgomery system.
407 */
408 int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
409
410 /* computes x/R == x (mod N) via Montgomery Reduction */
411 int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
412
413 /* returns 1 if a is a valid DR modulus */
414 int mp_dr_is_modulus(mp_int *a);
415
416 /* sets the value of "d" required for mp_dr_reduce */
417 void mp_dr_setup(mp_int *a, mp_digit *d);
418
419 /* reduces a modulo b using the Diminished Radix method */
420 int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
421
422 /* returns true if a can be reduced with mp_reduce_2k */
423 int mp_reduce_is_2k(mp_int *a);
424
425 /* determines k value for 2k reduction */
426 int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
427
428 /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
429 int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
430
431 /* returns true if a can be reduced with mp_reduce_2k_l */
432 int mp_reduce_is_2k_l(mp_int *a);
433
434 /* determines k value for 2k reduction */
435 int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
436
437 /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
438 int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
439
440 /* d = a**b (mod c) */
441 int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
442
443 /* ---> Primes <--- */
444
445 /* number of primes */
446 #ifdef MP_8BIT
447 #define PRIME_SIZE 31
448 #else
449 #define PRIME_SIZE 256
450 #endif
451
452 /* table of first PRIME_SIZE primes */
453 extern const mp_digit ltm_prime_tab[];
454
455 /* result=1 if a is divisible by one of the first PRIME_SIZE primes */
456 int mp_prime_is_divisible(mp_int *a, int *result);
457
458 /* performs one Fermat test of "a" using base "b".
459 * Sets result to 0 if composite or 1 if probable prime
460 */
461 int mp_prime_fermat(mp_int *a, mp_int *b, int *result);
462
463 /* performs one Miller-Rabin test of "a" using base "b".
464 * Sets result to 0 if composite or 1 if probable prime
465 */
466 int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
467
468 /* This gives [for a given bit size] the number of trials required
469 * such that Miller-Rabin gives a prob of failure lower than 2^-96
470 */
471 int mp_prime_rabin_miller_trials(int size);
472
473 /* performs t rounds of Miller-Rabin on "a" using the first
474 * t prime bases. Also performs an initial sieve of trial
475 * division. Determines if "a" is prime with probability
476 * of error no more than (1/4)**t.
477 *
478 * Sets result to 1 if probably prime, 0 otherwise
479 */
480 int mp_prime_is_prime(mp_int *a, int t, int *result);
481
482 /* finds the next prime after the number "a" using "t" trials
483 * of Miller-Rabin.
484 *
485 * bbs_style = 1 means the prime must be congruent to 3 mod 4
486 */
487 int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
488
489 /* makes a truly random prime of a given size (bytes),
490 * call with bbs = 1 if you want it to be congruent to 3 mod 4
491 *
492 * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
493 * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
494 * so it can be NULL
495 *
496 * The prime generated will be larger than 2^(8*size).
497 */
498 #define mp_prime_random(a, t, size, bbs, cb, dat) mp_prime_random_ex(a, t, ((size) * 8) + 1, (bbs==1)?LTM_PRIME_BBS:0, cb, dat)
499
500 /* makes a truly random prime of a given size (bits),
501 *
502 * Flags are as follows:
503 *
504 * LTM_PRIME_BBS - make prime congruent to 3 mod 4
505 * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
506 * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
507 * LTM_PRIME_2MSB_ON - make the 2nd highest bit one
508 *
509 * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can
510 * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself
511 * so it can be NULL
512 *
513 */
514 int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat);
515
516 /* ---> radix conversion <--- */
517 int mp_count_bits(mp_int *a);
518
519 int mp_unsigned_bin_size(mp_int *a);
520 int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c);
521 int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
522 int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
523
524 int mp_signed_bin_size(mp_int *a);
525 int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
526 int mp_to_signed_bin(mp_int *a, unsigned char *b);
527 int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
528
529 int mp_read_radix(mp_int *a, const char *str, int radix);
530 int mp_toradix(mp_int *a, char *str, int radix);
531 int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
532 int mp_radix_size(mp_int *a, int radix, int *size);
533
534 int mp_fread(mp_int *a, int radix, FILE *stream);
535 int mp_fwrite(mp_int *a, int radix, FILE *stream);
536
537 #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
538 #define mp_raw_size(mp) mp_signed_bin_size(mp)
539 #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str))
540 #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
541 #define mp_mag_size(mp) mp_unsigned_bin_size(mp)
542 #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str))
543
544 #define mp_tobinary(M, S) mp_toradix((M), (S), 2)
545 #define mp_tooctal(M, S) mp_toradix((M), (S), 8)
546 #define mp_todecimal(M, S) mp_toradix((M), (S), 10)
547 #define mp_tohex(M, S) mp_toradix((M), (S), 16)
548
549 /* lowlevel functions, do not call! */
550 int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
551 int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
552 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
553 int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
554 int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
555 int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
556 int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
557 int fast_s_mp_sqr(mp_int *a, mp_int *b);
558 int s_mp_sqr(mp_int *a, mp_int *b);
559 int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
560 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
561 int mp_karatsuba_sqr(mp_int *a, mp_int *b);
562 int mp_toom_sqr(mp_int *a, mp_int *b);
563 int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
564 int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
565 int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
566 int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
567 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
568 void bn_reverse(unsigned char *s, int len);
569
570 extern const char *mp_s_rmap;
571
572 #ifdef __cplusplus
573 }
574 #endif
575
576 #endif
577