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, tomstdenis@gmail.com, http://math.libtomcrypt.com |
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 | #ifndef MIN |
27 | #define MIN(x,y) ((x)<(y)?(x):(y)) |
28 | #endif |
29 | |
30 | #ifndef MAX |
31 | #define MAX(x,y) ((x)>(y)?(x):(y)) |
32 | #endif |
33 | |
34 | #ifdef __cplusplus |
35 | extern "C" { |
36 | |
37 | /* C++ compilers don't like assigning void * to mp_digit * */ |
38 | #define OPT_CAST(x) (x *) |
39 | |
40 | #else |
41 | |
42 | /* C on the other hand doesn't care */ |
43 | #define OPT_CAST(x) |
44 | |
45 | #endif |
46 | |
47 | |
48 | /* detect 64-bit mode if possible */ |
49 | #if defined(__x86_64__) |
50 | #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT)) |
51 | #define MP_64BIT |
52 | #endif |
53 | #endif |
54 | |
55 | /* some default configurations. |
56 | * |
57 | * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits |
58 | * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits |
59 | * |
60 | * At the very least a mp_digit must be able to hold 7 bits |
61 | * [any size beyond that is ok provided it doesn't overflow the data type] |
62 | */ |
63 | #ifdef MP_8BIT |
64 | typedef unsigned char mp_digit; |
65 | typedef unsigned short mp_word; |
66 | #elif defined(MP_16BIT) |
67 | typedef unsigned short mp_digit; |
68 | typedef unsigned long mp_word; |
69 | #elif defined(MP_64BIT) |
70 | /* for GCC only on supported platforms */ |
71 | #ifndef CRYPT |
72 | typedef unsigned long long ulong64; |
73 | typedef signed long long long64; |
74 | #endif |
75 | |
76 | typedef unsigned long mp_digit; |
77 | typedef unsigned long mp_word __attribute__ ((mode(TI))); |
78 | |
79 | #define DIGIT_BIT 60 |
80 | #else |
81 | /* this is the default case, 28-bit digits */ |
82 | |
83 | /* this is to make porting into LibTomCrypt easier :-) */ |
84 | #ifndef CRYPT |
85 | #if defined(_MSC_VER) || defined(__BORLANDC__) |
86 | typedef unsigned __int64 ulong64; |
87 | typedef signed __int64 long64; |
88 | #else |
89 | typedef unsigned long long ulong64; |
90 | typedef signed long long long64; |
91 | #endif |
92 | #endif |
93 | |
94 | typedef unsigned long mp_digit; |
95 | typedef ulong64 mp_word; |
96 | |
97 | #ifdef MP_31BIT |
98 | /* this is an extension that uses 31-bit digits */ |
99 | #define DIGIT_BIT 31 |
100 | #else |
101 | /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */ |
102 | #define DIGIT_BIT 28 |
103 | #define MP_28BIT |
104 | #endif |
105 | #endif |
106 | |
107 | /* define heap macros */ |
108 | #ifndef CRYPT |
109 | /* default to libc stuff */ |
110 | #ifndef XMALLOC |
111 | #define XMALLOC malloc |
112 | #define XFREE free |
113 | #define XREALLOC realloc |
114 | #define XCALLOC calloc |
115 | #else |
116 | /* prototypes for our heap functions */ |
117 | extern void *XMALLOC(size_t n); |
118 | extern void *XREALLOC(void *p, size_t n); |
119 | extern void *XCALLOC(size_t n, size_t s); |
120 | extern void XFREE(void *p); |
121 | #endif |
122 | #endif |
123 | |
124 | |
125 | /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */ |
126 | #ifndef DIGIT_BIT |
127 | #define DIGIT_BIT ((int)((CHAR_BIT * sizeof(mp_digit) - 1))) /* bits per digit */ |
128 | #endif |
129 | |
130 | #define MP_DIGIT_BIT DIGIT_BIT |
131 | #define MP_MASK ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1)) |
132 | #define MP_DIGIT_MAX MP_MASK |
133 | |
134 | /* equalities */ |
135 | #define MP_LT -1 /* less than */ |
136 | #define MP_EQ 0 /* equal to */ |
137 | #define MP_GT 1 /* greater than */ |
138 | |
139 | #define MP_ZPOS 0 /* positive integer */ |
140 | #define MP_NEG 1 /* negative */ |
141 | |
142 | #define MP_OKAY 0 /* ok result */ |
143 | #define MP_MEM -2 /* out of mem */ |
144 | #define MP_VAL -3 /* invalid input */ |
145 | #define MP_RANGE MP_VAL |
146 | |
147 | #define MP_YES 1 /* yes response */ |
148 | #define MP_NO 0 /* no response */ |
149 | |
150 | /* Primality generation flags */ |
151 | #define LTM_PRIME_BBS 0x0001 /* BBS style prime */ |
152 | #define LTM_PRIME_SAFE 0x0002 /* Safe prime (p-1)/2 == prime */ |
153 | #define LTM_PRIME_2MSB_ON 0x0008 /* force 2nd MSB to 1 */ |
154 | |
155 | typedef int mp_err; |
156 | |
157 | /* you'll have to tune these... */ |
158 | extern int KARATSUBA_MUL_CUTOFF, |
159 | KARATSUBA_SQR_CUTOFF, |
160 | TOOM_MUL_CUTOFF, |
161 | TOOM_SQR_CUTOFF; |
162 | |
163 | /* define this to use lower memory usage routines (exptmods mostly) */ |
164 | /* #define MP_LOW_MEM */ |
165 | |
166 | /* default precision */ |
167 | #ifndef MP_PREC |
168 | #ifndef MP_LOW_MEM |
169 | #define MP_PREC 32 /* default digits of precision */ |
170 | #else |
171 | #define MP_PREC 8 /* default digits of precision */ |
172 | #endif |
173 | #endif |
174 | |
175 | /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */ |
176 | #define MP_WARRAY (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1)) |
177 | |
178 | /* the infamous mp_int structure */ |
179 | typedef struct { |
180 | int used, alloc, sign; |
181 | mp_digit *dp; |
182 | } mp_int; |
183 | |
184 | /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */ |
185 | typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat); |
186 | |
187 | |
188 | #define USED(m) ((m)->used) |
189 | #define DIGIT(m,k) ((m)->dp[(k)]) |
190 | #define SIGN(m) ((m)->sign) |
191 | |
192 | /* error code to char* string */ |
193 | char *mp_error_to_string(int code); |
194 | |
195 | /* ---> init and deinit bignum functions <--- */ |
196 | /* init a bignum */ |
197 | int mp_init(mp_int *a); |
198 | |
199 | /* free a bignum */ |
200 | void mp_clear(mp_int *a); |
201 | |
202 | /* init a null terminated series of arguments */ |
203 | int mp_init_multi(mp_int *mp, ...); |
204 | |
205 | /* clear a null terminated series of arguments */ |
206 | void mp_clear_multi(mp_int *mp, ...); |
207 | |
208 | /* exchange two ints */ |
209 | void mp_exch(mp_int *a, mp_int *b); |
210 | |
211 | /* shrink ram required for a bignum */ |
212 | int mp_shrink(mp_int *a); |
213 | |
214 | /* grow an int to a given size */ |
215 | int mp_grow(mp_int *a, int size); |
216 | |
217 | /* init to a given number of digits */ |
218 | int mp_init_size(mp_int *a, int size); |
219 | |
220 | /* ---> Basic Manipulations <--- */ |
221 | #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO) |
222 | #define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO) |
223 | #define mp_isodd(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO) |
224 | |
225 | /* set to zero */ |
226 | void mp_zero(mp_int *a); |
227 | |
228 | /* set to a digit */ |
229 | void mp_set(mp_int *a, mp_digit b); |
230 | |
231 | /* set a 32-bit const */ |
232 | int mp_set_int(mp_int *a, unsigned long b); |
233 | |
234 | /* get a 32-bit value */ |
235 | unsigned long mp_get_int(mp_int * a); |
236 | |
237 | /* initialize and set a digit */ |
238 | int mp_init_set (mp_int * a, mp_digit b); |
239 | |
240 | /* initialize and set 32-bit value */ |
241 | int mp_init_set_int (mp_int * a, unsigned long b); |
242 | |
243 | /* copy, b = a */ |
244 | int mp_copy(mp_int *a, mp_int *b); |
245 | |
246 | /* inits and copies, a = b */ |
247 | int mp_init_copy(mp_int *a, mp_int *b); |
248 | |
249 | /* trim unused digits */ |
250 | void mp_clamp(mp_int *a); |
251 | |
252 | /* ---> digit manipulation <--- */ |
253 | |
254 | /* right shift by "b" digits */ |
255 | void mp_rshd(mp_int *a, int b); |
256 | |
257 | /* left shift by "b" digits */ |
258 | int mp_lshd(mp_int *a, int b); |
259 | |
260 | /* c = a / 2**b */ |
261 | int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d); |
262 | |
263 | /* b = a/2 */ |
264 | int mp_div_2(mp_int *a, mp_int *b); |
265 | |
266 | /* c = a * 2**b */ |
267 | int mp_mul_2d(mp_int *a, int b, mp_int *c); |
268 | |
269 | /* b = a*2 */ |
270 | int mp_mul_2(mp_int *a, mp_int *b); |
271 | |
272 | /* c = a mod 2**d */ |
273 | int mp_mod_2d(mp_int *a, int b, mp_int *c); |
274 | |
275 | /* computes a = 2**b */ |
276 | int mp_2expt(mp_int *a, int b); |
277 | |
278 | /* Counts the number of lsbs which are zero before the first zero bit */ |
279 | int mp_cnt_lsb(mp_int *a); |
280 | |
281 | /* I Love Earth! */ |
282 | |
283 | /* makes a pseudo-random int of a given size */ |
284 | int mp_rand(mp_int *a, int digits); |
285 | |
286 | /* ---> binary operations <--- */ |
287 | /* c = a XOR b */ |
288 | int mp_xor(mp_int *a, mp_int *b, mp_int *c); |
289 | |
290 | /* c = a OR b */ |
291 | int mp_or(mp_int *a, mp_int *b, mp_int *c); |
292 | |
293 | /* c = a AND b */ |
294 | int mp_and(mp_int *a, mp_int *b, mp_int *c); |
295 | |
296 | /* ---> Basic arithmetic <--- */ |
297 | |
298 | /* b = -a */ |
299 | int mp_neg(mp_int *a, mp_int *b); |
300 | |
301 | /* b = |a| */ |
302 | int mp_abs(mp_int *a, mp_int *b); |
303 | |
304 | /* compare a to b */ |
305 | int mp_cmp(mp_int *a, mp_int *b); |
306 | |
307 | /* compare |a| to |b| */ |
308 | int mp_cmp_mag(mp_int *a, mp_int *b); |
309 | |
310 | /* c = a + b */ |
311 | int mp_add(mp_int *a, mp_int *b, mp_int *c); |
312 | |
313 | /* c = a - b */ |
314 | int mp_sub(mp_int *a, mp_int *b, mp_int *c); |
315 | |
316 | /* c = a * b */ |
317 | int mp_mul(mp_int *a, mp_int *b, mp_int *c); |
318 | |
319 | /* b = a*a */ |
320 | int mp_sqr(mp_int *a, mp_int *b); |
321 | |
322 | /* a/b => cb + d == a */ |
323 | int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d); |
324 | |
325 | /* c = a mod b, 0 <= c < b */ |
326 | int mp_mod(mp_int *a, mp_int *b, mp_int *c); |
327 | |
328 | /* ---> single digit functions <--- */ |
329 | |
330 | /* compare against a single digit */ |
331 | int mp_cmp_d(mp_int *a, mp_digit b); |
332 | |
333 | /* c = a + b */ |
334 | int mp_add_d(mp_int *a, mp_digit b, mp_int *c); |
335 | |
336 | /* c = a - b */ |
337 | int mp_sub_d(mp_int *a, mp_digit b, mp_int *c); |
338 | |
339 | /* c = a * b */ |
340 | int mp_mul_d(mp_int *a, mp_digit b, mp_int *c); |
341 | |
342 | /* a/b => cb + d == a */ |
343 | int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d); |
344 | |
345 | /* a/3 => 3c + d == a */ |
346 | int mp_div_3(mp_int *a, mp_int *c, mp_digit *d); |
347 | |
348 | /* c = a**b */ |
349 | int mp_expt_d(mp_int *a, mp_digit b, mp_int *c); |
350 | |
351 | /* c = a mod b, 0 <= c < b */ |
352 | int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c); |
353 | |
354 | /* ---> number theory <--- */ |
355 | |
356 | /* d = a + b (mod c) */ |
357 | int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); |
358 | |
359 | /* d = a - b (mod c) */ |
360 | int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); |
361 | |
362 | /* d = a * b (mod c) */ |
363 | int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); |
364 | |
365 | /* c = a * a (mod b) */ |
366 | int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c); |
367 | |
368 | /* c = 1/a (mod b) */ |
369 | int mp_invmod(mp_int *a, mp_int *b, mp_int *c); |
370 | |
371 | /* c = (a, b) */ |
372 | int mp_gcd(mp_int *a, mp_int *b, mp_int *c); |
373 | |
374 | /* produces value such that U1*a + U2*b = U3 */ |
375 | int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3); |
376 | |
377 | /* c = [a, b] or (a*b)/(a, b) */ |
378 | int mp_lcm(mp_int *a, mp_int *b, mp_int *c); |
379 | |
380 | /* finds one of the b'th root of a, such that |c|**b <= |a| |
381 | * |
382 | * returns error if a < 0 and b is even |
383 | */ |
384 | int mp_n_root(mp_int *a, mp_digit b, mp_int *c); |
385 | |
386 | /* special sqrt algo */ |
387 | int mp_sqrt(mp_int *arg, mp_int *ret); |
388 | |
389 | /* is number a square? */ |
390 | int mp_is_square(mp_int *arg, int *ret); |
391 | |
392 | /* computes the jacobi c = (a | n) (or Legendre if b is prime) */ |
393 | int mp_jacobi(mp_int *a, mp_int *n, int *c); |
394 | |
395 | /* used to setup the Barrett reduction for a given modulus b */ |
396 | int mp_reduce_setup(mp_int *a, mp_int *b); |
397 | |
398 | /* Barrett Reduction, computes a (mod b) with a precomputed value c |
399 | * |
400 | * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely |
401 | * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code]. |
402 | */ |
403 | int mp_reduce(mp_int *a, mp_int *b, mp_int *c); |
404 | |
405 | /* setups the montgomery reduction */ |
406 | int mp_montgomery_setup(mp_int *a, mp_digit *mp); |
407 | |
408 | /* computes a = B**n mod b without division or multiplication useful for |
409 | * normalizing numbers in a Montgomery system. |
410 | */ |
411 | int mp_montgomery_calc_normalization(mp_int *a, mp_int *b); |
412 | |
413 | /* computes x/R == x (mod N) via Montgomery Reduction */ |
414 | int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); |
415 | |
416 | /* returns 1 if a is a valid DR modulus */ |
417 | int mp_dr_is_modulus(mp_int *a); |
418 | |
419 | /* sets the value of "d" required for mp_dr_reduce */ |
420 | void mp_dr_setup(mp_int *a, mp_digit *d); |
421 | |
422 | /* reduces a modulo b using the Diminished Radix method */ |
423 | int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp); |
424 | |
425 | /* returns true if a can be reduced with mp_reduce_2k */ |
426 | int mp_reduce_is_2k(mp_int *a); |
427 | |
428 | /* determines k value for 2k reduction */ |
429 | int mp_reduce_2k_setup(mp_int *a, mp_digit *d); |
430 | |
431 | /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ |
432 | int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d); |
433 | |
434 | /* returns true if a can be reduced with mp_reduce_2k_l */ |
435 | int mp_reduce_is_2k_l(mp_int *a); |
436 | |
437 | /* determines k value for 2k reduction */ |
438 | int mp_reduce_2k_setup_l(mp_int *a, mp_int *d); |
439 | |
440 | /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */ |
441 | int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d); |
442 | |
443 | /* d = a**b (mod c) */ |
444 | int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); |
445 | |
446 | /* ---> Primes <--- */ |
447 | |
448 | /* number of primes */ |
449 | #ifdef MP_8BIT |
450 | #define PRIME_SIZE 31 |
451 | #else |
452 | #define PRIME_SIZE 256 |
453 | #endif |
454 | |
455 | /* table of first PRIME_SIZE primes */ |
456 | extern const mp_digit ltm_prime_tab[]; |
457 | |
458 | /* result=1 if a is divisible by one of the first PRIME_SIZE primes */ |
459 | int mp_prime_is_divisible(mp_int *a, int *result); |
460 | |
461 | /* performs one Fermat test of "a" using base "b". |
462 | * Sets result to 0 if composite or 1 if probable prime |
463 | */ |
464 | int mp_prime_fermat(mp_int *a, mp_int *b, int *result); |
465 | |
466 | /* performs one Miller-Rabin test of "a" using base "b". |
467 | * Sets result to 0 if composite or 1 if probable prime |
468 | */ |
469 | int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result); |
470 | |
471 | /* This gives [for a given bit size] the number of trials required |
472 | * such that Miller-Rabin gives a prob of failure lower than 2^-96 |
473 | */ |
474 | int mp_prime_rabin_miller_trials(int size); |
475 | |
476 | /* performs t rounds of Miller-Rabin on "a" using the first |
477 | * t prime bases. Also performs an initial sieve of trial |
478 | * division. Determines if "a" is prime with probability |
479 | * of error no more than (1/4)**t. |
480 | * |
481 | * Sets result to 1 if probably prime, 0 otherwise |
482 | */ |
483 | int mp_prime_is_prime(mp_int *a, int t, int *result); |
484 | |
485 | /* finds the next prime after the number "a" using "t" trials |
486 | * of Miller-Rabin. |
487 | * |
488 | * bbs_style = 1 means the prime must be congruent to 3 mod 4 |
489 | */ |
490 | int mp_prime_next_prime(mp_int *a, int t, int bbs_style); |
491 | |
492 | /* makes a truly random prime of a given size (bytes), |
493 | * call with bbs = 1 if you want it to be congruent to 3 mod 4 |
494 | * |
495 | * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can |
496 | * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself |
497 | * so it can be NULL |
498 | * |
499 | * The prime generated will be larger than 2^(8*size). |
500 | */ |
501 | #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) |
502 | |
503 | /* makes a truly random prime of a given size (bits), |
504 | * |
505 | * Flags are as follows: |
506 | * |
507 | * LTM_PRIME_BBS - make prime congruent to 3 mod 4 |
508 | * LTM_PRIME_SAFE - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS) |
509 | * LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero |
510 | * LTM_PRIME_2MSB_ON - make the 2nd highest bit one |
511 | * |
512 | * You have to supply a callback which fills in a buffer with random bytes. "dat" is a parameter you can |
513 | * have passed to the callback (e.g. a state or something). This function doesn't use "dat" itself |
514 | * so it can be NULL |
515 | * |
516 | */ |
517 | int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); |
518 | |
519 | /* ---> radix conversion <--- */ |
520 | int mp_count_bits(mp_int *a); |
521 | |
522 | int mp_unsigned_bin_size(mp_int *a); |
523 | int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); |
524 | int mp_to_unsigned_bin(mp_int *a, unsigned char *b); |
525 | int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); |
526 | |
527 | int mp_signed_bin_size(mp_int *a); |
528 | int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); |
529 | int mp_to_signed_bin(mp_int *a, unsigned char *b); |
530 | int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); |
531 | |
532 | int mp_read_radix(mp_int *a, const char *str, int radix); |
533 | int mp_toradix(mp_int *a, char *str, int radix); |
534 | int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); |
535 | int mp_radix_size(mp_int *a, int radix, int *size); |
536 | |
537 | int mp_fread(mp_int *a, int radix, FILE *stream); |
538 | int mp_fwrite(mp_int *a, int radix, FILE *stream); |
539 | |
540 | #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len)) |
541 | #define mp_raw_size(mp) mp_signed_bin_size(mp) |
542 | #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str)) |
543 | #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len)) |
544 | #define mp_mag_size(mp) mp_unsigned_bin_size(mp) |
545 | #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str)) |
546 | |
547 | #define mp_tobinary(M, S) mp_toradix((M), (S), 2) |
548 | #define mp_tooctal(M, S) mp_toradix((M), (S), 8) |
549 | #define mp_todecimal(M, S) mp_toradix((M), (S), 10) |
550 | #define mp_tohex(M, S) mp_toradix((M), (S), 16) |
551 | |
552 | /* lowlevel functions, do not call! */ |
553 | int s_mp_add(mp_int *a, mp_int *b, mp_int *c); |
554 | int s_mp_sub(mp_int *a, mp_int *b, mp_int *c); |
555 | #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) |
556 | int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); |
557 | int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); |
558 | int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); |
559 | int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); |
560 | int fast_s_mp_sqr(mp_int *a, mp_int *b); |
561 | int s_mp_sqr(mp_int *a, mp_int *b); |
562 | int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c); |
563 | int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c); |
564 | int mp_karatsuba_sqr(mp_int *a, mp_int *b); |
565 | int mp_toom_sqr(mp_int *a, mp_int *b); |
566 | int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c); |
567 | int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c); |
568 | int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); |
569 | int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode); |
570 | int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode); |
571 | void bn_reverse(unsigned char *s, int len); |
572 | |
573 | extern const char *mp_s_rmap; |
574 | |
575 | #ifdef __cplusplus |
576 | } |
577 | #endif |
578 | |
579 | #endif |
580 | |
581 | |
582 | /* $Source$ */ |
583 | /* $Revision: 0.39 $ */ |
584 | /* $Date: 2006-04-06 19:49:59 +0000 $ */ |
585 | |