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: /cvsroot/tcl/libtommath/tommath.h,v $ */ |
---|
583 | /* Based on Tom's version 1.8 */ |
---|
584 | /* $Revision: 1.4 $ */ |
---|
585 | /* $Date: 2006/12/01 00:31:32 $ */ |
---|