crypto/external/bsd/heimdal/dist/lib/hcrypto/libtommath/tommath.h

   1 /*      $NetBSD: tommath.h,v 1.1.1.2 2014/04/24 12:45:31 pettai Exp $   */
   2
   3 /* LibTomMath, multiple-precision integer library -- Tom St Denis
   4  *
   5  * LibTomMath is a library that provides multiple-precision
   6  * integer arithmetic as well as number theoretic functionality.
   7  *
   8  * The library was designed directly after the MPI library by
   9  * Michael Fromberger but has been written from scratch with
  10  * additional optimizations in place.
  11  *
  12  * The library is free for all purposes without any express
  13  * guarantee it works.
  14  *
  15  * Tom St Denis, tomstdenis@gmail.com, http://math.libtomcrypt.com
  16  */
  17 #ifndef BN_H_
  18 #define BN_H_
  19
  20 #include <stdio.h>
  21 #include <string.h>
  22 #include <stdlib.h>
  23 #include <ctype.h>
  24 #include <limits.h>
  25
  26 #include <tommath_class.h>
  27
  28 #ifndef MIN
  29    #define MIN(x,y) ((x)<(y)?(x):(y))
  30 #endif
  31
  32 #ifndef MAX
  33    #define MAX(x,y) ((x)>(y)?(x):(y))
  34 #endif
  35
  36 #ifdef __cplusplus
  37 extern "C" {
  38
  39 /* C++ compilers don't like assigning void * to mp_digit * */
  40 #define  OPT_CAST(x)  (x *)
  41
  42 #else
  43
  44 /* C on the other hand doesn't care */
  45 #define  OPT_CAST(x)
  46
  47 #endif
  48
  49
  50 /* detect 64-bit mode if possible */
  51 #if defined(__x86_64__)
  52    #if !(defined(MP_64BIT) && defined(MP_16BIT) && defined(MP_8BIT))
  53       #define MP_64BIT
  54    #endif
  55 #endif
  56
  57 /* some default configurations.
  58  *
  59  * A "mp_digit" must be able to hold DIGIT_BIT + 1 bits
  60  * A "mp_word" must be able to hold 2*DIGIT_BIT + 1 bits
  61  *
  62  * At the very least a mp_digit must be able to hold 7 bits
  63  * [any size beyond that is ok provided it doesn't overflow the data type]
  64  */
  65 #ifdef MP_8BIT
  66    typedef unsigned char      mp_digit;
  67    typedef unsigned short     mp_word;
  68 #elif defined(MP_16BIT)
  69    typedef unsigned short     mp_digit;
  70    typedef unsigned long      mp_word;
  71 #elif defined(MP_64BIT)
  72    /* for GCC only on supported platforms */
  73 #ifndef CRYPT
  74    typedef unsigned long long ulong64;
  75    typedef signed long long   long64;
  76 #endif
  77
  78    typedef unsigned long      mp_digit;
  79    typedef unsigned long      mp_word __attribute__ ((mode(TI)));
  80
  81    #define DIGIT_BIT          60
  82 #else
  83    /* this is the default case, 28-bit digits */
  84
  85    /* this is to make porting into LibTomCrypt easier :-) */
  86 #ifndef CRYPT
  87    #if defined(_MSC_VER) || defined(__BORLANDC__)
  88       typedef unsigned __int64   ulong64;
  89       typedef signed __int64     long64;
  90    #else
  91       typedef unsigned long long ulong64;
  92       typedef signed long long   long64;
  93    #endif
  94 #endif
  95
  96    typedef unsigned long      mp_digit;
  97    typedef ulong64            mp_word;
  98
  99 #ifdef MP_31BIT
 100    /* this is an extension that uses 31-bit digits */
 101    #define DIGIT_BIT          31
 102 #else
 103    /* default case is 28-bit digits, defines MP_28BIT as a handy macro to test */
 104    #define DIGIT_BIT          28
 105    #define MP_28BIT
 106 #endif
 107 #endif
 108
 109 /* define heap macros */
 110 #ifndef CRYPT
 111    /* default to libc stuff */
 112    #ifndef XMALLOC
 113        #define XMALLOC  malloc
 114        #define XFREE    free
 115        #define XREALLOC realloc
 116        #define XCALLOC  calloc
 117    #else
 118       /* prototypes for our heap functions */
 119       extern void *XMALLOC(size_t n);
 120       extern void *XREALLOC(void *p, size_t n);
 121       extern void *XCALLOC(size_t n, size_t s);
 122       extern void XFREE(void *p);
 123    #endif
 124 #endif
 125
 126
 127 /* otherwise the bits per digit is calculated automatically from the size of a mp_digit */
 128 #ifndef DIGIT_BIT
 129    #define DIGIT_BIT     ((int)((CHAR_BIT * sizeof(mp_digit) - 1)))  /* bits per digit */
 130 #endif
 131
 132 #define MP_DIGIT_BIT     DIGIT_BIT
 133 #define MP_MASK          ((((mp_digit)1)<<((mp_digit)DIGIT_BIT))-((mp_digit)1))
 134 #define MP_DIGIT_MAX     MP_MASK
 135
 136 /* equalities */
 137 #define MP_LT        -1   /* less than */
 138 #define MP_EQ         0   /* equal to */
 139 #define MP_GT         1   /* greater than */
 140
 141 #define MP_ZPOS       0   /* positive integer */
 142 #define MP_NEG        1   /* negative */
 143
 144 #define MP_OKAY       0   /* ok result */
 145 #define MP_MEM        -2  /* out of mem */
 146 #define MP_VAL        -3  /* invalid input */
 147 #define MP_RANGE      MP_VAL
 148
 149 #define MP_YES        1   /* yes response */
 150 #define MP_NO         0   /* no response */
 151
 152 /* Primality generation flags */
 153 #define LTM_PRIME_BBS      0x0001 /* BBS style prime */
 154 #define LTM_PRIME_SAFE     0x0002 /* Safe prime (p-1)/2 == prime */
 155 #define LTM_PRIME_2MSB_ON  0x0008 /* force 2nd MSB to 1 */
 156
 157 typedef int           mp_err;
 158
 159 /* you'll have to tune these... */
 160 extern int KARATSUBA_MUL_CUTOFF,
 161            KARATSUBA_SQR_CUTOFF,
 162            TOOM_MUL_CUTOFF,
 163            TOOM_SQR_CUTOFF;
 164
 165 /* define this to use lower memory usage routines (exptmods mostly) */
 166 /* #define MP_LOW_MEM */
 167
 168 /* default precision */
 169 #ifndef MP_PREC
 170    #ifndef MP_LOW_MEM
 171       #define MP_PREC                 32     /* default digits of precision */
 172    #else
 173       #define MP_PREC                 8      /* default digits of precision */
 174    #endif
 175 #endif
 176
 177 /* size of comba arrays, should be at least 2 * 2**(BITS_PER_WORD - BITS_PER_DIGIT*2) */
 178 #define MP_WARRAY               (1 << (sizeof(mp_word) * CHAR_BIT - 2 * DIGIT_BIT + 1))
 179
 180 /* the infamous mp_int structure */
 181 typedef struct  {
 182     int used, alloc, sign;
 183     mp_digit *dp;
 184 } mp_int;
 185
 186 /* callback for mp_prime_random, should fill dst with random bytes and return how many read [upto len] */
 187 typedef int ltm_prime_callback(unsigned char *dst, int len, void *dat);
 188
 189
 190 #define USED(m)    ((m)->used)
 191 #define DIGIT(m,k) ((m)->dp[(k)])
 192 #define SIGN(m)    ((m)->sign)
 193
 194 /* error code to char* string */
 195 char *mp_error_to_string(int code);
 196
 197 /* ---> init and deinit bignum functions <--- */
 198 /* init a bignum */
 199 int mp_init(mp_int *a);
 200
 201 /* free a bignum */
 202 void mp_clear(mp_int *a);
 203
 204 /* init a null terminated series of arguments */
 205 int mp_init_multi(mp_int *mp, ...);
 206
 207 /* clear a null terminated series of arguments */
 208 void mp_clear_multi(mp_int *mp, ...);
 209
 210 /* exchange two ints */
 211 void mp_exch(mp_int *a, mp_int *b);
 212
 213 /* shrink ram required for a bignum */
 214 int mp_shrink(mp_int *a);
 215
 216 /* grow an int to a given size */
 217 int mp_grow(mp_int *a, int size);
 218
 219 /* init to a given number of digits */
 220 int mp_init_size(mp_int *a, int size);
 221
 222 /* ---> Basic Manipulations <--- */
 223 #define mp_iszero(a) (((a)->used == 0) ? MP_YES : MP_NO)
 224 #define mp_iseven(a) (((a)->used > 0 && (((a)->dp[0] & 1) == 0)) ? MP_YES : MP_NO)
 225 #define mp_isodd(a)  (((a)->used > 0 && (((a)->dp[0] & 1) == 1)) ? MP_YES : MP_NO)
 226 #define mp_isneg(a)  (((a)->sign) ? MP_YES : MP_NO)
 227
 228 /* set to zero */
 229 void mp_zero(mp_int *a);
 230
 231 /* set to zero, multi */
 232 void mp_zero_multi(mp_int *a, ...);
 233
 234 /* set to a digit */
 235 void mp_set(mp_int *a, mp_digit b);
 236
 237 /* set a 32-bit const */
 238 int mp_set_int(mp_int *a, unsigned long b);
 239
 240 /* get a 32-bit value */
 241 unsigned long mp_get_int(mp_int * a);
 242
 243 /* initialize and set a digit */
 244 int mp_init_set (mp_int * a, mp_digit b);
 245
 246 /* initialize and set 32-bit value */
 247 int mp_init_set_int (mp_int * a, unsigned long b);
 248
 249 /* copy, b = a */
 250 int mp_copy(mp_int *a, mp_int *b);
 251
 252 /* inits and copies, a = b */
 253 int mp_init_copy(mp_int *a, mp_int *b);
 254
 255 /* trim unused digits */
 256 void mp_clamp(mp_int *a);
 257
 258 /* ---> digit manipulation <--- */
 259
 260 /* right shift by "b" digits */
 261 void mp_rshd(mp_int *a, int b);
 262
 263 /* left shift by "b" digits */
 264 int mp_lshd(mp_int *a, int b);
 265
 266 /* c = a / 2**b */
 267 int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d);
 268
 269 /* b = a/2 */
 270 int mp_div_2(mp_int *a, mp_int *b);
 271
 272 /* c = a * 2**b */
 273 int mp_mul_2d(mp_int *a, int b, mp_int *c);
 274
 275 /* b = a*2 */
 276 int mp_mul_2(mp_int *a, mp_int *b);
 277
 278 /* c = a mod 2**d */
 279 int mp_mod_2d(mp_int *a, int b, mp_int *c);
 280
 281 /* computes a = 2**b */
 282 int mp_2expt(mp_int *a, int b);
 283
 284 /* Counts the number of lsbs which are zero before the first zero bit */
 285 int mp_cnt_lsb(mp_int *a);
 286
 287 /* I Love Earth! */
 288
 289 /* makes a pseudo-random int of a given size */
 290 int mp_rand(mp_int *a, int digits);
 291
 292 /* ---> binary operations <--- */
 293 /* c = a XOR b  */
 294 int mp_xor(mp_int *a, mp_int *b, mp_int *c);
 295
 296 /* c = a OR b */
 297 int mp_or(mp_int *a, mp_int *b, mp_int *c);
 298
 299 /* c = a AND b */
 300 int mp_and(mp_int *a, mp_int *b, mp_int *c);
 301
 302 /* ---> Basic arithmetic <--- */
 303
 304 /* b = -a */
 305 int mp_neg(mp_int *a, mp_int *b);
 306
 307 /* b = |a| */
 308 int mp_abs(mp_int *a, mp_int *b);
 309
 310 /* compare a to b */
 311 int mp_cmp(mp_int *a, mp_int *b);
 312
 313 /* compare |a| to |b| */
 314 int mp_cmp_mag(mp_int *a, mp_int *b);
 315
 316 /* c = a + b */
 317 int mp_add(mp_int *a, mp_int *b, mp_int *c);
 318
 319 /* c = a - b */
 320 int mp_sub(mp_int *a, mp_int *b, mp_int *c);
 321
 322 /* c = a * b */
 323 int mp_mul(mp_int *a, mp_int *b, mp_int *c);
 324
 325 /* b = a*a  */
 326 int mp_sqr(mp_int *a, mp_int *b);
 327
 328 /* a/b => cb + d == a */
 329 int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
 330
 331 /* c = a mod b, 0 <= c < b  */
 332 int mp_mod(mp_int *a, mp_int *b, mp_int *c);
 333
 334 /* ---> single digit functions <--- */
 335
 336 /* compare against a single digit */
 337 int mp_cmp_d(mp_int *a, mp_digit b);
 338
 339 /* c = a + b */
 340 int mp_add_d(mp_int *a, mp_digit b, mp_int *c);
 341
 342 /* c = a - b */
 343 int mp_sub_d(mp_int *a, mp_digit b, mp_int *c);
 344
 345 /* c = a * b */
 346 int mp_mul_d(mp_int *a, mp_digit b, mp_int *c);
 347
 348 /* a/b => cb + d == a */
 349 int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d);
 350
 351 /* a/3 => 3c + d == a */
 352 int mp_div_3(mp_int *a, mp_int *c, mp_digit *d);
 353
 354 /* c = a**b */
 355 int mp_expt_d(mp_int *a, mp_digit b, mp_int *c);
 356
 357 /* c = a mod b, 0 <= c < b  */
 358 int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c);
 359
 360 /* ---> number theory <--- */
 361
 362 /* d = a + b (mod c) */
 363 int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
 364
 365 /* d = a - b (mod c) */
 366 int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
 367
 368 /* d = a * b (mod c) */
 369 int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
 370
 371 /* c = a * a (mod b) */
 372 int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c);
 373
 374 /* c = 1/a (mod b) */
 375 int mp_invmod(mp_int *a, mp_int *b, mp_int *c);
 376
 377 /* c = (a, b) */
 378 int mp_gcd(mp_int *a, mp_int *b, mp_int *c);
 379
 380 /* produces value such that U1*a + U2*b = U3 */
 381 int mp_exteuclid(mp_int *a, mp_int *b, mp_int *U1, mp_int *U2, mp_int *U3);
 382
 383 /* c = [a, b] or (a*b)/(a, b) */
 384 int mp_lcm(mp_int *a, mp_int *b, mp_int *c);
 385
 386 /* finds one of the b'th root of a, such that |c|**b <= |a|
 387  *
 388  * returns error if a < 0 and b is even
 389  */
 390 int mp_n_root(mp_int *a, mp_digit b, mp_int *c);
 391
 392 /* special sqrt algo */
 393 int mp_sqrt(mp_int *arg, mp_int *ret);
 394
 395 /* is number a square? */
 396 int mp_is_square(mp_int *arg, int *ret);
 397
 398 /* computes the jacobi c = (a | n) (or Legendre if b is prime)  */
 399 int mp_jacobi(mp_int *a, mp_int *n, int *c);
 400
 401 /* used to setup the Barrett reduction for a given modulus b */
 402 int mp_reduce_setup(mp_int *a, mp_int *b);
 403
 404 /* Barrett Reduction, computes a (mod b) with a precomputed value c
 405  *
 406  * Assumes that 0 < a <= b*b, note if 0 > a > -(b*b) then you can merely
 407  * compute the reduction as -1 * mp_reduce(mp_abs(a)) [pseudo code].
 408  */
 409 int mp_reduce(mp_int *a, mp_int *b, mp_int *c);
 410
 411 /* setups the montgomery reduction */
 412 int mp_montgomery_setup(mp_int *a, mp_digit *mp);
 413
 414 /* computes a = B**n mod b without division or multiplication useful for
 415  * normalizing numbers in a Montgomery system.
 416  */
 417 int mp_montgomery_calc_normalization(mp_int *a, mp_int *b);
 418
 419 /* computes x/R == x (mod N) via Montgomery Reduction */
 420 int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
 421
 422 /* returns 1 if a is a valid DR modulus */
 423 int mp_dr_is_modulus(mp_int *a);
 424
 425 /* sets the value of "d" required for mp_dr_reduce */
 426 void mp_dr_setup(mp_int *a, mp_digit *d);
 427
 428 /* reduces a modulo b using the Diminished Radix method */
 429 int mp_dr_reduce(mp_int *a, mp_int *b, mp_digit mp);
 430
 431 /* returns true if a can be reduced with mp_reduce_2k */
 432 int mp_reduce_is_2k(mp_int *a);
 433
 434 /* determines k value for 2k reduction */
 435 int mp_reduce_2k_setup(mp_int *a, mp_digit *d);
 436
 437 /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
 438 int mp_reduce_2k(mp_int *a, mp_int *n, mp_digit d);
 439
 440 /* returns true if a can be reduced with mp_reduce_2k_l */
 441 int mp_reduce_is_2k_l(mp_int *a);
 442
 443 /* determines k value for 2k reduction */
 444 int mp_reduce_2k_setup_l(mp_int *a, mp_int *d);
 445
 446 /* reduces a modulo b where b is of the form 2**p - k [0 <= a] */
 447 int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d);
 448
 449 /* d = a**b (mod c) */
 450 int mp_exptmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d);
 451
 452 /* ---> Primes <--- */
 453
 454 /* number of primes */
 455 #ifdef MP_8BIT
 456    #define PRIME_SIZE      31
 457 #else
 458    #define PRIME_SIZE      256
 459 #endif
 460
 461 /* table of first PRIME_SIZE primes */
 462 extern const mp_digit ltm_prime_tab[];
 463
 464 /* result=1 if a is divisible by one of the first PRIME_SIZE primes */
 465 int mp_prime_is_divisible(mp_int *a, int *result);
 466
 467 /* performs one Fermat test of "a" using base "b".
 468  * Sets result to 0 if composite or 1 if probable prime
 469  */
 470 int mp_prime_fermat(mp_int *a, mp_int *b, int *result);
 471
 472 /* performs one Miller-Rabin test of "a" using base "b".
 473  * Sets result to 0 if composite or 1 if probable prime
 474  */
 475 int mp_prime_miller_rabin(mp_int *a, mp_int *b, int *result);
 476
 477 /* This gives [for a given bit size] the number of trials required
 478  * such that Miller-Rabin gives a prob of failure lower than 2^-96
 479  */
 480 int mp_prime_rabin_miller_trials(int size);
 481
 482 /* performs t rounds of Miller-Rabin on "a" using the first
 483  * t prime bases.  Also performs an initial sieve of trial
 484  * division.  Determines if "a" is prime with probability
 485  * of error no more than (1/4)**t.
 486  *
 487  * Sets result to 1 if probably prime, 0 otherwise
 488  */
 489 int mp_prime_is_prime(mp_int *a, int t, int *result);
 490
 491 /* finds the next prime after the number "a" using "t" trials
 492  * of Miller-Rabin.
 493  *
 494  * bbs_style = 1 means the prime must be congruent to 3 mod 4
 495  */
 496 int mp_prime_next_prime(mp_int *a, int t, int bbs_style);
 497
 498 /* makes a truly random prime of a given size (bytes),
 499  * call with bbs = 1 if you want it to be congruent to 3 mod 4
 500  *
 501  * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 502  * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 503  * so it can be NULL
 504  *
 505  * The prime generated will be larger than 2^(8*size).
 506  */
 507 #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)
 508
 509 /* makes a truly random prime of a given size (bits),
 510  *
 511  * Flags are as follows:
 512  *
 513  *   LTM_PRIME_BBS      - make prime congruent to 3 mod 4
 514  *   LTM_PRIME_SAFE     - make sure (p-1)/2 is prime as well (implies LTM_PRIME_BBS)
 515  *   LTM_PRIME_2MSB_OFF - make the 2nd highest bit zero
 516  *   LTM_PRIME_2MSB_ON  - make the 2nd highest bit one
 517  *
 518  * You have to supply a callback which fills in a buffer with random bytes.  "dat" is a parameter you can
 519  * have passed to the callback (e.g. a state or something).  This function doesn't use "dat" itself
 520  * so it can be NULL
 521  *
 522  */
 523 int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat);
 524
 525 int mp_find_prime(mp_int *a);
 526
 527 int mp_isprime(mp_int *a);
 528
 529 /* ---> radix conversion <--- */
 530 int mp_count_bits(mp_int *a);
 531
 532 int mp_unsigned_bin_size(mp_int *a);
 533 int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c);
 534 int mp_to_unsigned_bin(mp_int *a, unsigned char *b);
 535 int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
 536
 537 int mp_signed_bin_size(mp_int *a);
 538 int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c);
 539 int mp_to_signed_bin(mp_int *a,  unsigned char *b);
 540 int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen);
 541
 542 int mp_read_radix(mp_int *a, const char *str, int radix);
 543 int mp_toradix(mp_int *a, char *str, int radix);
 544 int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen);
 545 int mp_radix_size(mp_int *a, int radix, int *size);
 546
 547 int mp_fread(mp_int *a, int radix, FILE *stream);
 548 int mp_fwrite(mp_int *a, int radix, FILE *stream);
 549
 550 #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len))
 551 #define mp_raw_size(mp)           mp_signed_bin_size(mp)
 552 #define mp_toraw(mp, str)         mp_to_signed_bin((mp), (str))
 553 #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len))
 554 #define mp_mag_size(mp)           mp_unsigned_bin_size(mp)
 555 #define mp_tomag(mp, str)         mp_to_unsigned_bin((mp), (str))
 556
 557 #define mp_tobinary(M, S)  mp_toradix((M), (S), 2)
 558 #define mp_tooctal(M, S)   mp_toradix((M), (S), 8)
 559 #define mp_todecimal(M, S) mp_toradix((M), (S), 10)
 560 #define mp_tohex(M, S)     mp_toradix((M), (S), 16)
 561
 562 /* lowlevel functions, do not call! */
 563 int s_mp_add(mp_int *a, mp_int *b, mp_int *c);
 564 int s_mp_sub(mp_int *a, mp_int *b, mp_int *c);
 565 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1)
 566 int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
 567 int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
 568 int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
 569 int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs);
 570 int fast_s_mp_sqr(mp_int *a, mp_int *b);
 571 int s_mp_sqr(mp_int *a, mp_int *b);
 572 int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c);
 573 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c);
 574 int mp_karatsuba_sqr(mp_int *a, mp_int *b);
 575 int mp_toom_sqr(mp_int *a, mp_int *b);
 576 int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c);
 577 int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c);
 578 int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp);
 579 int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode);
 580 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode);
 581 void bn_reverse(unsigned char *s, int len);
 582
 583 extern const char *mp_s_rmap;
 584
 585 #ifdef __cplusplus
 586    }
 587 #endif
 588
 589 #endif
 590
 591
 592 /* Source: /cvs/libtom/libtommath/tommath.h,v  */
 593 /* Revision: 1.8  */
 594 /* Date: 2006/03/31 14:18:44  */