libs/libtommath/tommath.h

   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: /cvs/libtom/libtommath/tommath.h,v $ */
 583 /* $Revision: 1.8 $ */
 584 /* $Date: 2006/03/31 14:18:44 $ */