1 /* $NetBSD: tommath.h,v 1.2 2017/01/28 21:31:47 christos 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__) && !defined(__ILP32__) 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 const char* string */ 195 const 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, int t); 526 527 /* ---> radix conversion <--- */ 528 int mp_count_bits(mp_int *a); 529 530 int mp_unsigned_bin_size(mp_int *a); 531 int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); 532 int mp_to_unsigned_bin(mp_int *a, unsigned char *b); 533 int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); 534 535 int mp_signed_bin_size(mp_int *a); 536 int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); 537 int mp_to_signed_bin(mp_int *a, unsigned char *b); 538 int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); 539 540 int mp_read_radix(mp_int *a, const char *str, int radix); 541 int mp_toradix(mp_int *a, char *str, int radix); 542 int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); 543 int mp_radix_size(mp_int *a, int radix, int *size); 544 545 int mp_fread(mp_int *a, int radix, FILE *stream); 546 int mp_fwrite(mp_int *a, int radix, FILE *stream); 547 548 #define mp_read_raw(mp, str, len) mp_read_signed_bin((mp), (str), (len)) 549 #define mp_raw_size(mp) mp_signed_bin_size(mp) 550 #define mp_toraw(mp, str) mp_to_signed_bin((mp), (str)) 551 #define mp_read_mag(mp, str, len) mp_read_unsigned_bin((mp), (str), (len)) 552 #define mp_mag_size(mp) mp_unsigned_bin_size(mp) 553 #define mp_tomag(mp, str) mp_to_unsigned_bin((mp), (str)) 554 555 #define mp_tobinary(M, S) mp_toradix((M), (S), 2) 556 #define mp_tooctal(M, S) mp_toradix((M), (S), 8) 557 #define mp_todecimal(M, S) mp_toradix((M), (S), 10) 558 #define mp_tohex(M, S) mp_toradix((M), (S), 16) 559 560 /* lowlevel functions, do not call! */ 561 int s_mp_add(mp_int *a, mp_int *b, mp_int *c); 562 int s_mp_sub(mp_int *a, mp_int *b, mp_int *c); 563 #define s_mp_mul(a, b, c) s_mp_mul_digs(a, b, c, (a)->used + (b)->used + 1) 564 int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 565 int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 566 int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 567 int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 568 int fast_s_mp_sqr(mp_int *a, mp_int *b); 569 int s_mp_sqr(mp_int *a, mp_int *b); 570 int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c); 571 int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c); 572 int mp_karatsuba_sqr(mp_int *a, mp_int *b); 573 int mp_toom_sqr(mp_int *a, mp_int *b); 574 int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c); 575 int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c); 576 int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); 577 int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode); 578 int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode); 579 void bn_reverse(unsigned char *s, int len); 580 581 extern const char *mp_s_rmap; 582 583 #ifdef __cplusplus 584 } 585 #endif 586 587 #endif 588 589 590 /* Source: /cvs/libtom/libtommath/tommath.h,v */ 591 /* Revision: 1.8 */ 592 /* Date: 2006/03/31 14:18:44 */ 593