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 37extern "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 157typedef int mp_err; 158 159/* you'll have to tune these... */ 160extern 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 */ 181typedef 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] */ 187typedef 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 */ 195const char *mp_error_to_string(int code); 196 197/* ---> init and deinit bignum functions <--- */ 198/* init a bignum */ 199int mp_init(mp_int *a); 200 201/* free a bignum */ 202void mp_clear(mp_int *a); 203 204/* init a null terminated series of arguments */ 205int mp_init_multi(mp_int *mp, ...); 206 207/* clear a null terminated series of arguments */ 208void mp_clear_multi(mp_int *mp, ...); 209 210/* exchange two ints */ 211void mp_exch(mp_int *a, mp_int *b); 212 213/* shrink ram required for a bignum */ 214int mp_shrink(mp_int *a); 215 216/* grow an int to a given size */ 217int mp_grow(mp_int *a, int size); 218 219/* init to a given number of digits */ 220int 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 */ 229void mp_zero(mp_int *a); 230 231/* set to zero, multi */ 232void mp_zero_multi(mp_int *a, ...); 233 234/* set to a digit */ 235void mp_set(mp_int *a, mp_digit b); 236 237/* set a 32-bit const */ 238int mp_set_int(mp_int *a, unsigned long b); 239 240/* get a 32-bit value */ 241unsigned long mp_get_int(mp_int * a); 242 243/* initialize and set a digit */ 244int mp_init_set (mp_int * a, mp_digit b); 245 246/* initialize and set 32-bit value */ 247int mp_init_set_int (mp_int * a, unsigned long b); 248 249/* copy, b = a */ 250int mp_copy(mp_int *a, mp_int *b); 251 252/* inits and copies, a = b */ 253int mp_init_copy(mp_int *a, mp_int *b); 254 255/* trim unused digits */ 256void mp_clamp(mp_int *a); 257 258/* ---> digit manipulation <--- */ 259 260/* right shift by "b" digits */ 261void mp_rshd(mp_int *a, int b); 262 263/* left shift by "b" digits */ 264int mp_lshd(mp_int *a, int b); 265 266/* c = a / 2**b */ 267int mp_div_2d(mp_int *a, int b, mp_int *c, mp_int *d); 268 269/* b = a/2 */ 270int mp_div_2(mp_int *a, mp_int *b); 271 272/* c = a * 2**b */ 273int mp_mul_2d(mp_int *a, int b, mp_int *c); 274 275/* b = a*2 */ 276int mp_mul_2(mp_int *a, mp_int *b); 277 278/* c = a mod 2**d */ 279int mp_mod_2d(mp_int *a, int b, mp_int *c); 280 281/* computes a = 2**b */ 282int mp_2expt(mp_int *a, int b); 283 284/* Counts the number of lsbs which are zero before the first zero bit */ 285int mp_cnt_lsb(mp_int *a); 286 287/* I Love Earth! */ 288 289/* makes a pseudo-random int of a given size */ 290int mp_rand(mp_int *a, int digits); 291 292/* ---> binary operations <--- */ 293/* c = a XOR b */ 294int mp_xor(mp_int *a, mp_int *b, mp_int *c); 295 296/* c = a OR b */ 297int mp_or(mp_int *a, mp_int *b, mp_int *c); 298 299/* c = a AND b */ 300int mp_and(mp_int *a, mp_int *b, mp_int *c); 301 302/* ---> Basic arithmetic <--- */ 303 304/* b = -a */ 305int mp_neg(mp_int *a, mp_int *b); 306 307/* b = |a| */ 308int mp_abs(mp_int *a, mp_int *b); 309 310/* compare a to b */ 311int mp_cmp(mp_int *a, mp_int *b); 312 313/* compare |a| to |b| */ 314int mp_cmp_mag(mp_int *a, mp_int *b); 315 316/* c = a + b */ 317int mp_add(mp_int *a, mp_int *b, mp_int *c); 318 319/* c = a - b */ 320int mp_sub(mp_int *a, mp_int *b, mp_int *c); 321 322/* c = a * b */ 323int mp_mul(mp_int *a, mp_int *b, mp_int *c); 324 325/* b = a*a */ 326int mp_sqr(mp_int *a, mp_int *b); 327 328/* a/b => cb + d == a */ 329int mp_div(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 330 331/* c = a mod b, 0 <= c < b */ 332int mp_mod(mp_int *a, mp_int *b, mp_int *c); 333 334/* ---> single digit functions <--- */ 335 336/* compare against a single digit */ 337int mp_cmp_d(mp_int *a, mp_digit b); 338 339/* c = a + b */ 340int mp_add_d(mp_int *a, mp_digit b, mp_int *c); 341 342/* c = a - b */ 343int mp_sub_d(mp_int *a, mp_digit b, mp_int *c); 344 345/* c = a * b */ 346int mp_mul_d(mp_int *a, mp_digit b, mp_int *c); 347 348/* a/b => cb + d == a */ 349int mp_div_d(mp_int *a, mp_digit b, mp_int *c, mp_digit *d); 350 351/* a/3 => 3c + d == a */ 352int mp_div_3(mp_int *a, mp_int *c, mp_digit *d); 353 354/* c = a**b */ 355int mp_expt_d(mp_int *a, mp_digit b, mp_int *c); 356 357/* c = a mod b, 0 <= c < b */ 358int mp_mod_d(mp_int *a, mp_digit b, mp_digit *c); 359 360/* ---> number theory <--- */ 361 362/* d = a + b (mod c) */ 363int mp_addmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 364 365/* d = a - b (mod c) */ 366int mp_submod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 367 368/* d = a * b (mod c) */ 369int mp_mulmod(mp_int *a, mp_int *b, mp_int *c, mp_int *d); 370 371/* c = a * a (mod b) */ 372int mp_sqrmod(mp_int *a, mp_int *b, mp_int *c); 373 374/* c = 1/a (mod b) */ 375int mp_invmod(mp_int *a, mp_int *b, mp_int *c); 376 377/* c = (a, b) */ 378int mp_gcd(mp_int *a, mp_int *b, mp_int *c); 379 380/* produces value such that U1*a + U2*b = U3 */ 381int 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) */ 384int 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 */ 390int mp_n_root(mp_int *a, mp_digit b, mp_int *c); 391 392/* special sqrt algo */ 393int mp_sqrt(mp_int *arg, mp_int *ret); 394 395/* is number a square? */ 396int mp_is_square(mp_int *arg, int *ret); 397 398/* computes the jacobi c = (a | n) (or Legendre if b is prime) */ 399int mp_jacobi(mp_int *a, mp_int *n, int *c); 400 401/* used to setup the Barrett reduction for a given modulus b */ 402int 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 */ 409int mp_reduce(mp_int *a, mp_int *b, mp_int *c); 410 411/* setups the montgomery reduction */ 412int 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 */ 417int mp_montgomery_calc_normalization(mp_int *a, mp_int *b); 418 419/* computes x/R == x (mod N) via Montgomery Reduction */ 420int mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); 421 422/* returns 1 if a is a valid DR modulus */ 423int mp_dr_is_modulus(mp_int *a); 424 425/* sets the value of "d" required for mp_dr_reduce */ 426void mp_dr_setup(mp_int *a, mp_digit *d); 427 428/* reduces a modulo b using the Diminished Radix method */ 429int 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 */ 432int mp_reduce_is_2k(mp_int *a); 433 434/* determines k value for 2k reduction */ 435int 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] */ 438int 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 */ 441int mp_reduce_is_2k_l(mp_int *a); 442 443/* determines k value for 2k reduction */ 444int 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] */ 447int mp_reduce_2k_l(mp_int *a, mp_int *n, mp_int *d); 448 449/* d = a**b (mod c) */ 450int 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 */ 462extern const mp_digit ltm_prime_tab[]; 463 464/* result=1 if a is divisible by one of the first PRIME_SIZE primes */ 465int 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 */ 470int 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 */ 475int 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 */ 480int 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 */ 489int 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 */ 496int 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 */ 523int mp_prime_random_ex(mp_int *a, int t, int size, int flags, ltm_prime_callback cb, void *dat); 524 525int mp_find_prime(mp_int *a, int t); 526 527/* ---> radix conversion <--- */ 528int mp_count_bits(mp_int *a); 529 530int mp_unsigned_bin_size(mp_int *a); 531int mp_read_unsigned_bin(mp_int *a, const unsigned char *b, int c); 532int mp_to_unsigned_bin(mp_int *a, unsigned char *b); 533int mp_to_unsigned_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); 534 535int mp_signed_bin_size(mp_int *a); 536int mp_read_signed_bin(mp_int *a, const unsigned char *b, int c); 537int mp_to_signed_bin(mp_int *a, unsigned char *b); 538int mp_to_signed_bin_n (mp_int * a, unsigned char *b, unsigned long *outlen); 539 540int mp_read_radix(mp_int *a, const char *str, int radix); 541int mp_toradix(mp_int *a, char *str, int radix); 542int mp_toradix_n(mp_int * a, char *str, int radix, int maxlen); 543int mp_radix_size(mp_int *a, int radix, int *size); 544 545int mp_fread(mp_int *a, int radix, FILE *stream); 546int 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! */ 561int s_mp_add(mp_int *a, mp_int *b, mp_int *c); 562int 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) 564int fast_s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 565int s_mp_mul_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 566int fast_s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 567int s_mp_mul_high_digs(mp_int *a, mp_int *b, mp_int *c, int digs); 568int fast_s_mp_sqr(mp_int *a, mp_int *b); 569int s_mp_sqr(mp_int *a, mp_int *b); 570int mp_karatsuba_mul(mp_int *a, mp_int *b, mp_int *c); 571int mp_toom_mul(mp_int *a, mp_int *b, mp_int *c); 572int mp_karatsuba_sqr(mp_int *a, mp_int *b); 573int mp_toom_sqr(mp_int *a, mp_int *b); 574int fast_mp_invmod(mp_int *a, mp_int *b, mp_int *c); 575int mp_invmod_slow (mp_int * a, mp_int * b, mp_int * c); 576int fast_mp_montgomery_reduce(mp_int *a, mp_int *m, mp_digit mp); 577int mp_exptmod_fast(mp_int *G, mp_int *X, mp_int *P, mp_int *Y, int mode); 578int s_mp_exptmod (mp_int * G, mp_int * X, mp_int * P, mp_int * Y, int mode); 579void bn_reverse(unsigned char *s, int len); 580 581extern 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