crypto/bn/bn_prime.c

   1 /*
   2  * WARNING: do not edit!
   3  * Generated by crypto/bn/bn_prime.pl
   4  * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
   5  *
   6  * Licensed under the OpenSSL license (the "License").  You may not use
   7  * this file except in compliance with the License.  You can obtain a copy
   8  * in the file LICENSE in the source distribution or at
   9  * https://www.openssl.org/source/license.html
  10  */
  11
  12 #include <stdio.h>
  13 #include <time.h>
  14 #include "internal/cryptlib.h"
  15 #include "bn_lcl.h"
  16 #include <openssl/rand.h>
  17
  18 /*
  19  * The quick sieve algorithm approach to weeding out primes is Philip
  20  * Zimmermann's, as implemented in PGP.  I have had a read of his comments
  21  * and implemented my own version.
  22  */
  23 #include "bn_prime.h"
  24
  25 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
  26                    const BIGNUM *a1_odd, int k, BN_CTX *ctx,
  27                    BN_MONT_CTX *mont);
  28 static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods);
  29 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
  30                                   const BIGNUM *add, const BIGNUM *rem,
  31                                   BN_CTX *ctx);
  32
  33 static const int prime_offsets[480] = {
  34     13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
  35     89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163,
  36     167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229,
  37     233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293,
  38     299, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367,
  39     373, 377, 379, 383, 389, 391, 397, 401, 403, 409, 419, 421, 431, 433,
  40     437, 439, 443, 449, 457, 461, 463, 467, 479, 481, 487, 491, 493, 499,
  41     503, 509, 521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569,
  42     571, 577, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619, 629, 631,
  43     641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 689, 691, 697, 701,
  44     703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 767, 769,
  45     773, 779, 787, 793, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839,
  46     841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, 893, 899, 901,
  47     907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, 967, 971,
  48     977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, 1031,
  49     1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, 1087,
  50     1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151,
  51     1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213,
  52     1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, 1271,
  53     1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, 1319,
  54     1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373,
  55     1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, 1433,
  56     1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, 1489,
  57     1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549,
  58     1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609,
  59     1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, 1667,
  60     1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, 1721,
  61     1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1781,
  62     1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, 1843,
  63     1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901,
  64     1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, 1951,
  65     1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017,
  66     2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, 2071,
  67     2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, 2131,
  68     2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, 2197,
  69     2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2249,
  70     2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297,
  71     2309, 2311
  72 };
  73
  74 static const int prime_offset_count = 480;
  75 static const int prime_multiplier = 2310;
  76 static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits| <=
  77                                               * |prime_multiplier| */
  78 static const int first_prime_index = 5;
  79
  80 int BN_GENCB_call(BN_GENCB *cb, int a, int b)
  81 {
  82     /* No callback means continue */
  83     if (!cb)
  84         return 1;
  85     switch (cb->ver) {
  86     case 1:
  87         /* Deprecated-style callbacks */
  88         if (!cb->cb.cb_1)
  89             return 1;
  90         cb->cb.cb_1(a, b, cb->arg);
  91         return 1;
  92     case 2:
  93         /* New-style callbacks */
  94         return cb->cb.cb_2(a, b, cb);
  95     default:
  96         break;
  97     }
  98     /* Unrecognised callback type */
  99     return 0;
 100 }
 101
 102 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
 103                          const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
 104 {
 105     BIGNUM *t;
 106     int found = 0;
 107     int i, j, c1 = 0;
 108     BN_CTX *ctx = NULL;
 109     prime_t *mods = NULL;
 110     int checks = BN_prime_checks_for_size(bits);
 111
 112     if (bits < 2) {
 113         /* There are no prime numbers this small. */
 114         BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
 115         return 0;
 116     } else if (bits == 2 && safe) {
 117         /* The smallest safe prime (7) is three bits. */
 118         BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
 119         return 0;
 120     }
 121
 122     mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES);
 123     if (mods == NULL)
 124         goto err;
 125
 126     ctx = BN_CTX_new();
 127     if (ctx == NULL)
 128         goto err;
 129     BN_CTX_start(ctx);
 130     t = BN_CTX_get(ctx);
 131     if (!t)
 132         goto err;
 133  loop:
 134     /* make a random number and set the top and bottom bits */
 135     if (add == NULL) {
 136         if (!probable_prime(ret, bits, mods))
 137             goto err;
 138     } else {
 139         if (safe) {
 140             if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
 141                 goto err;
 142         } else {
 143             if (!bn_probable_prime_dh(ret, bits, add, rem, ctx))
 144                 goto err;
 145         }
 146     }
 147     /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
 148     if (!BN_GENCB_call(cb, 0, c1++))
 149         /* aborted */
 150         goto err;
 151
 152     if (!safe) {
 153         i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
 154         if (i == -1)
 155             goto err;
 156         if (i == 0)
 157             goto loop;
 158     } else {
 159         /*
 160          * for "safe prime" generation, check that (p-1)/2 is prime. Since a
 161          * prime is odd, We just need to divide by 2
 162          */
 163         if (!BN_rshift1(t, ret))
 164             goto err;
 165
 166         for (i = 0; i < checks; i++) {
 167             j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
 168             if (j == -1)
 169                 goto err;
 170             if (j == 0)
 171                 goto loop;
 172
 173             j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
 174             if (j == -1)
 175                 goto err;
 176             if (j == 0)
 177                 goto loop;
 178
 179             if (!BN_GENCB_call(cb, 2, c1 - 1))
 180                 goto err;
 181             /* We have a safe prime test pass */
 182         }
 183     }
 184     /* we have a prime :-) */
 185     found = 1;
 186  err:
 187     OPENSSL_free(mods);
 188     if (ctx != NULL)
 189         BN_CTX_end(ctx);
 190     BN_CTX_free(ctx);
 191     bn_check_top(ret);
 192     return found;
 193 }
 194
 195 int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
 196                    BN_GENCB *cb)
 197 {
 198     return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
 199 }
 200
 201 int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
 202                             int do_trial_division, BN_GENCB *cb)
 203 {
 204     int i, j, ret = -1;
 205     int k;
 206     BN_CTX *ctx = NULL;
 207     BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
 208     BN_MONT_CTX *mont = NULL;
 209     const BIGNUM *A = NULL;
 210
 211     if (BN_cmp(a, BN_value_one()) <= 0)
 212         return 0;
 213
 214     if (checks == BN_prime_checks)
 215         checks = BN_prime_checks_for_size(BN_num_bits(a));
 216
 217     /* first look for small factors */
 218     if (!BN_is_odd(a))
 219         /* a is even => a is prime if and only if a == 2 */
 220         return BN_is_word(a, 2);
 221     if (do_trial_division) {
 222         for (i = 1; i < NUMPRIMES; i++)
 223             if (BN_mod_word(a, primes[i]) == 0)
 224                 return 0;
 225         if (!BN_GENCB_call(cb, 1, -1))
 226             goto err;
 227     }
 228
 229     if (ctx_passed != NULL)
 230         ctx = ctx_passed;
 231     else if ((ctx = BN_CTX_new()) == NULL)
 232         goto err;
 233     BN_CTX_start(ctx);
 234
 235     /* A := abs(a) */
 236     if (a->neg) {
 237         BIGNUM *t;
 238         if ((t = BN_CTX_get(ctx)) == NULL)
 239             goto err;
 240         BN_copy(t, a);
 241         t->neg = 0;
 242         A = t;
 243     } else
 244         A = a;
 245     A1 = BN_CTX_get(ctx);
 246     A1_odd = BN_CTX_get(ctx);
 247     check = BN_CTX_get(ctx);
 248     if (check == NULL)
 249         goto err;
 250
 251     /* compute A1 := A - 1 */
 252     if (!BN_copy(A1, A))
 253         goto err;
 254     if (!BN_sub_word(A1, 1))
 255         goto err;
 256     if (BN_is_zero(A1)) {
 257         ret = 0;
 258         goto err;
 259     }
 260
 261     /* write  A1  as  A1_odd * 2^k */
 262     k = 1;
 263     while (!BN_is_bit_set(A1, k))
 264         k++;
 265     if (!BN_rshift(A1_odd, A1, k))
 266         goto err;
 267
 268     /* Montgomery setup for computations mod A */
 269     mont = BN_MONT_CTX_new();
 270     if (mont == NULL)
 271         goto err;
 272     if (!BN_MONT_CTX_set(mont, A, ctx))
 273         goto err;
 274
 275     for (i = 0; i < checks; i++) {
 276         if (!BN_pseudo_rand_range(check, A1))
 277             goto err;
 278         if (!BN_add_word(check, 1))
 279             goto err;
 280         /* now 1 <= check < A */
 281
 282         j = witness(check, A, A1, A1_odd, k, ctx, mont);
 283         if (j == -1)
 284             goto err;
 285         if (j) {
 286             ret = 0;
 287             goto err;
 288         }
 289         if (!BN_GENCB_call(cb, 1, i))
 290             goto err;
 291     }
 292     ret = 1;
 293  err:
 294     if (ctx != NULL) {
 295         BN_CTX_end(ctx);
 296         if (ctx_passed == NULL)
 297             BN_CTX_free(ctx);
 298     }
 299     BN_MONT_CTX_free(mont);
 300
 301     return (ret);
 302 }
 303
 304 int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx)
 305 {
 306     int i;
 307     int ret = 0;
 308
 309  loop:
 310     if (!BN_rand(rnd, bits, 0, 1))
 311         goto err;
 312
 313     /* we now have a random number 'rand' to test. */
 314
 315     for (i = 1; i < NUMPRIMES; i++) {
 316         /* check that rnd is a prime */
 317         if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
 318             goto loop;
 319         }
 320     }
 321     ret = 1;
 322
 323  err:
 324     bn_check_top(rnd);
 325     return (ret);
 326 }
 327
 328 int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx)
 329 {
 330     int i;
 331     BIGNUM *offset_index;
 332     BIGNUM *offset_count;
 333     int ret = 0;
 334
 335     OPENSSL_assert(bits > prime_multiplier_bits);
 336
 337     BN_CTX_start(ctx);
 338     if ((offset_index = BN_CTX_get(ctx)) == NULL)
 339         goto err;
 340     if ((offset_count = BN_CTX_get(ctx)) == NULL)
 341         goto err;
 342
 343     BN_add_word(offset_count, prime_offset_count);
 344
 345  loop:
 346     if (!BN_rand(rnd, bits - prime_multiplier_bits, 0, 1))
 347         goto err;
 348     if (BN_is_bit_set(rnd, bits))
 349         goto loop;
 350     if (!BN_rand_range(offset_index, offset_count))
 351         goto err;
 352
 353     BN_mul_word(rnd, prime_multiplier);
 354     BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]);
 355
 356     /* we now have a random number 'rand' to test. */
 357
 358     /* skip coprimes */
 359     for (i = first_prime_index; i < NUMPRIMES; i++) {
 360         /* check that rnd is a prime */
 361         if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
 362             goto loop;
 363         }
 364     }
 365     ret = 1;
 366
 367  err:
 368     BN_CTX_end(ctx);
 369     bn_check_top(rnd);
 370     return ret;
 371 }
 372
 373 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
 374                    const BIGNUM *a1_odd, int k, BN_CTX *ctx,
 375                    BN_MONT_CTX *mont)
 376 {
 377     if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
 378         return -1;
 379     if (BN_is_one(w))
 380         return 0;               /* probably prime */
 381     if (BN_cmp(w, a1) == 0)
 382         return 0;               /* w == -1 (mod a), 'a' is probably prime */
 383     while (--k) {
 384         if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
 385             return -1;
 386         if (BN_is_one(w))
 387             return 1;           /* 'a' is composite, otherwise a previous 'w'
 388                                  * would have been == -1 (mod 'a') */
 389         if (BN_cmp(w, a1) == 0)
 390             return 0;           /* w == -1 (mod a), 'a' is probably prime */
 391     }
 392     /*
 393      * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
 394      * it is neither -1 nor +1 -- so 'a' cannot be prime
 395      */
 396     bn_check_top(w);
 397     return 1;
 398 }
 399
 400 static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods)
 401 {
 402     int i;
 403     BN_ULONG delta;
 404     BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
 405     char is_single_word = bits <= BN_BITS2;
 406
 407  again:
 408     if (!BN_rand(rnd, bits, 1, 1))
 409         return (0);
 410     /* we now have a random number 'rnd' to test. */
 411     for (i = 1; i < NUMPRIMES; i++)
 412         mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]);
 413     /*
 414      * If bits is so small that it fits into a single word then we
 415      * additionally don't want to exceed that many bits.
 416      */
 417     if (is_single_word) {
 418         BN_ULONG size_limit;
 419
 420         if (bits == BN_BITS2) {
 421             /*
 422              * Shifting by this much has undefined behaviour so we do it a
 423              * different way
 424              */
 425             size_limit = ~((BN_ULONG)0) - BN_get_word(rnd);
 426         } else {
 427             size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1;
 428         }
 429         if (size_limit < maxdelta)
 430             maxdelta = size_limit;
 431     }
 432     delta = 0;
 433  loop:
 434     if (is_single_word) {
 435         BN_ULONG rnd_word = BN_get_word(rnd);
 436
 437         /*-
 438          * In the case that the candidate prime is a single word then
 439          * we check that:
 440          *   1) It's greater than primes[i] because we shouldn't reject
 441          *      3 as being a prime number because it's a multiple of
 442          *      three.
 443          *   2) That it's not a multiple of a known prime. We don't
 444          *      check that rnd-1 is also coprime to all the known
 445          *      primes because there aren't many small primes where
 446          *      that's true.
 447          */
 448         for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) {
 449             if ((mods[i] + delta) % primes[i] == 0) {
 450                 delta += 2;
 451                 if (delta > maxdelta)
 452                     goto again;
 453                 goto loop;
 454             }
 455         }
 456     } else {
 457         for (i = 1; i < NUMPRIMES; i++) {
 458             /*
 459              * check that rnd is not a prime and also that gcd(rnd-1,primes)
 460              * == 1 (except for 2)
 461              */
 462             if (((mods[i] + delta) % primes[i]) <= 1) {
 463                 delta += 2;
 464                 if (delta > maxdelta)
 465                     goto again;
 466                 goto loop;
 467             }
 468         }
 469     }
 470     if (!BN_add_word(rnd, delta))
 471         return (0);
 472     if (BN_num_bits(rnd) != bits)
 473         goto again;
 474     bn_check_top(rnd);
 475     return (1);
 476 }
 477
 478 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
 479                          const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
 480 {
 481     int i, ret = 0;
 482     BIGNUM *t1;
 483
 484     BN_CTX_start(ctx);
 485     if ((t1 = BN_CTX_get(ctx)) == NULL)
 486         goto err;
 487
 488     if (!BN_rand(rnd, bits, 0, 1))
 489         goto err;
 490
 491     /* we need ((rnd-rem) % add) == 0 */
 492
 493     if (!BN_mod(t1, rnd, add, ctx))
 494         goto err;
 495     if (!BN_sub(rnd, rnd, t1))
 496         goto err;
 497     if (rem == NULL) {
 498         if (!BN_add_word(rnd, 1))
 499             goto err;
 500     } else {
 501         if (!BN_add(rnd, rnd, rem))
 502             goto err;
 503     }
 504
 505     /* we now have a random number 'rand' to test. */
 506
 507  loop:
 508     for (i = 1; i < NUMPRIMES; i++) {
 509         /* check that rnd is a prime */
 510         if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
 511             if (!BN_add(rnd, rnd, add))
 512                 goto err;
 513             goto loop;
 514         }
 515     }
 516     ret = 1;
 517
 518  err:
 519     BN_CTX_end(ctx);
 520     bn_check_top(rnd);
 521     return (ret);
 522 }
 523
 524 static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
 525                                   const BIGNUM *rem, BN_CTX *ctx)
 526 {
 527     int i, ret = 0;
 528     BIGNUM *t1, *qadd, *q;
 529
 530     bits--;
 531     BN_CTX_start(ctx);
 532     t1 = BN_CTX_get(ctx);
 533     q = BN_CTX_get(ctx);
 534     qadd = BN_CTX_get(ctx);
 535     if (qadd == NULL)
 536         goto err;
 537
 538     if (!BN_rshift1(qadd, padd))
 539         goto err;
 540
 541     if (!BN_rand(q, bits, 0, 1))
 542         goto err;
 543
 544     /* we need ((rnd-rem) % add) == 0 */
 545     if (!BN_mod(t1, q, qadd, ctx))
 546         goto err;
 547     if (!BN_sub(q, q, t1))
 548         goto err;
 549     if (rem == NULL) {
 550         if (!BN_add_word(q, 1))
 551             goto err;
 552     } else {
 553         if (!BN_rshift1(t1, rem))
 554             goto err;
 555         if (!BN_add(q, q, t1))
 556             goto err;
 557     }
 558
 559     /* we now have a random number 'rand' to test. */
 560     if (!BN_lshift1(p, q))
 561         goto err;
 562     if (!BN_add_word(p, 1))
 563         goto err;
 564
 565  loop:
 566     for (i = 1; i < NUMPRIMES; i++) {
 567         /* check that p and q are prime */
 568         /*
 569          * check that for p and q gcd(p-1,primes) == 1 (except for 2)
 570          */
 571         if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) ||
 572             (BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) {
 573             if (!BN_add(p, p, padd))
 574                 goto err;
 575             if (!BN_add(q, q, qadd))
 576                 goto err;
 577             goto loop;
 578         }
 579     }
 580     ret = 1;
 581
 582  err:
 583     BN_CTX_end(ctx);
 584     bn_check_top(p);
 585     return (ret);
 586 }