2 * WARNING: do not edit!
3 * Generated by crypto/bn/bn_prime.pl
4 * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
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
14 #include "internal/cryptlib.h"
18 * The quick sieve algorithm approach to weeding out primes is Philip
19 * Zimmermann's, as implemented in PGP. I have had a read of his comments
20 * and implemented my own version.
24 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
25 const BIGNUM *a1_odd, int k, BN_CTX *ctx,
27 static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods);
28 static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
29 const BIGNUM *add, const BIGNUM *rem,
32 static const int prime_offsets[480] = {
33 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
34 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163,
35 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229,
36 233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293,
37 299, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367,
38 373, 377, 379, 383, 389, 391, 397, 401, 403, 409, 419, 421, 431, 433,
39 437, 439, 443, 449, 457, 461, 463, 467, 479, 481, 487, 491, 493, 499,
40 503, 509, 521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569,
41 571, 577, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619, 629, 631,
42 641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 689, 691, 697, 701,
43 703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 767, 769,
44 773, 779, 787, 793, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839,
45 841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, 893, 899, 901,
46 907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, 967, 971,
47 977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, 1031,
48 1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, 1087,
49 1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151,
50 1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213,
51 1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, 1271,
52 1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, 1319,
53 1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373,
54 1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, 1433,
55 1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, 1489,
56 1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549,
57 1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609,
58 1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, 1667,
59 1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, 1721,
60 1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1781,
61 1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, 1843,
62 1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901,
63 1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, 1951,
64 1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017,
65 2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, 2071,
66 2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, 2131,
67 2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, 2197,
68 2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2249,
69 2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297,
73 static const int prime_offset_count = 480;
74 static const int prime_multiplier = 2310;
75 static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits| <=
76 * |prime_multiplier| */
77 static const int first_prime_index = 5;
79 int BN_GENCB_call(BN_GENCB *cb, int a, int b)
81 /* No callback means continue */
86 /* Deprecated-style callbacks */
89 cb->cb.cb_1(a, b, cb->arg);
92 /* New-style callbacks */
93 return cb->cb.cb_2(a, b, cb);
97 /* Unrecognised callback type */
101 int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
102 const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
108 prime_t *mods = NULL;
109 int checks = BN_prime_checks_for_size(bits);
112 /* There are no prime numbers this small. */
113 BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
115 } else if (bits == 2 && safe) {
116 /* The smallest safe prime (7) is three bits. */
117 BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
121 mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES);
133 /* make a random number and set the top and bottom bits */
135 if (!probable_prime(ret, bits, mods))
139 if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
142 if (!bn_probable_prime_dh(ret, bits, add, rem, ctx))
147 if (!BN_GENCB_call(cb, 0, c1++))
152 i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
159 * for "safe prime" generation, check that (p-1)/2 is prime. Since a
160 * prime is odd, We just need to divide by 2
162 if (!BN_rshift1(t, ret))
165 for (i = 0; i < checks; i++) {
166 j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
172 j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
178 if (!BN_GENCB_call(cb, 2, c1 - 1))
180 /* We have a safe prime test pass */
183 /* we have a prime :-) */
194 int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
197 return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
200 int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
201 int do_trial_division, BN_GENCB *cb)
206 BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
207 BN_MONT_CTX *mont = NULL;
208 const BIGNUM *A = NULL;
210 if (BN_cmp(a, BN_value_one()) <= 0)
213 if (checks == BN_prime_checks)
214 checks = BN_prime_checks_for_size(BN_num_bits(a));
216 /* first look for small factors */
218 /* a is even => a is prime if and only if a == 2 */
219 return BN_is_word(a, 2);
220 if (do_trial_division) {
221 for (i = 1; i < NUMPRIMES; i++) {
222 BN_ULONG mod = BN_mod_word(a, primes[i]);
223 if (mod == (BN_ULONG)-1)
228 if (!BN_GENCB_call(cb, 1, -1))
232 if (ctx_passed != NULL)
234 else if ((ctx = BN_CTX_new()) == NULL)
241 if ((t = BN_CTX_get(ctx)) == NULL)
248 A1 = BN_CTX_get(ctx);
249 A1_odd = BN_CTX_get(ctx);
250 check = BN_CTX_get(ctx);
254 /* compute A1 := A - 1 */
257 if (!BN_sub_word(A1, 1))
259 if (BN_is_zero(A1)) {
264 /* write A1 as A1_odd * 2^k */
266 while (!BN_is_bit_set(A1, k))
268 if (!BN_rshift(A1_odd, A1, k))
271 /* Montgomery setup for computations mod A */
272 mont = BN_MONT_CTX_new();
275 if (!BN_MONT_CTX_set(mont, A, ctx))
278 for (i = 0; i < checks; i++) {
279 if (!BN_pseudo_rand_range(check, A1))
281 if (!BN_add_word(check, 1))
283 /* now 1 <= check < A */
285 j = witness(check, A, A1, A1_odd, k, ctx, mont);
292 if (!BN_GENCB_call(cb, 1, i))
299 if (ctx_passed == NULL)
302 BN_MONT_CTX_free(mont);
307 int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx)
313 if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
316 /* we now have a random number 'rand' to test. */
318 for (i = 1; i < NUMPRIMES; i++) {
319 /* check that rnd is a prime */
320 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
321 if (mod == (BN_ULONG)-1)
334 int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx)
337 BIGNUM *offset_index;
338 BIGNUM *offset_count;
341 OPENSSL_assert(bits > prime_multiplier_bits);
344 if ((offset_index = BN_CTX_get(ctx)) == NULL)
346 if ((offset_count = BN_CTX_get(ctx)) == NULL)
349 if (!BN_add_word(offset_count, prime_offset_count))
353 if (!BN_rand(rnd, bits - prime_multiplier_bits,
354 BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
356 if (BN_is_bit_set(rnd, bits))
358 if (!BN_rand_range(offset_index, offset_count))
361 if (!BN_mul_word(rnd, prime_multiplier)
362 || !BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]))
365 /* we now have a random number 'rand' to test. */
368 for (i = first_prime_index; i < NUMPRIMES; i++) {
369 /* check that rnd is a prime */
370 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
371 if (mod == (BN_ULONG)-1)
384 static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
385 const BIGNUM *a1_odd, int k, BN_CTX *ctx,
388 if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
391 return 0; /* probably prime */
392 if (BN_cmp(w, a1) == 0)
393 return 0; /* w == -1 (mod a), 'a' is probably prime */
395 if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
398 return 1; /* 'a' is composite, otherwise a previous 'w'
399 * would have been == -1 (mod 'a') */
400 if (BN_cmp(w, a1) == 0)
401 return 0; /* w == -1 (mod a), 'a' is probably prime */
404 * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
405 * it is neither -1 nor +1 -- so 'a' cannot be prime
411 static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods)
415 BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
416 char is_single_word = bits <= BN_BITS2;
419 if (!BN_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
421 /* we now have a random number 'rnd' to test. */
422 for (i = 1; i < NUMPRIMES; i++) {
423 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
424 if (mod == (BN_ULONG)-1)
426 mods[i] = (prime_t) mod;
429 * If bits is so small that it fits into a single word then we
430 * additionally don't want to exceed that many bits.
432 if (is_single_word) {
435 if (bits == BN_BITS2) {
437 * Shifting by this much has undefined behaviour so we do it a
440 size_limit = ~((BN_ULONG)0) - BN_get_word(rnd);
442 size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1;
444 if (size_limit < maxdelta)
445 maxdelta = size_limit;
449 if (is_single_word) {
450 BN_ULONG rnd_word = BN_get_word(rnd);
453 * In the case that the candidate prime is a single word then
455 * 1) It's greater than primes[i] because we shouldn't reject
456 * 3 as being a prime number because it's a multiple of
458 * 2) That it's not a multiple of a known prime. We don't
459 * check that rnd-1 is also coprime to all the known
460 * primes because there aren't many small primes where
463 for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) {
464 if ((mods[i] + delta) % primes[i] == 0) {
466 if (delta > maxdelta)
472 for (i = 1; i < NUMPRIMES; i++) {
474 * check that rnd is not a prime and also that gcd(rnd-1,primes)
475 * == 1 (except for 2)
477 if (((mods[i] + delta) % primes[i]) <= 1) {
479 if (delta > maxdelta)
485 if (!BN_add_word(rnd, delta))
487 if (BN_num_bits(rnd) != bits)
493 int bn_probable_prime_dh(BIGNUM *rnd, int bits,
494 const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
500 if ((t1 = BN_CTX_get(ctx)) == NULL)
503 if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
506 /* we need ((rnd-rem) % add) == 0 */
508 if (!BN_mod(t1, rnd, add, ctx))
510 if (!BN_sub(rnd, rnd, t1))
513 if (!BN_add_word(rnd, 1))
516 if (!BN_add(rnd, rnd, rem))
520 /* we now have a random number 'rand' to test. */
523 for (i = 1; i < NUMPRIMES; i++) {
524 /* check that rnd is a prime */
525 BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
526 if (mod == (BN_ULONG)-1)
529 if (!BN_add(rnd, rnd, add))
542 static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
543 const BIGNUM *rem, BN_CTX *ctx)
546 BIGNUM *t1, *qadd, *q;
550 t1 = BN_CTX_get(ctx);
552 qadd = BN_CTX_get(ctx);
556 if (!BN_rshift1(qadd, padd))
559 if (!BN_rand(q, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
562 /* we need ((rnd-rem) % add) == 0 */
563 if (!BN_mod(t1, q, qadd, ctx))
565 if (!BN_sub(q, q, t1))
568 if (!BN_add_word(q, 1))
571 if (!BN_rshift1(t1, rem))
573 if (!BN_add(q, q, t1))
577 /* we now have a random number 'rand' to test. */
578 if (!BN_lshift1(p, q))
580 if (!BN_add_word(p, 1))
584 for (i = 1; i < NUMPRIMES; i++) {
585 /* check that p and q are prime */
587 * check that for p and q gcd(p-1,primes) == 1 (except for 2)
589 BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]);
590 BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]);
591 if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1)
593 if (pmod == 0 || qmod == 0) {
594 if (!BN_add(p, p, padd))
596 if (!BN_add(q, q, qadd))