[331] | 1 | /*
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| 2 | * WARNING: do not edit!
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| 3 | * Generated by crypto/bn/bn_prime.pl
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| 4 | * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
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| 5 | *
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| 6 | * Licensed under the OpenSSL license (the "License"). You may not use
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| 7 | * this file except in compliance with the License. You can obtain a copy
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| 8 | * in the file LICENSE in the source distribution or at
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| 9 | * https://www.openssl.org/source/license.html
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| 10 | */
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| 11 |
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| 12 | #include <stdio.h>
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| 13 | #include <time.h>
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| 14 | #include "internal/cryptlib.h"
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| 15 | #include "bn_lcl.h"
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| 16 |
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| 17 | /*
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| 18 | * The quick sieve algorithm approach to weeding out primes is Philip
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| 19 | * Zimmermann's, as implemented in PGP. I have had a read of his comments
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| 20 | * and implemented my own version.
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| 21 | */
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| 22 | #include "bn_prime.h"
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| 23 |
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| 24 | static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
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| 25 | const BIGNUM *a1_odd, int k, BN_CTX *ctx,
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| 26 | BN_MONT_CTX *mont);
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| 27 | static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods);
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| 28 | static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
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| 29 | const BIGNUM *add, const BIGNUM *rem,
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| 30 | BN_CTX *ctx);
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| 31 |
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| 32 | static const int prime_offsets[480] = {
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| 33 | 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
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| 34 | 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163,
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| 35 | 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229,
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| 36 | 233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293,
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| 37 | 299, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367,
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| 38 | 373, 377, 379, 383, 389, 391, 397, 401, 403, 409, 419, 421, 431, 433,
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| 39 | 437, 439, 443, 449, 457, 461, 463, 467, 479, 481, 487, 491, 493, 499,
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| 40 | 503, 509, 521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569,
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| 41 | 571, 577, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619, 629, 631,
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| 42 | 641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 689, 691, 697, 701,
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| 43 | 703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 767, 769,
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| 44 | 773, 779, 787, 793, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839,
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| 45 | 841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, 893, 899, 901,
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| 46 | 907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, 967, 971,
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| 47 | 977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, 1031,
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| 48 | 1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, 1087,
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| 49 | 1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151,
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| 50 | 1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213,
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| 51 | 1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, 1271,
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| 52 | 1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, 1319,
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| 53 | 1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373,
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| 54 | 1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, 1433,
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| 55 | 1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, 1489,
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| 56 | 1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549,
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| 57 | 1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609,
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| 58 | 1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, 1667,
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| 59 | 1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, 1721,
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| 60 | 1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1781,
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| 61 | 1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, 1843,
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| 62 | 1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901,
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| 63 | 1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, 1951,
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| 64 | 1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017,
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| 65 | 2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, 2071,
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| 66 | 2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, 2131,
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| 67 | 2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, 2197,
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| 68 | 2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2249,
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| 69 | 2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297,
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| 70 | 2309, 2311
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| 71 | };
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| 72 |
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| 73 | static const int prime_offset_count = 480;
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| 74 | static const int prime_multiplier = 2310;
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| 75 | static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits| <=
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| 76 | * |prime_multiplier| */
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| 77 | static const int first_prime_index = 5;
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| 78 |
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| 79 | int BN_GENCB_call(BN_GENCB *cb, int a, int b)
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| 80 | {
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| 81 | /* No callback means continue */
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| 82 | if (!cb)
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| 83 | return 1;
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| 84 | switch (cb->ver) {
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| 85 | case 1:
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| 86 | /* Deprecated-style callbacks */
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| 87 | if (!cb->cb.cb_1)
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| 88 | return 1;
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| 89 | cb->cb.cb_1(a, b, cb->arg);
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| 90 | return 1;
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| 91 | case 2:
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| 92 | /* New-style callbacks */
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| 93 | return cb->cb.cb_2(a, b, cb);
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| 94 | default:
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| 95 | break;
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| 96 | }
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| 97 | /* Unrecognised callback type */
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| 98 | return 0;
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| 99 | }
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| 100 |
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| 101 | int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
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| 102 | const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
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| 103 | {
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| 104 | BIGNUM *t;
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| 105 | int found = 0;
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| 106 | int i, j, c1 = 0;
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| 107 | BN_CTX *ctx = NULL;
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| 108 | prime_t *mods = NULL;
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| 109 | int checks = BN_prime_checks_for_size(bits);
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| 110 |
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| 111 | if (bits < 2) {
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| 112 | /* There are no prime numbers this small. */
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| 113 | BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
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| 114 | return 0;
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| 115 | } else if (bits == 2 && safe) {
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| 116 | /* The smallest safe prime (7) is three bits. */
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| 117 | BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
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| 118 | return 0;
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| 119 | }
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| 120 |
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| 121 | mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES);
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| 122 | if (mods == NULL)
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| 123 | goto err;
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| 124 |
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| 125 | ctx = BN_CTX_new();
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| 126 | if (ctx == NULL)
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| 127 | goto err;
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| 128 | BN_CTX_start(ctx);
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| 129 | t = BN_CTX_get(ctx);
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| 130 | if (!t)
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| 131 | goto err;
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| 132 | loop:
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| 133 | /* make a random number and set the top and bottom bits */
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| 134 | if (add == NULL) {
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| 135 | if (!probable_prime(ret, bits, mods))
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| 136 | goto err;
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| 137 | } else {
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| 138 | if (safe) {
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| 139 | if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
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| 140 | goto err;
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| 141 | } else {
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| 142 | if (!bn_probable_prime_dh(ret, bits, add, rem, ctx))
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| 143 | goto err;
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| 144 | }
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| 145 | }
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| 146 |
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| 147 | if (!BN_GENCB_call(cb, 0, c1++))
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| 148 | /* aborted */
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| 149 | goto err;
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| 150 |
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| 151 | if (!safe) {
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| 152 | i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
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| 153 | if (i == -1)
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| 154 | goto err;
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| 155 | if (i == 0)
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| 156 | goto loop;
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| 157 | } else {
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| 158 | /*
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| 159 | * for "safe prime" generation, check that (p-1)/2 is prime. Since a
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| 160 | * prime is odd, We just need to divide by 2
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| 161 | */
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| 162 | if (!BN_rshift1(t, ret))
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| 163 | goto err;
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| 164 |
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| 165 | for (i = 0; i < checks; i++) {
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| 166 | j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
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| 167 | if (j == -1)
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| 168 | goto err;
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| 169 | if (j == 0)
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| 170 | goto loop;
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| 171 |
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| 172 | j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
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| 173 | if (j == -1)
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| 174 | goto err;
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| 175 | if (j == 0)
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| 176 | goto loop;
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| 177 |
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| 178 | if (!BN_GENCB_call(cb, 2, c1 - 1))
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| 179 | goto err;
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| 180 | /* We have a safe prime test pass */
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| 181 | }
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| 182 | }
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| 183 | /* we have a prime :-) */
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| 184 | found = 1;
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| 185 | err:
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| 186 | OPENSSL_free(mods);
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| 187 | if (ctx != NULL)
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| 188 | BN_CTX_end(ctx);
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| 189 | BN_CTX_free(ctx);
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| 190 | bn_check_top(ret);
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| 191 | return found;
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| 192 | }
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| 193 |
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| 194 | int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
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| 195 | BN_GENCB *cb)
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| 196 | {
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| 197 | return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
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| 198 | }
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| 199 |
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| 200 | int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
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| 201 | int do_trial_division, BN_GENCB *cb)
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| 202 | {
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| 203 | int i, j, ret = -1;
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| 204 | int k;
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| 205 | BN_CTX *ctx = NULL;
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| 206 | BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
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| 207 | BN_MONT_CTX *mont = NULL;
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| 208 | const BIGNUM *A = NULL;
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| 209 |
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| 210 | if (BN_cmp(a, BN_value_one()) <= 0)
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| 211 | return 0;
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| 212 |
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| 213 | if (checks == BN_prime_checks)
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| 214 | checks = BN_prime_checks_for_size(BN_num_bits(a));
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| 215 |
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| 216 | /* first look for small factors */
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| 217 | if (!BN_is_odd(a))
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| 218 | /* a is even => a is prime if and only if a == 2 */
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| 219 | return BN_is_word(a, 2);
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| 220 | if (do_trial_division) {
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| 221 | for (i = 1; i < NUMPRIMES; i++) {
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| 222 | BN_ULONG mod = BN_mod_word(a, primes[i]);
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| 223 | if (mod == (BN_ULONG)-1)
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| 224 | goto err;
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| 225 | if (mod == 0)
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| 226 | return 0;
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| 227 | }
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| 228 | if (!BN_GENCB_call(cb, 1, -1))
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| 229 | goto err;
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| 230 | }
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| 231 |
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| 232 | if (ctx_passed != NULL)
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| 233 | ctx = ctx_passed;
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| 234 | else if ((ctx = BN_CTX_new()) == NULL)
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| 235 | goto err;
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| 236 | BN_CTX_start(ctx);
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| 237 |
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| 238 | /* A := abs(a) */
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| 239 | if (a->neg) {
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| 240 | BIGNUM *t;
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| 241 | if ((t = BN_CTX_get(ctx)) == NULL)
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| 242 | goto err;
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| 243 | if (BN_copy(t, a) == NULL)
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| 244 | goto err;
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| 245 | t->neg = 0;
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| 246 | A = t;
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| 247 | } else
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| 248 | A = a;
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| 249 | A1 = BN_CTX_get(ctx);
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| 250 | A1_odd = BN_CTX_get(ctx);
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| 251 | check = BN_CTX_get(ctx);
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| 252 | if (check == NULL)
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| 253 | goto err;
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| 254 |
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| 255 | /* compute A1 := A - 1 */
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| 256 | if (!BN_copy(A1, A))
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| 257 | goto err;
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| 258 | if (!BN_sub_word(A1, 1))
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| 259 | goto err;
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| 260 | if (BN_is_zero(A1)) {
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| 261 | ret = 0;
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| 262 | goto err;
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| 263 | }
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| 264 |
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| 265 | /* write A1 as A1_odd * 2^k */
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| 266 | k = 1;
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| 267 | while (!BN_is_bit_set(A1, k))
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| 268 | k++;
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| 269 | if (!BN_rshift(A1_odd, A1, k))
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| 270 | goto err;
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| 271 |
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| 272 | /* Montgomery setup for computations mod A */
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| 273 | mont = BN_MONT_CTX_new();
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| 274 | if (mont == NULL)
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| 275 | goto err;
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| 276 | if (!BN_MONT_CTX_set(mont, A, ctx))
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| 277 | goto err;
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| 278 |
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| 279 | for (i = 0; i < checks; i++) {
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| 280 | if (!BN_pseudo_rand_range(check, A1))
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| 281 | goto err;
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| 282 | if (!BN_add_word(check, 1))
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| 283 | goto err;
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| 284 | /* now 1 <= check < A */
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| 285 |
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| 286 | j = witness(check, A, A1, A1_odd, k, ctx, mont);
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| 287 | if (j == -1)
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| 288 | goto err;
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| 289 | if (j) {
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| 290 | ret = 0;
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| 291 | goto err;
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| 292 | }
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| 293 | if (!BN_GENCB_call(cb, 1, i))
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| 294 | goto err;
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| 295 | }
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| 296 | ret = 1;
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| 297 | err:
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| 298 | if (ctx != NULL) {
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| 299 | BN_CTX_end(ctx);
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| 300 | if (ctx_passed == NULL)
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| 301 | BN_CTX_free(ctx);
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| 302 | }
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| 303 | BN_MONT_CTX_free(mont);
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| 304 |
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| 305 | return (ret);
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| 306 | }
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| 307 |
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| 308 | int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx)
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| 309 | {
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| 310 | int i;
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| 311 | int ret = 0;
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| 312 |
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| 313 | loop:
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| 314 | if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
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| 315 | goto err;
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| 316 |
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| 317 | /* we now have a random number 'rand' to test. */
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| 318 |
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| 319 | for (i = 1; i < NUMPRIMES; i++) {
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| 320 | /* check that rnd is a prime */
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| 321 | BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
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| 322 | if (mod == (BN_ULONG)-1)
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| 323 | goto err;
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| 324 | if (mod <= 1) {
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| 325 | goto loop;
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| 326 | }
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| 327 | }
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| 328 | ret = 1;
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| 329 |
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| 330 | err:
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| 331 | bn_check_top(rnd);
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| 332 | return (ret);
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| 333 | }
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| 334 |
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| 335 | int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx)
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| 336 | {
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| 337 | int i;
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| 338 | BIGNUM *offset_index;
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| 339 | BIGNUM *offset_count;
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| 340 | int ret = 0;
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| 341 |
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| 342 | OPENSSL_assert(bits > prime_multiplier_bits);
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| 343 |
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| 344 | BN_CTX_start(ctx);
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| 345 | if ((offset_index = BN_CTX_get(ctx)) == NULL)
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| 346 | goto err;
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| 347 | if ((offset_count = BN_CTX_get(ctx)) == NULL)
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| 348 | goto err;
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| 349 |
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| 350 | if (!BN_add_word(offset_count, prime_offset_count))
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| 351 | goto err;
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| 352 |
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| 353 | loop:
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| 354 | if (!BN_rand(rnd, bits - prime_multiplier_bits,
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| 355 | BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
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| 356 | goto err;
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| 357 | if (BN_is_bit_set(rnd, bits))
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| 358 | goto loop;
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| 359 | if (!BN_rand_range(offset_index, offset_count))
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| 360 | goto err;
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| 361 |
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| 362 | if (!BN_mul_word(rnd, prime_multiplier)
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| 363 | || !BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]))
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| 364 | goto err;
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| 365 |
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| 366 | /* we now have a random number 'rand' to test. */
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| 367 |
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| 368 | /* skip coprimes */
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| 369 | for (i = first_prime_index; i < NUMPRIMES; i++) {
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| 370 | /* check that rnd is a prime */
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| 371 | BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
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| 372 | if (mod == (BN_ULONG)-1)
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| 373 | goto err;
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| 374 | if (mod <= 1)
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| 375 | goto loop;
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| 376 | }
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| 377 | ret = 1;
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| 378 |
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| 379 | err:
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| 380 | BN_CTX_end(ctx);
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| 381 | bn_check_top(rnd);
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| 382 | return ret;
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| 383 | }
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| 384 |
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| 385 | static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
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| 386 | const BIGNUM *a1_odd, int k, BN_CTX *ctx,
|
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| 387 | BN_MONT_CTX *mont)
|
---|
| 388 | {
|
---|
| 389 | if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
|
---|
| 390 | return -1;
|
---|
| 391 | if (BN_is_one(w))
|
---|
| 392 | return 0; /* probably prime */
|
---|
| 393 | if (BN_cmp(w, a1) == 0)
|
---|
| 394 | return 0; /* w == -1 (mod a), 'a' is probably prime */
|
---|
| 395 | while (--k) {
|
---|
| 396 | if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
|
---|
| 397 | return -1;
|
---|
| 398 | if (BN_is_one(w))
|
---|
| 399 | return 1; /* 'a' is composite, otherwise a previous 'w'
|
---|
| 400 | * would have been == -1 (mod 'a') */
|
---|
| 401 | if (BN_cmp(w, a1) == 0)
|
---|
| 402 | return 0; /* w == -1 (mod a), 'a' is probably prime */
|
---|
| 403 | }
|
---|
| 404 | /*
|
---|
| 405 | * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
|
---|
| 406 | * it is neither -1 nor +1 -- so 'a' cannot be prime
|
---|
| 407 | */
|
---|
| 408 | bn_check_top(w);
|
---|
| 409 | return 1;
|
---|
| 410 | }
|
---|
| 411 |
|
---|
| 412 | static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods)
|
---|
| 413 | {
|
---|
| 414 | int i;
|
---|
| 415 | BN_ULONG delta;
|
---|
| 416 | BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
|
---|
| 417 | char is_single_word = bits <= BN_BITS2;
|
---|
| 418 |
|
---|
| 419 | again:
|
---|
| 420 | if (!BN_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD))
|
---|
| 421 | return (0);
|
---|
| 422 | /* we now have a random number 'rnd' to test. */
|
---|
| 423 | for (i = 1; i < NUMPRIMES; i++) {
|
---|
| 424 | BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
|
---|
| 425 | if (mod == (BN_ULONG)-1)
|
---|
| 426 | return 0;
|
---|
| 427 | mods[i] = (prime_t) mod;
|
---|
| 428 | }
|
---|
| 429 | /*
|
---|
| 430 | * If bits is so small that it fits into a single word then we
|
---|
| 431 | * additionally don't want to exceed that many bits.
|
---|
| 432 | */
|
---|
| 433 | if (is_single_word) {
|
---|
| 434 | BN_ULONG size_limit;
|
---|
| 435 |
|
---|
| 436 | if (bits == BN_BITS2) {
|
---|
| 437 | /*
|
---|
| 438 | * Shifting by this much has undefined behaviour so we do it a
|
---|
| 439 | * different way
|
---|
| 440 | */
|
---|
| 441 | size_limit = ~((BN_ULONG)0) - BN_get_word(rnd);
|
---|
| 442 | } else {
|
---|
| 443 | size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1;
|
---|
| 444 | }
|
---|
| 445 | if (size_limit < maxdelta)
|
---|
| 446 | maxdelta = size_limit;
|
---|
| 447 | }
|
---|
| 448 | delta = 0;
|
---|
| 449 | loop:
|
---|
| 450 | if (is_single_word) {
|
---|
| 451 | BN_ULONG rnd_word = BN_get_word(rnd);
|
---|
| 452 |
|
---|
| 453 | /*-
|
---|
| 454 | * In the case that the candidate prime is a single word then
|
---|
| 455 | * we check that:
|
---|
| 456 | * 1) It's greater than primes[i] because we shouldn't reject
|
---|
| 457 | * 3 as being a prime number because it's a multiple of
|
---|
| 458 | * three.
|
---|
| 459 | * 2) That it's not a multiple of a known prime. We don't
|
---|
| 460 | * check that rnd-1 is also coprime to all the known
|
---|
| 461 | * primes because there aren't many small primes where
|
---|
| 462 | * that's true.
|
---|
| 463 | */
|
---|
| 464 | for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) {
|
---|
| 465 | if ((mods[i] + delta) % primes[i] == 0) {
|
---|
| 466 | delta += 2;
|
---|
| 467 | if (delta > maxdelta)
|
---|
| 468 | goto again;
|
---|
| 469 | goto loop;
|
---|
| 470 | }
|
---|
| 471 | }
|
---|
| 472 | } else {
|
---|
| 473 | for (i = 1; i < NUMPRIMES; i++) {
|
---|
| 474 | /*
|
---|
| 475 | * check that rnd is not a prime and also that gcd(rnd-1,primes)
|
---|
| 476 | * == 1 (except for 2)
|
---|
| 477 | */
|
---|
| 478 | if (((mods[i] + delta) % primes[i]) <= 1) {
|
---|
| 479 | delta += 2;
|
---|
| 480 | if (delta > maxdelta)
|
---|
| 481 | goto again;
|
---|
| 482 | goto loop;
|
---|
| 483 | }
|
---|
| 484 | }
|
---|
| 485 | }
|
---|
| 486 | if (!BN_add_word(rnd, delta))
|
---|
| 487 | return (0);
|
---|
| 488 | if (BN_num_bits(rnd) != bits)
|
---|
| 489 | goto again;
|
---|
| 490 | bn_check_top(rnd);
|
---|
| 491 | return (1);
|
---|
| 492 | }
|
---|
| 493 |
|
---|
| 494 | int bn_probable_prime_dh(BIGNUM *rnd, int bits,
|
---|
| 495 | const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
|
---|
| 496 | {
|
---|
| 497 | int i, ret = 0;
|
---|
| 498 | BIGNUM *t1;
|
---|
| 499 |
|
---|
| 500 | BN_CTX_start(ctx);
|
---|
| 501 | if ((t1 = BN_CTX_get(ctx)) == NULL)
|
---|
| 502 | goto err;
|
---|
| 503 |
|
---|
| 504 | if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
|
---|
| 505 | goto err;
|
---|
| 506 |
|
---|
| 507 | /* we need ((rnd-rem) % add) == 0 */
|
---|
| 508 |
|
---|
| 509 | if (!BN_mod(t1, rnd, add, ctx))
|
---|
| 510 | goto err;
|
---|
| 511 | if (!BN_sub(rnd, rnd, t1))
|
---|
| 512 | goto err;
|
---|
| 513 | if (rem == NULL) {
|
---|
| 514 | if (!BN_add_word(rnd, 1))
|
---|
| 515 | goto err;
|
---|
| 516 | } else {
|
---|
| 517 | if (!BN_add(rnd, rnd, rem))
|
---|
| 518 | goto err;
|
---|
| 519 | }
|
---|
| 520 |
|
---|
| 521 | /* we now have a random number 'rand' to test. */
|
---|
| 522 |
|
---|
| 523 | loop:
|
---|
| 524 | for (i = 1; i < NUMPRIMES; i++) {
|
---|
| 525 | /* check that rnd is a prime */
|
---|
| 526 | BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]);
|
---|
| 527 | if (mod == (BN_ULONG)-1)
|
---|
| 528 | goto err;
|
---|
| 529 | if (mod <= 1) {
|
---|
| 530 | if (!BN_add(rnd, rnd, add))
|
---|
| 531 | goto err;
|
---|
| 532 | goto loop;
|
---|
| 533 | }
|
---|
| 534 | }
|
---|
| 535 | ret = 1;
|
---|
| 536 |
|
---|
| 537 | err:
|
---|
| 538 | BN_CTX_end(ctx);
|
---|
| 539 | bn_check_top(rnd);
|
---|
| 540 | return (ret);
|
---|
| 541 | }
|
---|
| 542 |
|
---|
| 543 | static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
|
---|
| 544 | const BIGNUM *rem, BN_CTX *ctx)
|
---|
| 545 | {
|
---|
| 546 | int i, ret = 0;
|
---|
| 547 | BIGNUM *t1, *qadd, *q;
|
---|
| 548 |
|
---|
| 549 | bits--;
|
---|
| 550 | BN_CTX_start(ctx);
|
---|
| 551 | t1 = BN_CTX_get(ctx);
|
---|
| 552 | q = BN_CTX_get(ctx);
|
---|
| 553 | qadd = BN_CTX_get(ctx);
|
---|
| 554 | if (qadd == NULL)
|
---|
| 555 | goto err;
|
---|
| 556 |
|
---|
| 557 | if (!BN_rshift1(qadd, padd))
|
---|
| 558 | goto err;
|
---|
| 559 |
|
---|
| 560 | if (!BN_rand(q, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD))
|
---|
| 561 | goto err;
|
---|
| 562 |
|
---|
| 563 | /* we need ((rnd-rem) % add) == 0 */
|
---|
| 564 | if (!BN_mod(t1, q, qadd, ctx))
|
---|
| 565 | goto err;
|
---|
| 566 | if (!BN_sub(q, q, t1))
|
---|
| 567 | goto err;
|
---|
| 568 | if (rem == NULL) {
|
---|
| 569 | if (!BN_add_word(q, 1))
|
---|
| 570 | goto err;
|
---|
| 571 | } else {
|
---|
| 572 | if (!BN_rshift1(t1, rem))
|
---|
| 573 | goto err;
|
---|
| 574 | if (!BN_add(q, q, t1))
|
---|
| 575 | goto err;
|
---|
| 576 | }
|
---|
| 577 |
|
---|
| 578 | /* we now have a random number 'rand' to test. */
|
---|
| 579 | if (!BN_lshift1(p, q))
|
---|
| 580 | goto err;
|
---|
| 581 | if (!BN_add_word(p, 1))
|
---|
| 582 | goto err;
|
---|
| 583 |
|
---|
| 584 | loop:
|
---|
| 585 | for (i = 1; i < NUMPRIMES; i++) {
|
---|
| 586 | /* check that p and q are prime */
|
---|
| 587 | /*
|
---|
| 588 | * check that for p and q gcd(p-1,primes) == 1 (except for 2)
|
---|
| 589 | */
|
---|
| 590 | BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]);
|
---|
| 591 | BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]);
|
---|
| 592 | if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1)
|
---|
| 593 | goto err;
|
---|
| 594 | if (pmod == 0 || qmod == 0) {
|
---|
| 595 | if (!BN_add(p, p, padd))
|
---|
| 596 | goto err;
|
---|
| 597 | if (!BN_add(q, q, qadd))
|
---|
| 598 | goto err;
|
---|
| 599 | goto loop;
|
---|
| 600 | }
|
---|
| 601 | }
|
---|
| 602 | ret = 1;
|
---|
| 603 |
|
---|
| 604 | err:
|
---|
| 605 | BN_CTX_end(ctx);
|
---|
| 606 | bn_check_top(p);
|
---|
| 607 | return (ret);
|
---|
| 608 | }
|
---|