586 lines
17 KiB
C
586 lines
17 KiB
C
/*
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* WARNING: do not edit!
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* Generated by crypto/bn/bn_prime.pl
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* Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved.
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*
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* Licensed under the OpenSSL license (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*/
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#include <stdio.h>
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#include <time.h>
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#include "internal/cryptlib.h"
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#include "bn_lcl.h"
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#include <openssl/rand.h>
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/*
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* The quick sieve algorithm approach to weeding out primes is Philip
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* Zimmermann's, as implemented in PGP. I have had a read of his comments
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* and implemented my own version.
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*/
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#include "bn_prime.h"
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static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
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const BIGNUM *a1_odd, int k, BN_CTX *ctx,
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BN_MONT_CTX *mont);
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static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods);
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static int probable_prime_dh_safe(BIGNUM *rnd, int bits,
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const BIGNUM *add, const BIGNUM *rem,
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BN_CTX *ctx);
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static const int prime_offsets[480] = {
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13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
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89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163,
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167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229,
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233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293,
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299, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367,
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373, 377, 379, 383, 389, 391, 397, 401, 403, 409, 419, 421, 431, 433,
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437, 439, 443, 449, 457, 461, 463, 467, 479, 481, 487, 491, 493, 499,
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503, 509, 521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569,
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571, 577, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619, 629, 631,
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641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 689, 691, 697, 701,
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703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 767, 769,
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773, 779, 787, 793, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839,
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841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, 893, 899, 901,
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907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, 967, 971,
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977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, 1031,
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1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, 1087,
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1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151,
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1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213,
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1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, 1271,
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1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, 1319,
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1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373,
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1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, 1433,
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1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, 1489,
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1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549,
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1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609,
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1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, 1667,
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1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, 1721,
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1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1781,
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1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, 1843,
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1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901,
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1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, 1951,
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1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017,
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2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, 2071,
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2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, 2131,
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2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, 2197,
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2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2249,
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2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297,
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2309, 2311
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};
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static const int prime_offset_count = 480;
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static const int prime_multiplier = 2310;
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static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits| <=
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* |prime_multiplier| */
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static const int first_prime_index = 5;
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int BN_GENCB_call(BN_GENCB *cb, int a, int b)
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{
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/* No callback means continue */
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if (!cb)
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return 1;
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switch (cb->ver) {
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case 1:
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/* Deprecated-style callbacks */
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if (!cb->cb.cb_1)
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return 1;
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cb->cb.cb_1(a, b, cb->arg);
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return 1;
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case 2:
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/* New-style callbacks */
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return cb->cb.cb_2(a, b, cb);
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default:
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break;
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}
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/* Unrecognised callback type */
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return 0;
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}
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int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe,
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const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb)
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{
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BIGNUM *t;
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int found = 0;
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int i, j, c1 = 0;
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BN_CTX *ctx = NULL;
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prime_t *mods = NULL;
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int checks = BN_prime_checks_for_size(bits);
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if (bits < 2) {
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/* There are no prime numbers this small. */
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BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
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return 0;
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} else if (bits == 2 && safe) {
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/* The smallest safe prime (7) is three bits. */
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BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL);
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return 0;
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}
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mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES);
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if (mods == NULL)
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goto err;
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ctx = BN_CTX_new();
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if (ctx == NULL)
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goto err;
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BN_CTX_start(ctx);
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t = BN_CTX_get(ctx);
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if (!t)
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goto err;
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loop:
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/* make a random number and set the top and bottom bits */
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if (add == NULL) {
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if (!probable_prime(ret, bits, mods))
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goto err;
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} else {
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if (safe) {
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if (!probable_prime_dh_safe(ret, bits, add, rem, ctx))
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goto err;
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} else {
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if (!bn_probable_prime_dh(ret, bits, add, rem, ctx))
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goto err;
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}
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}
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/* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */
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if (!BN_GENCB_call(cb, 0, c1++))
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/* aborted */
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goto err;
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if (!safe) {
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i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb);
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if (i == -1)
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goto err;
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if (i == 0)
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goto loop;
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} else {
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/*
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* for "safe prime" generation, check that (p-1)/2 is prime. Since a
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* prime is odd, We just need to divide by 2
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*/
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if (!BN_rshift1(t, ret))
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goto err;
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for (i = 0; i < checks; i++) {
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j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb);
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if (j == -1)
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goto err;
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if (j == 0)
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goto loop;
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j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb);
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if (j == -1)
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goto err;
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if (j == 0)
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goto loop;
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if (!BN_GENCB_call(cb, 2, c1 - 1))
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goto err;
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/* We have a safe prime test pass */
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}
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}
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/* we have a prime :-) */
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found = 1;
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err:
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OPENSSL_free(mods);
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if (ctx != NULL)
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BN_CTX_end(ctx);
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BN_CTX_free(ctx);
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bn_check_top(ret);
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return found;
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}
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int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
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BN_GENCB *cb)
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{
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return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb);
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}
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int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed,
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int do_trial_division, BN_GENCB *cb)
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{
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int i, j, ret = -1;
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int k;
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BN_CTX *ctx = NULL;
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BIGNUM *A1, *A1_odd, *check; /* taken from ctx */
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BN_MONT_CTX *mont = NULL;
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const BIGNUM *A = NULL;
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if (BN_cmp(a, BN_value_one()) <= 0)
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return 0;
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if (checks == BN_prime_checks)
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checks = BN_prime_checks_for_size(BN_num_bits(a));
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/* first look for small factors */
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if (!BN_is_odd(a))
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/* a is even => a is prime if and only if a == 2 */
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return BN_is_word(a, 2);
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if (do_trial_division) {
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for (i = 1; i < NUMPRIMES; i++)
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if (BN_mod_word(a, primes[i]) == 0)
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return 0;
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if (!BN_GENCB_call(cb, 1, -1))
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goto err;
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}
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if (ctx_passed != NULL)
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ctx = ctx_passed;
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else if ((ctx = BN_CTX_new()) == NULL)
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goto err;
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BN_CTX_start(ctx);
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/* A := abs(a) */
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if (a->neg) {
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BIGNUM *t;
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if ((t = BN_CTX_get(ctx)) == NULL)
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goto err;
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BN_copy(t, a);
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t->neg = 0;
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A = t;
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} else
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A = a;
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A1 = BN_CTX_get(ctx);
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A1_odd = BN_CTX_get(ctx);
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check = BN_CTX_get(ctx);
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if (check == NULL)
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goto err;
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/* compute A1 := A - 1 */
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if (!BN_copy(A1, A))
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goto err;
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if (!BN_sub_word(A1, 1))
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goto err;
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if (BN_is_zero(A1)) {
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ret = 0;
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goto err;
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}
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/* write A1 as A1_odd * 2^k */
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k = 1;
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while (!BN_is_bit_set(A1, k))
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k++;
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if (!BN_rshift(A1_odd, A1, k))
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goto err;
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/* Montgomery setup for computations mod A */
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mont = BN_MONT_CTX_new();
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if (mont == NULL)
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goto err;
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if (!BN_MONT_CTX_set(mont, A, ctx))
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goto err;
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for (i = 0; i < checks; i++) {
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if (!BN_pseudo_rand_range(check, A1))
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goto err;
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if (!BN_add_word(check, 1))
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goto err;
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/* now 1 <= check < A */
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j = witness(check, A, A1, A1_odd, k, ctx, mont);
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if (j == -1)
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goto err;
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if (j) {
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ret = 0;
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goto err;
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}
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if (!BN_GENCB_call(cb, 1, i))
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goto err;
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}
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ret = 1;
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err:
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if (ctx != NULL) {
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BN_CTX_end(ctx);
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if (ctx_passed == NULL)
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BN_CTX_free(ctx);
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}
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BN_MONT_CTX_free(mont);
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return (ret);
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}
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int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx)
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{
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int i;
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int ret = 0;
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loop:
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if (!BN_rand(rnd, bits, 0, 1))
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goto err;
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/* we now have a random number 'rand' to test. */
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for (i = 1; i < NUMPRIMES; i++) {
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/* check that rnd is a prime */
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if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
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goto loop;
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}
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}
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ret = 1;
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err:
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bn_check_top(rnd);
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return (ret);
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}
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int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx)
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{
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int i;
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BIGNUM *offset_index;
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BIGNUM *offset_count;
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int ret = 0;
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OPENSSL_assert(bits > prime_multiplier_bits);
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BN_CTX_start(ctx);
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if ((offset_index = BN_CTX_get(ctx)) == NULL)
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goto err;
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if ((offset_count = BN_CTX_get(ctx)) == NULL)
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goto err;
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BN_add_word(offset_count, prime_offset_count);
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loop:
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if (!BN_rand(rnd, bits - prime_multiplier_bits, 0, 1))
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goto err;
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if (BN_is_bit_set(rnd, bits))
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goto loop;
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if (!BN_rand_range(offset_index, offset_count))
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goto err;
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BN_mul_word(rnd, prime_multiplier);
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BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]);
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/* we now have a random number 'rand' to test. */
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/* skip coprimes */
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for (i = first_prime_index; i < NUMPRIMES; i++) {
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/* check that rnd is a prime */
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if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
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goto loop;
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}
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}
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ret = 1;
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err:
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BN_CTX_end(ctx);
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bn_check_top(rnd);
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return ret;
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}
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static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1,
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const BIGNUM *a1_odd, int k, BN_CTX *ctx,
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BN_MONT_CTX *mont)
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{
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if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */
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return -1;
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if (BN_is_one(w))
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return 0; /* probably prime */
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if (BN_cmp(w, a1) == 0)
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return 0; /* w == -1 (mod a), 'a' is probably prime */
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while (--k) {
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if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */
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return -1;
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if (BN_is_one(w))
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return 1; /* 'a' is composite, otherwise a previous 'w'
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* would have been == -1 (mod 'a') */
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if (BN_cmp(w, a1) == 0)
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return 0; /* w == -1 (mod a), 'a' is probably prime */
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}
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/*
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* If we get here, 'w' is the (a-1)/2-th power of the original 'w', and
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* it is neither -1 nor +1 -- so 'a' cannot be prime
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*/
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bn_check_top(w);
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return 1;
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}
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static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods)
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{
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int i;
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BN_ULONG delta;
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BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1];
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char is_single_word = bits <= BN_BITS2;
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again:
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if (!BN_rand(rnd, bits, 1, 1))
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return (0);
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/* we now have a random number 'rnd' to test. */
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for (i = 1; i < NUMPRIMES; i++)
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mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]);
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/*
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* If bits is so small that it fits into a single word then we
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* additionally don't want to exceed that many bits.
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*/
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if (is_single_word) {
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BN_ULONG size_limit;
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if (bits == BN_BITS2) {
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/*
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* Shifting by this much has undefined behaviour so we do it a
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* different way
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*/
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size_limit = ~((BN_ULONG)0) - BN_get_word(rnd);
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} else {
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size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1;
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}
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if (size_limit < maxdelta)
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maxdelta = size_limit;
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}
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delta = 0;
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loop:
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if (is_single_word) {
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BN_ULONG rnd_word = BN_get_word(rnd);
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/*-
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* In the case that the candidate prime is a single word then
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* we check that:
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* 1) It's greater than primes[i] because we shouldn't reject
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* 3 as being a prime number because it's a multiple of
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* three.
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* 2) That it's not a multiple of a known prime. We don't
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* check that rnd-1 is also coprime to all the known
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* primes because there aren't many small primes where
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* that's true.
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*/
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for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) {
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if ((mods[i] + delta) % primes[i] == 0) {
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delta += 2;
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if (delta > maxdelta)
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goto again;
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goto loop;
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}
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}
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} else {
|
|
for (i = 1; i < NUMPRIMES; i++) {
|
|
/*
|
|
* check that rnd is not a prime and also that gcd(rnd-1,primes)
|
|
* == 1 (except for 2)
|
|
*/
|
|
if (((mods[i] + delta) % primes[i]) <= 1) {
|
|
delta += 2;
|
|
if (delta > maxdelta)
|
|
goto again;
|
|
goto loop;
|
|
}
|
|
}
|
|
}
|
|
if (!BN_add_word(rnd, delta))
|
|
return (0);
|
|
if (BN_num_bits(rnd) != bits)
|
|
goto again;
|
|
bn_check_top(rnd);
|
|
return (1);
|
|
}
|
|
|
|
int bn_probable_prime_dh(BIGNUM *rnd, int bits,
|
|
const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx)
|
|
{
|
|
int i, ret = 0;
|
|
BIGNUM *t1;
|
|
|
|
BN_CTX_start(ctx);
|
|
if ((t1 = BN_CTX_get(ctx)) == NULL)
|
|
goto err;
|
|
|
|
if (!BN_rand(rnd, bits, 0, 1))
|
|
goto err;
|
|
|
|
/* we need ((rnd-rem) % add) == 0 */
|
|
|
|
if (!BN_mod(t1, rnd, add, ctx))
|
|
goto err;
|
|
if (!BN_sub(rnd, rnd, t1))
|
|
goto err;
|
|
if (rem == NULL) {
|
|
if (!BN_add_word(rnd, 1))
|
|
goto err;
|
|
} else {
|
|
if (!BN_add(rnd, rnd, rem))
|
|
goto err;
|
|
}
|
|
|
|
/* we now have a random number 'rand' to test. */
|
|
|
|
loop:
|
|
for (i = 1; i < NUMPRIMES; i++) {
|
|
/* check that rnd is a prime */
|
|
if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) {
|
|
if (!BN_add(rnd, rnd, add))
|
|
goto err;
|
|
goto loop;
|
|
}
|
|
}
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
bn_check_top(rnd);
|
|
return (ret);
|
|
}
|
|
|
|
static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd,
|
|
const BIGNUM *rem, BN_CTX *ctx)
|
|
{
|
|
int i, ret = 0;
|
|
BIGNUM *t1, *qadd, *q;
|
|
|
|
bits--;
|
|
BN_CTX_start(ctx);
|
|
t1 = BN_CTX_get(ctx);
|
|
q = BN_CTX_get(ctx);
|
|
qadd = BN_CTX_get(ctx);
|
|
if (qadd == NULL)
|
|
goto err;
|
|
|
|
if (!BN_rshift1(qadd, padd))
|
|
goto err;
|
|
|
|
if (!BN_rand(q, bits, 0, 1))
|
|
goto err;
|
|
|
|
/* we need ((rnd-rem) % add) == 0 */
|
|
if (!BN_mod(t1, q, qadd, ctx))
|
|
goto err;
|
|
if (!BN_sub(q, q, t1))
|
|
goto err;
|
|
if (rem == NULL) {
|
|
if (!BN_add_word(q, 1))
|
|
goto err;
|
|
} else {
|
|
if (!BN_rshift1(t1, rem))
|
|
goto err;
|
|
if (!BN_add(q, q, t1))
|
|
goto err;
|
|
}
|
|
|
|
/* we now have a random number 'rand' to test. */
|
|
if (!BN_lshift1(p, q))
|
|
goto err;
|
|
if (!BN_add_word(p, 1))
|
|
goto err;
|
|
|
|
loop:
|
|
for (i = 1; i < NUMPRIMES; i++) {
|
|
/* check that p and q are prime */
|
|
/*
|
|
* check that for p and q gcd(p-1,primes) == 1 (except for 2)
|
|
*/
|
|
if ((BN_mod_word(p, (BN_ULONG)primes[i]) == 0) ||
|
|
(BN_mod_word(q, (BN_ULONG)primes[i]) == 0)) {
|
|
if (!BN_add(p, p, padd))
|
|
goto err;
|
|
if (!BN_add(q, q, qadd))
|
|
goto err;
|
|
goto loop;
|
|
}
|
|
}
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
bn_check_top(p);
|
|
return (ret);
|
|
}
|