/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) * All rights reserved. * * This package is an SSL implementation written * by Eric Young (eay@cryptsoft.com). * The implementation was written so as to conform with Netscapes SSL. * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson (tjh@cryptsoft.com). * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgement: * "This product includes cryptographic software written by * Eric Young (eay@cryptsoft.com)" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence * [including the GNU Public Licence.] */ /* ==================================================================== * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * * 1. Redistributions of source code must retain the above copyright * notice, this list of conditions and the following disclaimer. * * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in * the documentation and/or other materials provided with the * distribution. * * 3. All advertising materials mentioning features or use of this * software must display the following acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" * * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to * endorse or promote products derived from this software without * prior written permission. For written permission, please contact * openssl-core@openssl.org. * * 5. Products derived from this software may not be called "OpenSSL" * nor may "OpenSSL" appear in their names without prior written * permission of the OpenSSL Project. * * 6. Redistributions of any form whatsoever must retain the following * acknowledgment: * "This product includes software developed by the OpenSSL Project * for use in the OpenSSL Toolkit (http://www.openssl.org/)" * * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED * OF THE POSSIBILITY OF SUCH DAMAGE. * ==================================================================== * * This product includes cryptographic software written by Eric Young * (eay@cryptsoft.com). This product includes software written by Tim * Hudson (tjh@cryptsoft.com). * */ #include #include #include "internal/cryptlib.h" #include "bn_lcl.h" #include /* * NB: these functions have been "upgraded", the deprecated versions (which * are compatibility wrappers using these functions) are in bn_depr.c. - * Geoff */ /* * The quick sieve algorithm approach to weeding out primes is Philip * Zimmermann's, as implemented in PGP. I have had a read of his comments * and implemented my own version. */ #include "bn_prime.h" static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont); static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods); static int probable_prime_dh_safe(BIGNUM *rnd, int bits, const BIGNUM *add, const BIGNUM *rem, BN_CTX *ctx); static const int prime_offsets[480] = { 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 197, 199, 211, 221, 223, 227, 229, 233, 239, 241, 247, 251, 257, 263, 269, 271, 277, 281, 283, 289, 293, 299, 307, 311, 313, 317, 323, 331, 337, 347, 349, 353, 359, 361, 367, 373, 377, 379, 383, 389, 391, 397, 401, 403, 409, 419, 421, 431, 433, 437, 439, 443, 449, 457, 461, 463, 467, 479, 481, 487, 491, 493, 499, 503, 509, 521, 523, 527, 529, 533, 541, 547, 551, 557, 559, 563, 569, 571, 577, 587, 589, 593, 599, 601, 607, 611, 613, 617, 619, 629, 631, 641, 643, 647, 653, 659, 661, 667, 673, 677, 683, 689, 691, 697, 701, 703, 709, 713, 719, 727, 731, 733, 739, 743, 751, 757, 761, 767, 769, 773, 779, 787, 793, 797, 799, 809, 811, 817, 821, 823, 827, 829, 839, 841, 851, 853, 857, 859, 863, 871, 877, 881, 883, 887, 893, 899, 901, 907, 911, 919, 923, 929, 937, 941, 943, 947, 949, 953, 961, 967, 971, 977, 983, 989, 991, 997, 1003, 1007, 1009, 1013, 1019, 1021, 1027, 1031, 1033, 1037, 1039, 1049, 1051, 1061, 1063, 1069, 1073, 1079, 1081, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1121, 1123, 1129, 1139, 1147, 1151, 1153, 1157, 1159, 1163, 1171, 1181, 1187, 1189, 1193, 1201, 1207, 1213, 1217, 1219, 1223, 1229, 1231, 1237, 1241, 1247, 1249, 1259, 1261, 1271, 1273, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1313, 1319, 1321, 1327, 1333, 1339, 1343, 1349, 1357, 1361, 1363, 1367, 1369, 1373, 1381, 1387, 1391, 1399, 1403, 1409, 1411, 1417, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1457, 1459, 1469, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1501, 1511, 1513, 1517, 1523, 1531, 1537, 1541, 1543, 1549, 1553, 1559, 1567, 1571, 1577, 1579, 1583, 1591, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1633, 1637, 1643, 1649, 1651, 1657, 1663, 1667, 1669, 1679, 1681, 1691, 1693, 1697, 1699, 1703, 1709, 1711, 1717, 1721, 1723, 1733, 1739, 1741, 1747, 1751, 1753, 1759, 1763, 1769, 1777, 1781, 1783, 1787, 1789, 1801, 1807, 1811, 1817, 1819, 1823, 1829, 1831, 1843, 1847, 1849, 1853, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1891, 1901, 1907, 1909, 1913, 1919, 1921, 1927, 1931, 1933, 1937, 1943, 1949, 1951, 1957, 1961, 1963, 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2021, 2027, 2029, 2033, 2039, 2041, 2047, 2053, 2059, 2063, 2069, 2071, 2077, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2117, 2119, 2129, 2131, 2137, 2141, 2143, 2147, 2153, 2159, 2161, 2171, 2173, 2179, 2183, 2197, 2201, 2203, 2207, 2209, 2213, 2221, 2227, 2231, 2237, 2239, 2243, 2249, 2251, 2257, 2263, 2267, 2269, 2273, 2279, 2281, 2287, 2291, 2293, 2297, 2309, 2311 }; static const int prime_offset_count = 480; static const int prime_multiplier = 2310; static const int prime_multiplier_bits = 11; /* 2^|prime_multiplier_bits| <= * |prime_multiplier| */ static const int first_prime_index = 5; int BN_GENCB_call(BN_GENCB *cb, int a, int b) { /* No callback means continue */ if (!cb) return 1; switch (cb->ver) { case 1: /* Deprecated-style callbacks */ if (!cb->cb.cb_1) return 1; cb->cb.cb_1(a, b, cb->arg); return 1; case 2: /* New-style callbacks */ return cb->cb.cb_2(a, b, cb); default: break; } /* Unrecognised callback type */ return 0; } int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, const BIGNUM *rem, BN_GENCB *cb) { BIGNUM *t; int found = 0; int i, j, c1 = 0; BN_CTX *ctx = NULL; prime_t *mods = NULL; int checks = BN_prime_checks_for_size(bits); mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES); if (mods == NULL) goto err; if (bits < 2) { /* There are no prime numbers this small. */ BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL); return 0; } else if (bits == 2 && safe) { /* The smallest safe prime (7) is three bits. */ BNerr(BN_F_BN_GENERATE_PRIME_EX, BN_R_BITS_TOO_SMALL); return 0; } ctx = BN_CTX_new(); if (ctx == NULL) goto err; BN_CTX_start(ctx); t = BN_CTX_get(ctx); if (!t) goto err; loop: /* make a random number and set the top and bottom bits */ if (add == NULL) { if (!probable_prime(ret, bits, mods)) goto err; } else { if (safe) { if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) goto err; } else { if (!bn_probable_prime_dh(ret, bits, add, rem, ctx)) goto err; } } /* if (BN_mod_word(ret,(BN_ULONG)3) == 1) goto loop; */ if (!BN_GENCB_call(cb, 0, c1++)) /* aborted */ goto err; if (!safe) { i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); if (i == -1) goto err; if (i == 0) goto loop; } else { /* * for "safe prime" generation, check that (p-1)/2 is prime. Since a * prime is odd, We just need to divide by 2 */ if (!BN_rshift1(t, ret)) goto err; for (i = 0; i < checks; i++) { j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, cb); if (j == -1) goto err; if (j == 0) goto loop; j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, cb); if (j == -1) goto err; if (j == 0) goto loop; if (!BN_GENCB_call(cb, 2, c1 - 1)) goto err; /* We have a safe prime test pass */ } } /* we have a prime :-) */ found = 1; err: OPENSSL_free(mods); if (ctx != NULL) BN_CTX_end(ctx); BN_CTX_free(ctx); bn_check_top(ret); return found; } int BN_is_prime_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, BN_GENCB *cb) { return BN_is_prime_fasttest_ex(a, checks, ctx_passed, 0, cb); } int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx_passed, int do_trial_division, BN_GENCB *cb) { int i, j, ret = -1; int k; BN_CTX *ctx = NULL; BIGNUM *A1, *A1_odd, *check; /* taken from ctx */ BN_MONT_CTX *mont = NULL; const BIGNUM *A = NULL; if (BN_cmp(a, BN_value_one()) <= 0) return 0; if (checks == BN_prime_checks) checks = BN_prime_checks_for_size(BN_num_bits(a)); /* first look for small factors */ if (!BN_is_odd(a)) /* a is even => a is prime if and only if a == 2 */ return BN_is_word(a, 2); if (do_trial_division) { for (i = 1; i < NUMPRIMES; i++) if (BN_mod_word(a, primes[i]) == 0) return 0; if (!BN_GENCB_call(cb, 1, -1)) goto err; } if (ctx_passed != NULL) ctx = ctx_passed; else if ((ctx = BN_CTX_new()) == NULL) goto err; BN_CTX_start(ctx); /* A := abs(a) */ if (a->neg) { BIGNUM *t; if ((t = BN_CTX_get(ctx)) == NULL) goto err; BN_copy(t, a); t->neg = 0; A = t; } else A = a; A1 = BN_CTX_get(ctx); A1_odd = BN_CTX_get(ctx); check = BN_CTX_get(ctx); if (check == NULL) goto err; /* compute A1 := A - 1 */ if (!BN_copy(A1, A)) goto err; if (!BN_sub_word(A1, 1)) goto err; if (BN_is_zero(A1)) { ret = 0; goto err; } /* write A1 as A1_odd * 2^k */ k = 1; while (!BN_is_bit_set(A1, k)) k++; if (!BN_rshift(A1_odd, A1, k)) goto err; /* Montgomery setup for computations mod A */ mont = BN_MONT_CTX_new(); if (mont == NULL) goto err; if (!BN_MONT_CTX_set(mont, A, ctx)) goto err; for (i = 0; i < checks; i++) { if (!BN_pseudo_rand_range(check, A1)) goto err; if (!BN_add_word(check, 1)) goto err; /* now 1 <= check < A */ j = witness(check, A, A1, A1_odd, k, ctx, mont); if (j == -1) goto err; if (j) { ret = 0; goto err; } if (!BN_GENCB_call(cb, 1, i)) goto err; } ret = 1; err: if (ctx != NULL) { BN_CTX_end(ctx); if (ctx_passed == NULL) BN_CTX_free(ctx); } BN_MONT_CTX_free(mont); return (ret); } int bn_probable_prime_dh_retry(BIGNUM *rnd, int bits, BN_CTX *ctx) { int i; int ret = 0; loop: if (!BN_rand(rnd, bits, 0, 1)) goto err; /* we now have a random number 'rand' to test. */ for (i = 1; i < NUMPRIMES; i++) { /* check that rnd is a prime */ if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { goto loop; } } ret = 1; err: bn_check_top(rnd); return (ret); } int bn_probable_prime_dh_coprime(BIGNUM *rnd, int bits, BN_CTX *ctx) { int i; BIGNUM *offset_index; BIGNUM *offset_count; int ret = 0; OPENSSL_assert(bits > prime_multiplier_bits); BN_CTX_start(ctx); if ((offset_index = BN_CTX_get(ctx)) == NULL) goto err; if ((offset_count = BN_CTX_get(ctx)) == NULL) goto err; BN_add_word(offset_count, prime_offset_count); loop: if (!BN_rand(rnd, bits - prime_multiplier_bits, 0, 1)) goto err; if (BN_is_bit_set(rnd, bits)) goto loop; if (!BN_rand_range(offset_index, offset_count)) goto err; BN_mul_word(rnd, prime_multiplier); BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)]); /* we now have a random number 'rand' to test. */ /* skip coprimes */ for (i = first_prime_index; i < NUMPRIMES; i++) { /* check that rnd is a prime */ if (BN_mod_word(rnd, (BN_ULONG)primes[i]) <= 1) { goto loop; } } ret = 1; err: BN_CTX_end(ctx); bn_check_top(rnd); return ret; } static int witness(BIGNUM *w, const BIGNUM *a, const BIGNUM *a1, const BIGNUM *a1_odd, int k, BN_CTX *ctx, BN_MONT_CTX *mont) { if (!BN_mod_exp_mont(w, w, a1_odd, a, ctx, mont)) /* w := w^a1_odd mod a */ return -1; if (BN_is_one(w)) return 0; /* probably prime */ if (BN_cmp(w, a1) == 0) return 0; /* w == -1 (mod a), 'a' is probably prime */ while (--k) { if (!BN_mod_mul(w, w, w, a, ctx)) /* w := w^2 mod a */ return -1; if (BN_is_one(w)) return 1; /* 'a' is composite, otherwise a previous 'w' * would have been == -1 (mod 'a') */ if (BN_cmp(w, a1) == 0) return 0; /* w == -1 (mod a), 'a' is probably prime */ } /* * If we get here, 'w' is the (a-1)/2-th power of the original 'w', and * it is neither -1 nor +1 -- so 'a' cannot be prime */ bn_check_top(w); return 1; } static int probable_prime(BIGNUM *rnd, int bits, prime_t *mods) { int i; BN_ULONG delta; BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; char is_single_word = bits <= BN_BITS2; again: if (!BN_rand(rnd, bits, 1, 1)) return (0); /* we now have a random number 'rnd' to test. */ for (i = 1; i < NUMPRIMES; i++) mods[i] = (prime_t) BN_mod_word(rnd, (BN_ULONG)primes[i]); /* * If bits is so small that it fits into a single word then we * additionally don't want to exceed that many bits. */ if (is_single_word) { BN_ULONG size_limit; if (bits == BN_BITS2) { /* * Shifting by this much has undefined behaviour so we do it a * different way */ size_limit = ~((BN_ULONG)0) - BN_get_word(rnd); } else { size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1; } if (size_limit < maxdelta) maxdelta = size_limit; } delta = 0; loop: if (is_single_word) { BN_ULONG rnd_word = BN_get_word(rnd); /*- * In the case that the candidate prime is a single word then * we check that: * 1) It's greater than primes[i] because we shouldn't reject * 3 as being a prime number because it's a multiple of * three. * 2) That it's not a multiple of a known prime. We don't * check that rnd-1 is also coprime to all the known * primes because there aren't many small primes where * that's true. */ for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) { if ((mods[i] + delta) % primes[i] == 0) { delta += 2; if (delta > maxdelta) goto again; goto loop; } } } 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); }