diff options
Diffstat (limited to 'openssl-1.1.0h/crypto/bn/bn_prime.c')
| -rw-r--r-- | openssl-1.1.0h/crypto/bn/bn_prime.c | 596 |
1 files changed, 596 insertions, 0 deletions
diff --git a/openssl-1.1.0h/crypto/bn/bn_prime.c b/openssl-1.1.0h/crypto/bn/bn_prime.c new file mode 100644 index 0000000..616389c --- /dev/null +++ b/openssl-1.1.0h/crypto/bn/bn_prime.c @@ -0,0 +1,596 @@ +/* + * WARNING: do not edit! + * Generated by crypto/bn/bn_prime.pl + * Copyright 1995-2016 The OpenSSL Project Authors. All Rights Reserved. + * + * Licensed under the OpenSSL license (the "License"). You may not use + * this file except in compliance with the License. You can obtain a copy + * in the file LICENSE in the source distribution or at + * https://www.openssl.org/source/license.html + */ + +#include <stdio.h> +#include <time.h> +#include "internal/cryptlib.h" +#include "bn_lcl.h" + +/* + * 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); + + 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; + } + + mods = OPENSSL_zalloc(sizeof(*mods) * NUMPRIMES); + if (mods == NULL) + goto err; + + 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_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; + + 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++) { + BN_ULONG mod = BN_mod_word(a, primes[i]); + if (mod == (BN_ULONG)-1) + goto err; + if (mod == 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); + + 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, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD)) + goto err; + + /* we now have a random number 'rand' to test. */ + + for (i = 1; i < NUMPRIMES; i++) { + /* check that rnd is a prime */ + BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]); + if (mod == (BN_ULONG)-1) + goto err; + if (mod <= 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; + + if (!BN_add_word(offset_count, prime_offset_count)) + goto err; + + loop: + if (!BN_rand(rnd, bits - prime_multiplier_bits, + BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD)) + goto err; + if (BN_is_bit_set(rnd, bits)) + goto loop; + if (!BN_rand_range(offset_index, offset_count)) + goto err; + + if (!BN_mul_word(rnd, prime_multiplier) + || !BN_add_word(rnd, prime_offsets[BN_get_word(offset_index)])) + goto err; + + /* 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 */ + BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]); + if (mod == (BN_ULONG)-1) + goto err; + if (mod <= 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, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD)) + return (0); + /* we now have a random number 'rnd' to test. */ + for (i = 1; i < NUMPRIMES; i++) { + BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]); + if (mod == (BN_ULONG)-1) + return 0; + mods[i] = (prime_t) mod; + } + /* + * 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, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD)) + 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 */ + BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]); + if (mod == (BN_ULONG)-1) + goto err; + if (mod <= 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, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD)) + 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) + */ + BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]); + BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]); + if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1) + goto err; + if (pmod == 0 || qmod == 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); +} |