| /* 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 <openssl/bn.h> |
| |
| #include <openssl/err.h> |
| #include <openssl/mem.h> |
| |
| #include "internal.h" |
| |
| /* number of Miller-Rabin iterations for an error rate of less than 2^-80 |
| * for random 'b'-bit input, b >= 100 (taken from table 4.4 in the Handbook |
| * of Applied Cryptography [Menezes, van Oorschot, Vanstone; CRC Press 1996]; |
| * original paper: Damgaard, Landrock, Pomerance: Average case error estimates |
| * for the strong probable prime test. -- Math. Comp. 61 (1993) 177-194) */ |
| #define BN_prime_checks_for_size(b) ((b) >= 1300 ? 2 : \ |
| (b) >= 850 ? 3 : \ |
| (b) >= 650 ? 4 : \ |
| (b) >= 550 ? 5 : \ |
| (b) >= 450 ? 6 : \ |
| (b) >= 400 ? 7 : \ |
| (b) >= 350 ? 8 : \ |
| (b) >= 300 ? 9 : \ |
| (b) >= 250 ? 12 : \ |
| (b) >= 200 ? 15 : \ |
| (b) >= 150 ? 18 : \ |
| /* b >= 100 */ 27) |
| |
| /* 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. */ |
| |
| /* NUMPRIMES is the number of primes that fit into a uint16_t. */ |
| #define NUMPRIMES 2048 |
| |
| /* primes contains all the primes that fit into a uint16_t. */ |
| static const uint16_t primes[NUMPRIMES] = { |
| 2, 3, 5, 7, 11, 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, 173, 179, 181, 191, 193, |
| 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, |
| 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, |
| 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, |
| 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, |
| 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, |
| 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, |
| 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, |
| 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, |
| 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, |
| 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, |
| 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, |
| 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, |
| 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, |
| 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, |
| 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, |
| 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, |
| 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, |
| 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, |
| 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, |
| 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, |
| 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, |
| 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, |
| 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, |
| 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, |
| 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, |
| 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, |
| 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, |
| 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, |
| 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, |
| 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, |
| 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, |
| 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, |
| 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, |
| 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, |
| 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, |
| 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, |
| 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, |
| 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, |
| 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, |
| 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, |
| 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, |
| 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, |
| 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, |
| 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, |
| 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, |
| 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, |
| 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, |
| 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, |
| 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, |
| 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, |
| 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, |
| 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, |
| 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, |
| 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, |
| 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, |
| 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, |
| 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, |
| 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, |
| 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, |
| 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, |
| 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, |
| 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, |
| 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, |
| 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, |
| 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, |
| 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, |
| 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, |
| 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, |
| 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, |
| 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, |
| 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, |
| 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, |
| 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, |
| 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, |
| 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, |
| 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, |
| 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, |
| 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, |
| 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, |
| 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, |
| 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, |
| 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, |
| 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, |
| 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, |
| 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, |
| 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, |
| 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, |
| 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, |
| 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, |
| 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, |
| 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, |
| 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, |
| 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, |
| 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, |
| 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, |
| 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, |
| 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, |
| 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, |
| 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, |
| 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, |
| 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, |
| 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, |
| 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, |
| 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, |
| 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, |
| 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, |
| 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, |
| 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, |
| 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, |
| 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, |
| 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, |
| 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, |
| 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, |
| 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, |
| 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, |
| 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, |
| 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, |
| 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, |
| 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, |
| 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, |
| 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, |
| 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, |
| 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, |
| 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, |
| 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, |
| 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, |
| 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, |
| 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, |
| 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, |
| 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, |
| 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, |
| 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, |
| 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, |
| 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, |
| 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, |
| 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, |
| 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, |
| 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, |
| 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, |
| 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, |
| 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, |
| 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, |
| 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, |
| 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, |
| 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, |
| 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, |
| 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, |
| 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, |
| 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, |
| 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, |
| 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, |
| 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, |
| 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, |
| 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, |
| 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, |
| 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, |
| 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, |
| 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, |
| 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, |
| 15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, |
| 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, |
| 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, |
| 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, |
| 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, |
| 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, |
| 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, |
| 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, |
| 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, |
| 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, |
| 16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, |
| 16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, |
| 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, |
| 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, |
| 16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, |
| 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, |
| 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, |
| 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, |
| 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, |
| 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, |
| 17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, |
| 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, |
| 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, |
| 17851, 17863, |
| }; |
| |
| 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); |
| static int probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, |
| const BIGNUM *rem, BN_CTX *ctx); |
| static int probable_prime_dh_safe(BIGNUM *rnd, int bits, const BIGNUM *add, |
| const BIGNUM *rem, BN_CTX *ctx); |
| |
| void BN_GENCB_set(BN_GENCB *callback, |
| int (*f)(int event, int n, struct bn_gencb_st *), |
| void *arg) { |
| callback->callback = f; |
| callback->arg = arg; |
| } |
| |
| int BN_GENCB_call(BN_GENCB *callback, int event, int n) { |
| if (!callback) { |
| return 1; |
| } |
| |
| return callback->callback(event, n, callback); |
| } |
| |
| 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; |
| int checks = BN_prime_checks_for_size(bits); |
| |
| if (bits < 2) { |
| /* There are no prime numbers this small. */ |
| OPENSSL_PUT_ERROR(BN, BN_R_BITS_TOO_SMALL); |
| return 0; |
| } else if (bits == 2 && safe) { |
| /* The smallest safe prime (7) is three bits. */ |
| OPENSSL_PUT_ERROR(BN, 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)) { |
| goto err; |
| } |
| } else { |
| if (safe) { |
| if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) { |
| goto err; |
| } |
| } else { |
| if (!probable_prime_dh(ret, bits, add, rem, ctx)) { |
| goto err; |
| } |
| } |
| } |
| |
| if (!BN_GENCB_call(cb, BN_GENCB_GENERATED, c1++)) { |
| /* aborted */ |
| goto err; |
| } |
| |
| if (!safe) { |
| i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); |
| if (i == -1) { |
| goto err; |
| } else 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, NULL); |
| if (j == -1) { |
| goto err; |
| } else if (j == 0) { |
| goto loop; |
| } |
| |
| j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, NULL); |
| if (j == -1) { |
| goto err; |
| } else if (j == 0) { |
| goto loop; |
| } |
| |
| if (!BN_GENCB_call(cb, i, c1 - 1)) { |
| goto err; |
| } |
| /* We have a safe prime test pass */ |
| } |
| } |
| |
| /* we have a prime :-) */ |
| found = 1; |
| |
| err: |
| if (ctx != NULL) { |
| BN_CTX_end(ctx); |
| BN_CTX_free(ctx); |
| } |
| |
| return found; |
| } |
| |
| int BN_primality_test(int *is_probably_prime, const BIGNUM *candidate, |
| int checks, BN_CTX *ctx, int do_trial_division, |
| BN_GENCB *cb) { |
| switch (BN_is_prime_fasttest_ex(candidate, checks, ctx, do_trial_division, cb)) { |
| case 1: |
| *is_probably_prime = 1; |
| return 1; |
| case 0: |
| *is_probably_prime = 0; |
| return 1; |
| default: |
| *is_probably_prime = 0; |
| return 0; |
| } |
| } |
| |
| int BN_is_prime_ex(const BIGNUM *candidate, int checks, BN_CTX *ctx, BN_GENCB *cb) { |
| return BN_is_prime_fasttest_ex(candidate, checks, ctx, 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++) { |
| 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); |
| |
| /* A := abs(a) */ |
| if (a->neg) { |
| BIGNUM *t = BN_CTX_get(ctx); |
| if (t == NULL || !BN_copy(t, a)) { |
| goto err; |
| } |
| 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); |
| } |
| } |
| if (mont != NULL) { |
| BN_MONT_CTX_free(mont); |
| } |
| |
| 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 */ |
| return 1; |
| } |
| |
| static BN_ULONG get_word(const BIGNUM *bn) { |
| if (bn->top == 1) { |
| return bn->d[0]; |
| } |
| return 0; |
| } |
| |
| static int probable_prime(BIGNUM *rnd, int bits) { |
| int i; |
| uint16_t mods[NUMPRIMES]; |
| 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] = (uint16_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) { |
| /* Avoid undefined behavior. */ |
| size_limit = ~((BN_ULONG)0) - get_word(rnd); |
| } else { |
| size_limit = (((BN_ULONG)1) << bits) - get_word(rnd) - 1; |
| } |
| if (size_limit < maxdelta) { |
| maxdelta = size_limit; |
| } |
| } |
| delta = 0; |
| |
| loop: |
| if (is_single_word) { |
| BN_ULONG rnd_word = 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) != (unsigned)bits) { |
| goto again; |
| } |
| |
| return 1; |
| } |
| |
| static int 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); |
| 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); |
| return ret; |
| } |
