Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 1 | /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
| 2 | * All rights reserved. |
| 3 | * |
| 4 | * This package is an SSL implementation written |
| 5 | * by Eric Young (eay@cryptsoft.com). |
| 6 | * The implementation was written so as to conform with Netscapes SSL. |
| 7 | * |
| 8 | * This library is free for commercial and non-commercial use as long as |
| 9 | * the following conditions are aheared to. The following conditions |
| 10 | * apply to all code found in this distribution, be it the RC4, RSA, |
| 11 | * lhash, DES, etc., code; not just the SSL code. The SSL documentation |
| 12 | * included with this distribution is covered by the same copyright terms |
| 13 | * except that the holder is Tim Hudson (tjh@cryptsoft.com). |
| 14 | * |
| 15 | * Copyright remains Eric Young's, and as such any Copyright notices in |
| 16 | * the code are not to be removed. |
| 17 | * If this package is used in a product, Eric Young should be given attribution |
| 18 | * as the author of the parts of the library used. |
| 19 | * This can be in the form of a textual message at program startup or |
| 20 | * in documentation (online or textual) provided with the package. |
| 21 | * |
| 22 | * Redistribution and use in source and binary forms, with or without |
| 23 | * modification, are permitted provided that the following conditions |
| 24 | * are met: |
| 25 | * 1. Redistributions of source code must retain the copyright |
| 26 | * notice, this list of conditions and the following disclaimer. |
| 27 | * 2. Redistributions in binary form must reproduce the above copyright |
| 28 | * notice, this list of conditions and the following disclaimer in the |
| 29 | * documentation and/or other materials provided with the distribution. |
| 30 | * 3. All advertising materials mentioning features or use of this software |
| 31 | * must display the following acknowledgement: |
| 32 | * "This product includes cryptographic software written by |
| 33 | * Eric Young (eay@cryptsoft.com)" |
| 34 | * The word 'cryptographic' can be left out if the rouines from the library |
| 35 | * being used are not cryptographic related :-). |
| 36 | * 4. If you include any Windows specific code (or a derivative thereof) from |
| 37 | * the apps directory (application code) you must include an acknowledgement: |
| 38 | * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" |
| 39 | * |
| 40 | * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
| 41 | * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 42 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| 43 | * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| 44 | * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| 45 | * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| 46 | * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 47 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| 48 | * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| 49 | * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| 50 | * SUCH DAMAGE. |
| 51 | * |
| 52 | * The licence and distribution terms for any publically available version or |
| 53 | * derivative of this code cannot be changed. i.e. this code cannot simply be |
| 54 | * copied and put under another distribution licence |
| 55 | * [including the GNU Public Licence.] |
| 56 | */ |
| 57 | /* ==================================================================== |
| 58 | * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved. |
| 59 | * |
| 60 | * Redistribution and use in source and binary forms, with or without |
| 61 | * modification, are permitted provided that the following conditions |
| 62 | * are met: |
| 63 | * |
| 64 | * 1. Redistributions of source code must retain the above copyright |
| 65 | * notice, this list of conditions and the following disclaimer. |
| 66 | * |
| 67 | * 2. Redistributions in binary form must reproduce the above copyright |
| 68 | * notice, this list of conditions and the following disclaimer in |
| 69 | * the documentation and/or other materials provided with the |
| 70 | * distribution. |
| 71 | * |
| 72 | * 3. All advertising materials mentioning features or use of this |
| 73 | * software must display the following acknowledgment: |
| 74 | * "This product includes software developed by the OpenSSL Project |
| 75 | * for use in the OpenSSL Toolkit. (http://www.openssl.org/)" |
| 76 | * |
| 77 | * 4. The names "OpenSSL Toolkit" and "OpenSSL Project" must not be used to |
| 78 | * endorse or promote products derived from this software without |
| 79 | * prior written permission. For written permission, please contact |
| 80 | * openssl-core@openssl.org. |
| 81 | * |
| 82 | * 5. Products derived from this software may not be called "OpenSSL" |
| 83 | * nor may "OpenSSL" appear in their names without prior written |
| 84 | * permission of the OpenSSL Project. |
| 85 | * |
| 86 | * 6. Redistributions of any form whatsoever must retain the following |
| 87 | * acknowledgment: |
| 88 | * "This product includes software developed by the OpenSSL Project |
| 89 | * for use in the OpenSSL Toolkit (http://www.openssl.org/)" |
| 90 | * |
| 91 | * THIS SOFTWARE IS PROVIDED BY THE OpenSSL PROJECT ``AS IS'' AND ANY |
| 92 | * EXPRESSED OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| 93 | * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
| 94 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE OpenSSL PROJECT OR |
| 95 | * ITS CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, |
| 96 | * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT |
| 97 | * NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| 98 | * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| 99 | * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, |
| 100 | * STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
| 101 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED |
| 102 | * OF THE POSSIBILITY OF SUCH DAMAGE. |
| 103 | * ==================================================================== |
| 104 | * |
| 105 | * This product includes cryptographic software written by Eric Young |
| 106 | * (eay@cryptsoft.com). This product includes software written by Tim |
| 107 | * Hudson (tjh@cryptsoft.com). */ |
| 108 | |
| 109 | #include <openssl/bn.h> |
| 110 | |
| 111 | #include <openssl/err.h> |
| 112 | #include <openssl/mem.h> |
| 113 | |
| 114 | #include "internal.h" |
| 115 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 116 | /* The quick sieve algorithm approach to weeding out primes is Philip |
| 117 | * Zimmermann's, as implemented in PGP. I have had a read of his comments and |
| 118 | * implemented my own version. */ |
| 119 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 120 | #define NUMPRIMES 2048 |
| 121 | |
| 122 | /* primes contains all the primes that fit into a uint16_t. */ |
| 123 | static const uint16_t primes[NUMPRIMES] = { |
| 124 | 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, |
| 125 | 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, |
| 126 | 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, |
| 127 | 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, |
| 128 | 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, |
| 129 | 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, |
| 130 | 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, |
| 131 | 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, |
| 132 | 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, |
| 133 | 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, |
| 134 | 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, |
| 135 | 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, |
| 136 | 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, |
| 137 | 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, |
| 138 | 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, |
| 139 | 983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, |
| 140 | 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, |
| 141 | 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, |
| 142 | 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, |
| 143 | 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, |
| 144 | 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, |
| 145 | 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, |
| 146 | 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, |
| 147 | 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, |
| 148 | 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, |
| 149 | 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, |
| 150 | 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, |
| 151 | 1973, 1979, 1987, 1993, 1997, 1999, 2003, 2011, 2017, 2027, 2029, |
| 152 | 2039, 2053, 2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, |
| 153 | 2129, 2131, 2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, |
| 154 | 2221, 2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293, |
| 155 | 2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371, 2377, |
| 156 | 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 2441, 2447, |
| 157 | 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551, |
| 158 | 2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633, 2647, 2657, 2659, |
| 159 | 2663, 2671, 2677, 2683, 2687, 2689, 2693, 2699, 2707, 2711, 2713, |
| 160 | 2719, 2729, 2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791, 2797, |
| 161 | 2801, 2803, 2819, 2833, 2837, 2843, 2851, 2857, 2861, 2879, 2887, |
| 162 | 2897, 2903, 2909, 2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, |
| 163 | 2999, 3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, |
| 164 | 3083, 3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, |
| 165 | 3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271, |
| 166 | 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343, 3347, 3359, |
| 167 | 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 3449, 3457, 3461, |
| 168 | 3463, 3467, 3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533, 3539, |
| 169 | 3541, 3547, 3557, 3559, 3571, 3581, 3583, 3593, 3607, 3613, 3617, |
| 170 | 3623, 3631, 3637, 3643, 3659, 3671, 3673, 3677, 3691, 3697, 3701, |
| 171 | 3709, 3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779, 3793, 3797, |
| 172 | 3803, 3821, 3823, 3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, |
| 173 | 3907, 3911, 3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, |
| 174 | 4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073, |
| 175 | 4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153, 4157, |
| 176 | 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243, 4253, |
| 177 | 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327, 4337, 4339, 4349, |
| 178 | 4357, 4363, 4373, 4391, 4397, 4409, 4421, 4423, 4441, 4447, 4451, |
| 179 | 4457, 4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519, 4523, 4547, |
| 180 | 4549, 4561, 4567, 4583, 4591, 4597, 4603, 4621, 4637, 4639, 4643, |
| 181 | 4649, 4651, 4657, 4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729, |
| 182 | 4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, |
| 183 | 4831, 4861, 4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, |
| 184 | 4943, 4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009, |
| 185 | 5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099, 5101, |
| 186 | 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189, 5197, 5209, |
| 187 | 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281, 5297, 5303, 5309, |
| 188 | 5323, 5333, 5347, 5351, 5381, 5387, 5393, 5399, 5407, 5413, 5417, |
| 189 | 5419, 5431, 5437, 5441, 5443, 5449, 5471, 5477, 5479, 5483, 5501, |
| 190 | 5503, 5507, 5519, 5521, 5527, 5531, 5557, 5563, 5569, 5573, 5581, |
| 191 | 5591, 5623, 5639, 5641, 5647, 5651, 5653, 5657, 5659, 5669, 5683, |
| 192 | 5689, 5693, 5701, 5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, |
| 193 | 5791, 5801, 5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, |
| 194 | 5861, 5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953, |
| 195 | 5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067, 6073, |
| 196 | 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143, 6151, 6163, |
| 197 | 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229, 6247, 6257, 6263, |
| 198 | 6269, 6271, 6277, 6287, 6299, 6301, 6311, 6317, 6323, 6329, 6337, |
| 199 | 6343, 6353, 6359, 6361, 6367, 6373, 6379, 6389, 6397, 6421, 6427, |
| 200 | 6449, 6451, 6469, 6473, 6481, 6491, 6521, 6529, 6547, 6551, 6553, |
| 201 | 6563, 6569, 6571, 6577, 6581, 6599, 6607, 6619, 6637, 6653, 6659, |
| 202 | 6661, 6673, 6679, 6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, |
| 203 | 6761, 6763, 6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, |
| 204 | 6841, 6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947, |
| 205 | 6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001, 7013, |
| 206 | 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109, 7121, 7127, |
| 207 | 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211, 7213, 7219, 7229, |
| 208 | 7237, 7243, 7247, 7253, 7283, 7297, 7307, 7309, 7321, 7331, 7333, |
| 209 | 7349, 7351, 7369, 7393, 7411, 7417, 7433, 7451, 7457, 7459, 7477, |
| 210 | 7481, 7487, 7489, 7499, 7507, 7517, 7523, 7529, 7537, 7541, 7547, |
| 211 | 7549, 7559, 7561, 7573, 7577, 7583, 7589, 7591, 7603, 7607, 7621, |
| 212 | 7639, 7643, 7649, 7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, |
| 213 | 7723, 7727, 7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, |
| 214 | 7841, 7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927, |
| 215 | 7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039, 8053, |
| 216 | 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117, 8123, 8147, |
| 217 | 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221, 8231, 8233, 8237, |
| 218 | 8243, 8263, 8269, 8273, 8287, 8291, 8293, 8297, 8311, 8317, 8329, |
| 219 | 8353, 8363, 8369, 8377, 8387, 8389, 8419, 8423, 8429, 8431, 8443, |
| 220 | 8447, 8461, 8467, 8501, 8513, 8521, 8527, 8537, 8539, 8543, 8563, |
| 221 | 8573, 8581, 8597, 8599, 8609, 8623, 8627, 8629, 8641, 8647, 8663, |
| 222 | 8669, 8677, 8681, 8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, |
| 223 | 8741, 8747, 8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, |
| 224 | 8837, 8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933, |
| 225 | 8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013, 9029, |
| 226 | 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127, 9133, 9137, |
| 227 | 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203, 9209, 9221, 9227, |
| 228 | 9239, 9241, 9257, 9277, 9281, 9283, 9293, 9311, 9319, 9323, 9337, |
| 229 | 9341, 9343, 9349, 9371, 9377, 9391, 9397, 9403, 9413, 9419, 9421, |
| 230 | 9431, 9433, 9437, 9439, 9461, 9463, 9467, 9473, 9479, 9491, 9497, |
| 231 | 9511, 9521, 9533, 9539, 9547, 9551, 9587, 9601, 9613, 9619, 9623, |
| 232 | 9629, 9631, 9643, 9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, |
| 233 | 9733, 9739, 9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, |
| 234 | 9817, 9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901, |
| 235 | 9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007, 10009, 10037, |
| 236 | 10039, 10061, 10067, 10069, 10079, 10091, 10093, 10099, 10103, 10111, 10133, |
| 237 | 10139, 10141, 10151, 10159, 10163, 10169, 10177, 10181, 10193, 10211, 10223, |
| 238 | 10243, 10247, 10253, 10259, 10267, 10271, 10273, 10289, 10301, 10303, 10313, |
| 239 | 10321, 10331, 10333, 10337, 10343, 10357, 10369, 10391, 10399, 10427, 10429, |
| 240 | 10433, 10453, 10457, 10459, 10463, 10477, 10487, 10499, 10501, 10513, 10529, |
| 241 | 10531, 10559, 10567, 10589, 10597, 10601, 10607, 10613, 10627, 10631, 10639, |
| 242 | 10651, 10657, 10663, 10667, 10687, 10691, 10709, 10711, 10723, 10729, 10733, |
| 243 | 10739, 10753, 10771, 10781, 10789, 10799, 10831, 10837, 10847, 10853, 10859, |
| 244 | 10861, 10867, 10883, 10889, 10891, 10903, 10909, 10937, 10939, 10949, 10957, |
| 245 | 10973, 10979, 10987, 10993, 11003, 11027, 11047, 11057, 11059, 11069, 11071, |
| 246 | 11083, 11087, 11093, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, |
| 247 | 11173, 11177, 11197, 11213, 11239, 11243, 11251, 11257, 11261, 11273, 11279, |
| 248 | 11287, 11299, 11311, 11317, 11321, 11329, 11351, 11353, 11369, 11383, 11393, |
| 249 | 11399, 11411, 11423, 11437, 11443, 11447, 11467, 11471, 11483, 11489, 11491, |
| 250 | 11497, 11503, 11519, 11527, 11549, 11551, 11579, 11587, 11593, 11597, 11617, |
| 251 | 11621, 11633, 11657, 11677, 11681, 11689, 11699, 11701, 11717, 11719, 11731, |
| 252 | 11743, 11777, 11779, 11783, 11789, 11801, 11807, 11813, 11821, 11827, 11831, |
| 253 | 11833, 11839, 11863, 11867, 11887, 11897, 11903, 11909, 11923, 11927, 11933, |
| 254 | 11939, 11941, 11953, 11959, 11969, 11971, 11981, 11987, 12007, 12011, 12037, |
| 255 | 12041, 12043, 12049, 12071, 12073, 12097, 12101, 12107, 12109, 12113, 12119, |
| 256 | 12143, 12149, 12157, 12161, 12163, 12197, 12203, 12211, 12227, 12239, 12241, |
| 257 | 12251, 12253, 12263, 12269, 12277, 12281, 12289, 12301, 12323, 12329, 12343, |
| 258 | 12347, 12373, 12377, 12379, 12391, 12401, 12409, 12413, 12421, 12433, 12437, |
| 259 | 12451, 12457, 12473, 12479, 12487, 12491, 12497, 12503, 12511, 12517, 12527, |
| 260 | 12539, 12541, 12547, 12553, 12569, 12577, 12583, 12589, 12601, 12611, 12613, |
| 261 | 12619, 12637, 12641, 12647, 12653, 12659, 12671, 12689, 12697, 12703, 12713, |
| 262 | 12721, 12739, 12743, 12757, 12763, 12781, 12791, 12799, 12809, 12821, 12823, |
| 263 | 12829, 12841, 12853, 12889, 12893, 12899, 12907, 12911, 12917, 12919, 12923, |
| 264 | 12941, 12953, 12959, 12967, 12973, 12979, 12983, 13001, 13003, 13007, 13009, |
| 265 | 13033, 13037, 13043, 13049, 13063, 13093, 13099, 13103, 13109, 13121, 13127, |
| 266 | 13147, 13151, 13159, 13163, 13171, 13177, 13183, 13187, 13217, 13219, 13229, |
| 267 | 13241, 13249, 13259, 13267, 13291, 13297, 13309, 13313, 13327, 13331, 13337, |
| 268 | 13339, 13367, 13381, 13397, 13399, 13411, 13417, 13421, 13441, 13451, 13457, |
| 269 | 13463, 13469, 13477, 13487, 13499, 13513, 13523, 13537, 13553, 13567, 13577, |
| 270 | 13591, 13597, 13613, 13619, 13627, 13633, 13649, 13669, 13679, 13681, 13687, |
| 271 | 13691, 13693, 13697, 13709, 13711, 13721, 13723, 13729, 13751, 13757, 13759, |
| 272 | 13763, 13781, 13789, 13799, 13807, 13829, 13831, 13841, 13859, 13873, 13877, |
| 273 | 13879, 13883, 13901, 13903, 13907, 13913, 13921, 13931, 13933, 13963, 13967, |
| 274 | 13997, 13999, 14009, 14011, 14029, 14033, 14051, 14057, 14071, 14081, 14083, |
| 275 | 14087, 14107, 14143, 14149, 14153, 14159, 14173, 14177, 14197, 14207, 14221, |
| 276 | 14243, 14249, 14251, 14281, 14293, 14303, 14321, 14323, 14327, 14341, 14347, |
| 277 | 14369, 14387, 14389, 14401, 14407, 14411, 14419, 14423, 14431, 14437, 14447, |
| 278 | 14449, 14461, 14479, 14489, 14503, 14519, 14533, 14537, 14543, 14549, 14551, |
| 279 | 14557, 14561, 14563, 14591, 14593, 14621, 14627, 14629, 14633, 14639, 14653, |
| 280 | 14657, 14669, 14683, 14699, 14713, 14717, 14723, 14731, 14737, 14741, 14747, |
| 281 | 14753, 14759, 14767, 14771, 14779, 14783, 14797, 14813, 14821, 14827, 14831, |
| 282 | 14843, 14851, 14867, 14869, 14879, 14887, 14891, 14897, 14923, 14929, 14939, |
| 283 | 14947, 14951, 14957, 14969, 14983, 15013, 15017, 15031, 15053, 15061, 15073, |
| 284 | 15077, 15083, 15091, 15101, 15107, 15121, 15131, 15137, 15139, 15149, 15161, |
| 285 | 15173, 15187, 15193, 15199, 15217, 15227, 15233, 15241, 15259, 15263, 15269, |
| 286 | 15271, 15277, 15287, 15289, 15299, 15307, 15313, 15319, 15329, 15331, 15349, |
| 287 | 15359, 15361, 15373, 15377, 15383, 15391, 15401, 15413, 15427, 15439, 15443, |
| 288 | 15451, 15461, 15467, 15473, 15493, 15497, 15511, 15527, 15541, 15551, 15559, |
| 289 | 15569, 15581, 15583, 15601, 15607, 15619, 15629, 15641, 15643, 15647, 15649, |
| 290 | 15661, 15667, 15671, 15679, 15683, 15727, 15731, 15733, 15737, 15739, 15749, |
| 291 | 15761, 15767, 15773, 15787, 15791, 15797, 15803, 15809, 15817, 15823, 15859, |
| 292 | 15877, 15881, 15887, 15889, 15901, 15907, 15913, 15919, 15923, 15937, 15959, |
| 293 | 15971, 15973, 15991, 16001, 16007, 16033, 16057, 16061, 16063, 16067, 16069, |
| 294 | 16073, 16087, 16091, 16097, 16103, 16111, 16127, 16139, 16141, 16183, 16187, |
| 295 | 16189, 16193, 16217, 16223, 16229, 16231, 16249, 16253, 16267, 16273, 16301, |
| 296 | 16319, 16333, 16339, 16349, 16361, 16363, 16369, 16381, 16411, 16417, 16421, |
| 297 | 16427, 16433, 16447, 16451, 16453, 16477, 16481, 16487, 16493, 16519, 16529, |
| 298 | 16547, 16553, 16561, 16567, 16573, 16603, 16607, 16619, 16631, 16633, 16649, |
| 299 | 16651, 16657, 16661, 16673, 16691, 16693, 16699, 16703, 16729, 16741, 16747, |
| 300 | 16759, 16763, 16787, 16811, 16823, 16829, 16831, 16843, 16871, 16879, 16883, |
| 301 | 16889, 16901, 16903, 16921, 16927, 16931, 16937, 16943, 16963, 16979, 16981, |
| 302 | 16987, 16993, 17011, 17021, 17027, 17029, 17033, 17041, 17047, 17053, 17077, |
| 303 | 17093, 17099, 17107, 17117, 17123, 17137, 17159, 17167, 17183, 17189, 17191, |
| 304 | 17203, 17207, 17209, 17231, 17239, 17257, 17291, 17293, 17299, 17317, 17321, |
| 305 | 17327, 17333, 17341, 17351, 17359, 17377, 17383, 17387, 17389, 17393, 17401, |
| 306 | 17417, 17419, 17431, 17443, 17449, 17467, 17471, 17477, 17483, 17489, 17491, |
| 307 | 17497, 17509, 17519, 17539, 17551, 17569, 17573, 17579, 17581, 17597, 17599, |
| 308 | 17609, 17623, 17627, 17657, 17659, 17669, 17681, 17683, 17707, 17713, 17729, |
| 309 | 17737, 17747, 17749, 17761, 17783, 17789, 17791, 17807, 17827, 17837, 17839, |
| 310 | 17851, 17863, |
| 311 | }; |
| 312 | |
Robert Sloan | 572a4e2 | 2017-04-17 10:52:19 -0700 | [diff] [blame] | 313 | /* BN_prime_checks_for_size returns the number of Miller-Rabin iterations |
| 314 | * necessary for a 'bits'-bit prime, in order to maintain an error rate greater |
| 315 | * than the security level for an RSA prime of that many bits (calculated using |
| 316 | * the FIPS SP 800-57 security level and 186-4 Section F.1; original paper: |
| 317 | * Damgaard, Landrock, Pomerance: Average case error estimates for the strong |
| 318 | * probable prime test. -- Math. Comp. 61 (1993) 177-194) */ |
| 319 | static int BN_prime_checks_for_size(int bits) { |
| 320 | if (bits >= 3747) { |
| 321 | return 3; |
| 322 | } |
| 323 | if (bits >= 1345) { |
| 324 | return 4; |
| 325 | } |
| 326 | if (bits >= 476) { |
| 327 | return 5; |
| 328 | } |
| 329 | if (bits >= 400) { |
| 330 | return 6; |
| 331 | } |
| 332 | if (bits >= 308) { |
| 333 | return 8; |
| 334 | } |
| 335 | if (bits >= 205) { |
| 336 | return 13; |
| 337 | } |
| 338 | if (bits >= 155) { |
| 339 | return 19; |
| 340 | } |
| 341 | return 28; |
| 342 | } |
| 343 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 344 | static int probable_prime(BIGNUM *rnd, int bits); |
| 345 | static int probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, |
| 346 | const BIGNUM *rem, BN_CTX *ctx); |
| 347 | static int probable_prime_dh_safe(BIGNUM *rnd, int bits, const BIGNUM *add, |
| 348 | const BIGNUM *rem, BN_CTX *ctx); |
| 349 | |
| 350 | void BN_GENCB_set(BN_GENCB *callback, |
| 351 | int (*f)(int event, int n, struct bn_gencb_st *), |
| 352 | void *arg) { |
| 353 | callback->callback = f; |
| 354 | callback->arg = arg; |
| 355 | } |
| 356 | |
| 357 | int BN_GENCB_call(BN_GENCB *callback, int event, int n) { |
| 358 | if (!callback) { |
| 359 | return 1; |
| 360 | } |
| 361 | |
| 362 | return callback->callback(event, n, callback); |
| 363 | } |
| 364 | |
| 365 | int BN_generate_prime_ex(BIGNUM *ret, int bits, int safe, const BIGNUM *add, |
| 366 | const BIGNUM *rem, BN_GENCB *cb) { |
| 367 | BIGNUM *t; |
| 368 | int found = 0; |
| 369 | int i, j, c1 = 0; |
| 370 | BN_CTX *ctx; |
| 371 | int checks = BN_prime_checks_for_size(bits); |
| 372 | |
| 373 | if (bits < 2) { |
| 374 | /* There are no prime numbers this small. */ |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 375 | OPENSSL_PUT_ERROR(BN, BN_R_BITS_TOO_SMALL); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 376 | return 0; |
| 377 | } else if (bits == 2 && safe) { |
| 378 | /* The smallest safe prime (7) is three bits. */ |
Kenny Root | b849459 | 2015-09-25 02:29:14 +0000 | [diff] [blame] | 379 | OPENSSL_PUT_ERROR(BN, BN_R_BITS_TOO_SMALL); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 380 | return 0; |
| 381 | } |
| 382 | |
| 383 | ctx = BN_CTX_new(); |
| 384 | if (ctx == NULL) { |
| 385 | goto err; |
| 386 | } |
| 387 | BN_CTX_start(ctx); |
| 388 | t = BN_CTX_get(ctx); |
| 389 | if (!t) { |
| 390 | goto err; |
| 391 | } |
| 392 | |
| 393 | loop: |
| 394 | /* make a random number and set the top and bottom bits */ |
| 395 | if (add == NULL) { |
| 396 | if (!probable_prime(ret, bits)) { |
| 397 | goto err; |
| 398 | } |
| 399 | } else { |
| 400 | if (safe) { |
| 401 | if (!probable_prime_dh_safe(ret, bits, add, rem, ctx)) { |
| 402 | goto err; |
| 403 | } |
| 404 | } else { |
| 405 | if (!probable_prime_dh(ret, bits, add, rem, ctx)) { |
| 406 | goto err; |
| 407 | } |
| 408 | } |
| 409 | } |
| 410 | |
| 411 | if (!BN_GENCB_call(cb, BN_GENCB_GENERATED, c1++)) { |
| 412 | /* aborted */ |
| 413 | goto err; |
| 414 | } |
| 415 | |
| 416 | if (!safe) { |
| 417 | i = BN_is_prime_fasttest_ex(ret, checks, ctx, 0, cb); |
| 418 | if (i == -1) { |
| 419 | goto err; |
| 420 | } else if (i == 0) { |
| 421 | goto loop; |
| 422 | } |
| 423 | } else { |
| 424 | /* for "safe prime" generation, check that (p-1)/2 is prime. Since a prime |
| 425 | * is odd, We just need to divide by 2 */ |
| 426 | if (!BN_rshift1(t, ret)) { |
| 427 | goto err; |
| 428 | } |
| 429 | |
| 430 | for (i = 0; i < checks; i++) { |
| 431 | j = BN_is_prime_fasttest_ex(ret, 1, ctx, 0, NULL); |
| 432 | if (j == -1) { |
| 433 | goto err; |
| 434 | } else if (j == 0) { |
| 435 | goto loop; |
| 436 | } |
| 437 | |
| 438 | j = BN_is_prime_fasttest_ex(t, 1, ctx, 0, NULL); |
| 439 | if (j == -1) { |
| 440 | goto err; |
| 441 | } else if (j == 0) { |
| 442 | goto loop; |
| 443 | } |
| 444 | |
| 445 | if (!BN_GENCB_call(cb, i, c1 - 1)) { |
| 446 | goto err; |
| 447 | } |
| 448 | /* We have a safe prime test pass */ |
| 449 | } |
| 450 | } |
| 451 | |
| 452 | /* we have a prime :-) */ |
| 453 | found = 1; |
| 454 | |
| 455 | err: |
| 456 | if (ctx != NULL) { |
| 457 | BN_CTX_end(ctx); |
| 458 | BN_CTX_free(ctx); |
| 459 | } |
| 460 | |
| 461 | return found; |
| 462 | } |
| 463 | |
| 464 | int BN_primality_test(int *is_probably_prime, const BIGNUM *candidate, |
| 465 | int checks, BN_CTX *ctx, int do_trial_division, |
| 466 | BN_GENCB *cb) { |
| 467 | switch (BN_is_prime_fasttest_ex(candidate, checks, ctx, do_trial_division, cb)) { |
| 468 | case 1: |
| 469 | *is_probably_prime = 1; |
| 470 | return 1; |
| 471 | case 0: |
| 472 | *is_probably_prime = 0; |
| 473 | return 1; |
| 474 | default: |
| 475 | *is_probably_prime = 0; |
| 476 | return 0; |
| 477 | } |
| 478 | } |
| 479 | |
| 480 | int BN_is_prime_ex(const BIGNUM *candidate, int checks, BN_CTX *ctx, BN_GENCB *cb) { |
| 481 | return BN_is_prime_fasttest_ex(candidate, checks, ctx, 0, cb); |
| 482 | } |
| 483 | |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 484 | int BN_is_prime_fasttest_ex(const BIGNUM *a, int checks, BN_CTX *ctx, |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 485 | int do_trial_division, BN_GENCB *cb) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 486 | if (BN_cmp(a, BN_value_one()) <= 0) { |
| 487 | return 0; |
| 488 | } |
| 489 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 490 | /* first look for small factors */ |
| 491 | if (!BN_is_odd(a)) { |
| 492 | /* a is even => a is prime if and only if a == 2 */ |
| 493 | return BN_is_word(a, 2); |
| 494 | } |
| 495 | |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 496 | /* Enhanced Miller-Rabin does not work for three. */ |
| 497 | if (BN_is_word(a, 3)) { |
| 498 | return 1; |
| 499 | } |
| 500 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 501 | if (do_trial_division) { |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 502 | for (int i = 1; i < NUMPRIMES; i++) { |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 503 | BN_ULONG mod = BN_mod_word(a, primes[i]); |
| 504 | if (mod == (BN_ULONG)-1) { |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 505 | return -1; |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 506 | } |
| 507 | if (mod == 0) { |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 508 | return BN_is_word(a, primes[i]); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 509 | } |
| 510 | } |
| 511 | |
| 512 | if (!BN_GENCB_call(cb, 1, -1)) { |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 513 | return -1; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 514 | } |
| 515 | } |
| 516 | |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 517 | int ret = -1; |
| 518 | BN_CTX *ctx_allocated = NULL; |
| 519 | if (ctx == NULL) { |
| 520 | ctx_allocated = BN_CTX_new(); |
| 521 | if (ctx_allocated == NULL) { |
| 522 | return -1; |
| 523 | } |
| 524 | ctx = ctx_allocated; |
| 525 | } |
| 526 | |
| 527 | enum bn_primality_result_t result; |
| 528 | if (!BN_enhanced_miller_rabin_primality_test(&result, a, checks, ctx, cb)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 529 | goto err; |
| 530 | } |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 531 | |
| 532 | ret = (result == bn_probably_prime); |
| 533 | |
| 534 | err: |
| 535 | BN_CTX_free(ctx_allocated); |
| 536 | return ret; |
| 537 | } |
| 538 | |
| 539 | int BN_enhanced_miller_rabin_primality_test( |
| 540 | enum bn_primality_result_t *out_result, const BIGNUM *w, int iterations, |
| 541 | BN_CTX *ctx, BN_GENCB *cb) { |
| 542 | /* Enhanced Miller-Rabin is only valid on odd integers greater than 3. */ |
| 543 | if (!BN_is_odd(w) || BN_cmp_word(w, 3) <= 0) { |
| 544 | OPENSSL_PUT_ERROR(BN, BN_R_INVALID_INPUT); |
| 545 | return 0; |
| 546 | } |
| 547 | |
| 548 | if (iterations == BN_prime_checks) { |
| 549 | iterations = BN_prime_checks_for_size(BN_num_bits(w)); |
| 550 | } |
| 551 | |
| 552 | int ret = 0; |
| 553 | BN_MONT_CTX *mont = NULL; |
| 554 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 555 | BN_CTX_start(ctx); |
| 556 | |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 557 | BIGNUM *w1 = BN_CTX_get(ctx); |
| 558 | if (w1 == NULL || |
| 559 | !BN_copy(w1, w) || |
| 560 | !BN_sub_word(w1, 1)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 561 | goto err; |
| 562 | } |
| 563 | |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 564 | /* Write w1 as m*2^a (Steps 1 and 2). */ |
| 565 | int a = 0; |
| 566 | while (!BN_is_bit_set(w1, a)) { |
| 567 | a++; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 568 | } |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 569 | BIGNUM *m = BN_CTX_get(ctx); |
| 570 | if (m == NULL || |
| 571 | !BN_rshift(m, w1, a)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 572 | goto err; |
| 573 | } |
| 574 | |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 575 | BIGNUM *b = BN_CTX_get(ctx); |
| 576 | BIGNUM *g = BN_CTX_get(ctx); |
| 577 | BIGNUM *z = BN_CTX_get(ctx); |
| 578 | BIGNUM *x = BN_CTX_get(ctx); |
| 579 | BIGNUM *x1 = BN_CTX_get(ctx); |
| 580 | if (b == NULL || |
| 581 | g == NULL || |
| 582 | z == NULL || |
| 583 | x == NULL || |
| 584 | x1 == NULL) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 585 | goto err; |
| 586 | } |
| 587 | |
| 588 | /* Montgomery setup for computations mod A */ |
| 589 | mont = BN_MONT_CTX_new(); |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 590 | if (mont == NULL || |
| 591 | !BN_MONT_CTX_set(mont, w, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 592 | goto err; |
| 593 | } |
| 594 | |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 595 | /* The following loop performs in inner iteration of the Enhanced Miller-Rabin |
| 596 | * Primality test (Step 4). */ |
| 597 | for (int i = 1; i <= iterations; i++) { |
| 598 | /* Step 4.1-4.2 */ |
| 599 | if (!BN_rand_range_ex(b, 2, w1)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 600 | goto err; |
| 601 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 602 | |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 603 | /* Step 4.3-4.4 */ |
| 604 | if (!BN_gcd(g, b, w, ctx)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 605 | goto err; |
| 606 | } |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 607 | if (BN_cmp_word(g, 1) > 0) { |
| 608 | *out_result = bn_composite; |
| 609 | ret = 1; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 610 | goto err; |
| 611 | } |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 612 | |
| 613 | /* Step 4.5 */ |
| 614 | if (!BN_mod_exp_mont(z, b, m, w, ctx, mont)) { |
| 615 | goto err; |
| 616 | } |
| 617 | |
| 618 | /* Step 4.6 */ |
| 619 | if (BN_is_one(z) || BN_cmp(z, w1) == 0) { |
| 620 | goto loop; |
| 621 | } |
| 622 | |
| 623 | /* Step 4.7 */ |
| 624 | for (int j = 1; j < a; j++) { |
| 625 | if (!BN_copy(x, z) || !BN_mod_mul(z, x, x, w, ctx)) { |
| 626 | goto err; |
| 627 | } |
| 628 | if (BN_cmp(z, w1) == 0) { |
| 629 | goto loop; |
| 630 | } |
| 631 | if (BN_is_one(z)) { |
| 632 | goto composite; |
| 633 | } |
| 634 | } |
| 635 | |
| 636 | /* Step 4.8-4.9 */ |
| 637 | if (!BN_copy(x, z) || !BN_mod_mul(z, x, x, w, ctx)) { |
| 638 | goto err; |
| 639 | } |
| 640 | |
| 641 | /* Step 4.10-4.11 */ |
| 642 | if (!BN_is_one(z) && !BN_copy(x, z)) { |
| 643 | goto err; |
| 644 | } |
| 645 | |
| 646 | composite: |
| 647 | /* Step 4.12-4.14 */ |
| 648 | if (!BN_copy(x1, x) || |
| 649 | !BN_sub_word(x1, 1) || |
| 650 | !BN_gcd(g, x1, w, ctx)) { |
| 651 | goto err; |
| 652 | } |
| 653 | if (BN_cmp_word(g, 1) > 0) { |
| 654 | *out_result = bn_composite; |
| 655 | } else { |
| 656 | *out_result = bn_non_prime_power_composite; |
| 657 | } |
| 658 | |
| 659 | ret = 1; |
| 660 | goto err; |
| 661 | |
| 662 | loop: |
| 663 | /* Step 4.15 */ |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 664 | if (!BN_GENCB_call(cb, 1, i)) { |
| 665 | goto err; |
| 666 | } |
| 667 | } |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 668 | |
| 669 | *out_result = bn_probably_prime; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 670 | ret = 1; |
| 671 | |
| 672 | err: |
Robert Sloan | 9254e68 | 2017-04-24 09:42:06 -0700 | [diff] [blame] | 673 | BN_MONT_CTX_free(mont); |
| 674 | BN_CTX_end(ctx); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 675 | |
| 676 | return ret; |
| 677 | } |
| 678 | |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 679 | static int probable_prime(BIGNUM *rnd, int bits) { |
| 680 | int i; |
| 681 | uint16_t mods[NUMPRIMES]; |
| 682 | BN_ULONG delta; |
| 683 | BN_ULONG maxdelta = BN_MASK2 - primes[NUMPRIMES - 1]; |
| 684 | char is_single_word = bits <= BN_BITS2; |
| 685 | |
| 686 | again: |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 687 | if (!BN_rand(rnd, bits, BN_RAND_TOP_TWO, BN_RAND_BOTTOM_ODD)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 688 | return 0; |
| 689 | } |
| 690 | |
| 691 | /* we now have a random number 'rnd' to test. */ |
| 692 | for (i = 1; i < NUMPRIMES; i++) { |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 693 | BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]); |
| 694 | if (mod == (BN_ULONG)-1) { |
| 695 | return 0; |
| 696 | } |
| 697 | mods[i] = (uint16_t)mod; |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 698 | } |
| 699 | /* If bits is so small that it fits into a single word then we |
| 700 | * additionally don't want to exceed that many bits. */ |
| 701 | if (is_single_word) { |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 702 | BN_ULONG size_limit; |
| 703 | if (bits == BN_BITS2) { |
| 704 | /* Avoid undefined behavior. */ |
Robert Sloan | 572a4e2 | 2017-04-17 10:52:19 -0700 | [diff] [blame] | 705 | size_limit = ~((BN_ULONG)0) - BN_get_word(rnd); |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 706 | } else { |
Robert Sloan | 572a4e2 | 2017-04-17 10:52:19 -0700 | [diff] [blame] | 707 | size_limit = (((BN_ULONG)1) << bits) - BN_get_word(rnd) - 1; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 708 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 709 | if (size_limit < maxdelta) { |
| 710 | maxdelta = size_limit; |
| 711 | } |
| 712 | } |
| 713 | delta = 0; |
| 714 | |
| 715 | loop: |
| 716 | if (is_single_word) { |
Robert Sloan | 572a4e2 | 2017-04-17 10:52:19 -0700 | [diff] [blame] | 717 | BN_ULONG rnd_word = BN_get_word(rnd); |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 718 | |
| 719 | /* In the case that the candidate prime is a single word then |
| 720 | * we check that: |
| 721 | * 1) It's greater than primes[i] because we shouldn't reject |
| 722 | * 3 as being a prime number because it's a multiple of |
| 723 | * three. |
| 724 | * 2) That it's not a multiple of a known prime. We don't |
| 725 | * check that rnd-1 is also coprime to all the known |
| 726 | * primes because there aren't many small primes where |
| 727 | * that's true. */ |
| 728 | for (i = 1; i < NUMPRIMES && primes[i] < rnd_word; i++) { |
| 729 | if ((mods[i] + delta) % primes[i] == 0) { |
| 730 | delta += 2; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 731 | if (delta > maxdelta) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 732 | goto again; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 733 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 734 | goto loop; |
| 735 | } |
| 736 | } |
| 737 | } else { |
| 738 | for (i = 1; i < NUMPRIMES; i++) { |
| 739 | /* check that rnd is not a prime and also |
| 740 | * that gcd(rnd-1,primes) == 1 (except for 2) */ |
| 741 | if (((mods[i] + delta) % primes[i]) <= 1) { |
| 742 | delta += 2; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 743 | if (delta > maxdelta) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 744 | goto again; |
Adam Langley | e9ada86 | 2015-05-11 17:20:37 -0700 | [diff] [blame] | 745 | } |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 746 | goto loop; |
| 747 | } |
| 748 | } |
| 749 | } |
| 750 | |
| 751 | if (!BN_add_word(rnd, delta)) { |
| 752 | return 0; |
| 753 | } |
Kenny Root | e99801b | 2015-11-06 15:31:15 -0800 | [diff] [blame] | 754 | if (BN_num_bits(rnd) != (unsigned)bits) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 755 | goto again; |
| 756 | } |
| 757 | |
| 758 | return 1; |
| 759 | } |
| 760 | |
| 761 | static int probable_prime_dh(BIGNUM *rnd, int bits, const BIGNUM *add, |
| 762 | const BIGNUM *rem, BN_CTX *ctx) { |
| 763 | int i, ret = 0; |
| 764 | BIGNUM *t1; |
| 765 | |
| 766 | BN_CTX_start(ctx); |
| 767 | if ((t1 = BN_CTX_get(ctx)) == NULL) { |
| 768 | goto err; |
| 769 | } |
| 770 | |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 771 | if (!BN_rand(rnd, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 772 | goto err; |
| 773 | } |
| 774 | |
| 775 | /* we need ((rnd-rem) % add) == 0 */ |
| 776 | |
| 777 | if (!BN_mod(t1, rnd, add, ctx)) { |
| 778 | goto err; |
| 779 | } |
| 780 | if (!BN_sub(rnd, rnd, t1)) { |
| 781 | goto err; |
| 782 | } |
| 783 | if (rem == NULL) { |
| 784 | if (!BN_add_word(rnd, 1)) { |
| 785 | goto err; |
| 786 | } |
| 787 | } else { |
| 788 | if (!BN_add(rnd, rnd, rem)) { |
| 789 | goto err; |
| 790 | } |
| 791 | } |
| 792 | /* we now have a random number 'rand' to test. */ |
| 793 | |
| 794 | loop: |
| 795 | for (i = 1; i < NUMPRIMES; i++) { |
| 796 | /* check that rnd is a prime */ |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 797 | BN_ULONG mod = BN_mod_word(rnd, (BN_ULONG)primes[i]); |
| 798 | if (mod == (BN_ULONG)-1) { |
| 799 | goto err; |
| 800 | } |
| 801 | if (mod <= 1) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 802 | if (!BN_add(rnd, rnd, add)) { |
| 803 | goto err; |
| 804 | } |
| 805 | goto loop; |
| 806 | } |
| 807 | } |
| 808 | |
| 809 | ret = 1; |
| 810 | |
| 811 | err: |
| 812 | BN_CTX_end(ctx); |
| 813 | return ret; |
| 814 | } |
| 815 | |
| 816 | static int probable_prime_dh_safe(BIGNUM *p, int bits, const BIGNUM *padd, |
| 817 | const BIGNUM *rem, BN_CTX *ctx) { |
| 818 | int i, ret = 0; |
| 819 | BIGNUM *t1, *qadd, *q; |
| 820 | |
| 821 | bits--; |
| 822 | BN_CTX_start(ctx); |
| 823 | t1 = BN_CTX_get(ctx); |
| 824 | q = BN_CTX_get(ctx); |
| 825 | qadd = BN_CTX_get(ctx); |
| 826 | if (qadd == NULL) { |
| 827 | goto err; |
| 828 | } |
| 829 | |
| 830 | if (!BN_rshift1(qadd, padd)) { |
| 831 | goto err; |
| 832 | } |
| 833 | |
David Benjamin | f0c4a6c | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 834 | if (!BN_rand(q, bits, BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ODD)) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 835 | goto err; |
| 836 | } |
| 837 | |
| 838 | /* we need ((rnd-rem) % add) == 0 */ |
| 839 | if (!BN_mod(t1, q, qadd, ctx)) { |
| 840 | goto err; |
| 841 | } |
| 842 | |
| 843 | if (!BN_sub(q, q, t1)) { |
| 844 | goto err; |
| 845 | } |
| 846 | |
| 847 | if (rem == NULL) { |
| 848 | if (!BN_add_word(q, 1)) { |
| 849 | goto err; |
| 850 | } |
| 851 | } else { |
| 852 | if (!BN_rshift1(t1, rem)) { |
| 853 | goto err; |
| 854 | } |
| 855 | if (!BN_add(q, q, t1)) { |
| 856 | goto err; |
| 857 | } |
| 858 | } |
| 859 | |
| 860 | /* we now have a random number 'rand' to test. */ |
| 861 | if (!BN_lshift1(p, q)) { |
| 862 | goto err; |
| 863 | } |
| 864 | if (!BN_add_word(p, 1)) { |
| 865 | goto err; |
| 866 | } |
| 867 | |
| 868 | loop: |
| 869 | for (i = 1; i < NUMPRIMES; i++) { |
| 870 | /* check that p and q are prime */ |
| 871 | /* check that for p and q |
| 872 | * gcd(p-1,primes) == 1 (except for 2) */ |
David Benjamin | c895d6b | 2016-08-11 13:26:41 -0400 | [diff] [blame] | 873 | BN_ULONG pmod = BN_mod_word(p, (BN_ULONG)primes[i]); |
| 874 | BN_ULONG qmod = BN_mod_word(q, (BN_ULONG)primes[i]); |
| 875 | if (pmod == (BN_ULONG)-1 || qmod == (BN_ULONG)-1) { |
| 876 | goto err; |
| 877 | } |
| 878 | if (pmod == 0 || qmod == 0) { |
Adam Langley | d9e397b | 2015-01-22 14:27:53 -0800 | [diff] [blame] | 879 | if (!BN_add(p, p, padd)) { |
| 880 | goto err; |
| 881 | } |
| 882 | if (!BN_add(q, q, qadd)) { |
| 883 | goto err; |
| 884 | } |
| 885 | goto loop; |
| 886 | } |
| 887 | } |
| 888 | |
| 889 | ret = 1; |
| 890 | |
| 891 | err: |
| 892 | BN_CTX_end(ctx); |
| 893 | return ret; |
| 894 | } |