/* $Id: random_prime.C,v 1.17 2004/05/14 23:16:36 dm Exp $ */

/*
 *
 * Copyright (C) 1998 David Mazieres (dm@uun.org)
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License as
 * published by the Free Software Foundation; either version 2, or (at
 * your option) any later version.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307
 * USA
 *
 */

#include "crypt.h"
#include "prime.h"
#undef setbit

const u_int small_primes[] =
{
  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, 17881, 0
};

const int num_small_primes
  = sizeof (small_primes) / sizeof (small_primes[0]) - 1;
const u_int odd_sieve[2] = { 1, 2 };
//static const bigint two (2);

inline u_long
quickmod (const bigint &p, u_long d)
{
  return mpn_mod_1 (p._mp_d, p._mp_size, d);
}

static bool
fermat2_test (const bigint &n, bigint *t1, bigint *t2)
{
  *t1 = 1;
  for (int i = mpz_sizeinbase2 (&n); i-- > 0;) {
    mpz_square (t2, t1);
    t1->swap (t2);
    if (t1->_mp_size > n._mp_size)
      mpz_tdiv_r (t1, t1, &n);
    if (n.getbit (i))
      *t1 <<= 1;
  }
  if (*t1 > n)
    mpz_tdiv_r (t1, t1, &n);
  return *t1 == 2;
}
static bool
fermat2_test (const bigint &n)
{
  bigint t1, t2;
  return fermat2_test (n, &t1, &t2);
}

prime_finder::prime_finder (const bigint &pp, const u_int *s, u_int ss)
  : p (pp), sieve (s), sievesize (ss), inc (0), maxinc (-1)
{
  assert (p > 0);
  sievepos = quickmod (p, sievesize);
  calcmods ();
}

prime_finder::~prime_finder ()
{
  bzero (mods, nprimes * sizeof (mods[0]));
}

void
prime_finder::calcmods ()
{
  p += (u_int) inc;
  if (maxinc != -1)
    maxinc -= inc;
  inc = 0;
  for (int i = 0; i < nprimes; i++)
    mods[i] = quickmod (p, small_primes[i]);
}

bigint &
prime_finder::next_weak ()
{
  for (;;) {
  nextinc:
    u_int step = sieve[sievepos];
    sievepos = (sievepos + step) % sievesize;
    inc += step;
    if ((u_int) inc >= (u_int) maxinc)
      return tmp = 0;
    if (inc < 0)
      calcmods ();

    for (int i = 0; i < nprimes; i++) {
#if 1
      while (mods[i] + inc >= (int) small_primes[i]) {
	mods[i] -= small_primes[i];
	if (!(mods[i] + inc))
	  goto nextinc;
      }
#else
      if (mods[i] + inc >= (int) small_primes[i]) {
	mods[i] = (u_int) (mods[i] + inc) % small_primes[i] - inc;
	if (!(mods[i] + inc))
	  goto nextinc;
      }
#endif
    }
    return tmp = p + inc;
  }
}

bigint &
prime_finder::next_fermat ()
{
  bigint t1, t2;
  for (;;) {
    next_weak ();
    if (!tmp || fermat2_test (tmp, &t1, &t2))
      return tmp;
  }
}

bigint &
prime_finder::next_strong (u_int iter)
{
  bigint t1, t2;
  for (;;) {
    next_weak ();
    if (!tmp || (fermat2_test (tmp, &t1, &t2) && tmp.probab_prime (iter)))
      return tmp;
  }
}

bigint
prime_search (const bigint &start, u_int range, const u_int *sieve,
	      const u_int sievesize, u_int iter)
{
  bigint t1, t2;
  vec<bigint> pvec;
  prime_finder pf (start, sieve, sievesize);
  pf.setmax (range);
  bigint *pp;
  while (mpz_sgn (pp = &pf.next_weak ()))
    pvec.push_back (*pp);
  while (!pvec.empty ()) {
    u_int i = rnd.getword () % pvec.size ();
    pp = pvec.base () + i;
    if (fermat2_test (*pp, &t1, &t2) && pp->probab_prime (iter))
      return *pp;
    swap (*pp, pvec.back ());
    pvec.pop_back ();
  }
  return 0;
}

/* If q and 2q+1 are prime, then q is congruent to 11, 23, or 29 mod 30 */
const u_int srpprime_sieve[] = {
  11, 10,  9,  8,  7,  6,  5,  4,  3,  2,
  1, 12, 11, 10,  9,  8,  7,  6,  5,  4,
  3,  2,  1,  6,  5,  4,  3,  2,  1, 12
};

bigint
srpprime_search (const bigint &start, u_int iter)
{
  prime_finder pf (start, srpprime_sieve,
		   sizeof (srpprime_sieve) / sizeof (srpprime_sieve[0]));
  bigint n, t1, t2;
  int mods[prime_finder::nprimes];

  for (;;) {
    n = pf.getp () << 1;
    n.setbit (0, 1);
    for (int i = 0; i < prime_finder::nprimes; i++)
      mods[i] = quickmod (n, small_primes[i]);

    u_int inc = 0;
  nextq:
    while ((int) inc >= 0) {
      const bigint &q = pf.next_weak ();
      u_int inc = pf.getinc () << 1;

      for (int i = 0; i < prime_finder::nprimes; i++)
	if (mods[i] + inc >= small_primes[i]) {
	  mods[i] = (mods[i] + inc) % small_primes[i] - inc;
	  if (!(mods[i] + inc))
	    goto nextq;
	}

      if (!fermat2_test (q, &t1, &t2))
	continue;
      n = q << 1;
      n.setbit (0, 1);
      /* Note by the logic of srpprime_test, we don't need to check
       * n.probab_prime (iter). */
      if (fermat2_test (n, &t1, &t2) && q.probab_prime (iter))
	return n;
    }

    pf.calcmods ();
  }
}

bigint
random_bigint (size_t bits)
{
  if (!bits)
    return 0;
  zcbuf buf (bits + 7 >> 3);
  rnd.getbytes (buf, buf.size);
  bigint ret;
  buf[0] &= 0xff >> (-bits & 7);
  mpz_set_rawmag_be (&ret, buf, buf.size);
  ret.setbit (bits - 1, true);
  if (ret.nbits () != bits)
    panic ("|ret| = %d, bits = %d\n", (int) ret.nbits (), (int) bits);
  return ret;
}

bigint
random_zn (const bigint &n)
{
  assert (sgn (n) > 0);
  const int bits = mpz_sizeinbase2 (&n);
  zcbuf buf (bits + 7 >> 3);
  bigint ret;

  do {
    rnd.getbytes (buf, buf.size);
    buf[0] &= 0xff >> (-bits & 7);
    mpz_set_rawmag_be (&ret, buf, buf.size);
  } while (ret >= n);

  return ret;
}

/* Miller-Rabin primality test.  Similar to mpz_probab_prime, but this
 * uses a strong random number generator and hence can be used when an
 * untrusted party has supplied the prime to be tested.  */
bool
prime_test (const bigint &n, u_int iter)
{
  if (n <= 7) {
    if (sgn (n) <= 0)
      return false;
    u_int in = n.getui ();
    return in != 1 && in != 4 && in != 6;
  }
  if (!n.getbit (0))
    return false;

  bigint n1 = n - 1;
  u_int s = mpz_scan1 (&n1, 0);
  bigint r = n1 >> s;
  u_int nlimbs = n._mp_size;
  mp_limb_t mask = ((mp_limb_t) -1
		    >> (-mpz_sizeinbase2 (&n) & 8*GMP_LIMB_SIZE - 1));
  bigint a, y;
  _mpz_realloc (&a, n._mp_alloc);

  while (iter--) {
    do {
      rnd.getbytes (a._mp_d, GMP_LIMB_SIZE * (a._mp_size = nlimbs));
      a._mp_d[nlimbs-1] &= mask;
    } while (a >= n - 1 || a <= 1);
    y = powm (a, r, n);
    if (y != 1)
      for (u_int j = s - 1; y != n1; j--) {
	if (!j)
	  return false;
	mpz_square (&a, &y);
	mpz_mod (&y, &a, &n);
	if (y == 1)
	  return false;
      }
  }

  return true;
}

/*
 * This test verifies SRP primes (using a trivial instantiation of
 * Pocklington's algorithm).  An SRP prime n is valid if both n and
 * (n-1)/2 are prime.
 *
 * Suppose q is a prime, and n = 2 * q + 1.
 *
 * If 3 divides n or 2^{n-1} != 1 mod n, then we know n is composite.
 *
 * Otherwise, suppose some prime p > 3 non-trivially divides n.
 *
 *    p <= q, so GCD(p - 1, q) = 1
 *    some u consequently satisfies q * u = 1 mod p - 1.
 * 
 *    4 = 2^2
 *    4 = 2^{(n-1)/q}
 *    4 = 2^{uq(n-1)/q} mod p
 *    4 = (2^{(n-1)})^u mod p
 * 
 *    Recall we are assuming 2^{n-1} = 1 mod n.
 *    Since p divides n, 2^{n-1} = 1 mod p
 *    (2^{(n-1)})^u = 1^u = 1 mod p
 *
 *    Combining the two results, 4 = 1 mod p.
 *    We assumed p > 3, so p >= 5 and we have a contradiction.
 *
 * It must therefore follow that no such p divides n, and n is prime.
 */
bool
srpprime_test (const bigint &n, u_int iter)
{
  if (!n.getbit (0) || (n._mp_size <= 1 && n < 5))
    return false;
  if (!quickmod (n, 3) || !fermat2_test (n))
    return false;

  bigint q = n >> 1;
  for (int i = 0; i < num_small_primes; i++)
    if (!quickmod (q, small_primes[i]))
      return false;
  return prime_test (q, iter);
}