Merge pull request #662 from KAYLukas/feat/rand-prime-perf
randomProbablePrime: Don't consider multiples of 3 and 5
This commit is contained in:
Sanjana Rajan
GitHub
commit
dd4c05ae84
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@ -27,7 +27,7 @@ import BN from 'bn.js';
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import random from '../random';
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export default {
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randomProbablePrime, isProbablePrime, fermat, millerRabin
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randomProbablePrime, isProbablePrime, fermat, millerRabin, divisionTest
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};
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/**
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@ -39,20 +39,27 @@ export default {
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*/
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async function randomProbablePrime(bits, e, k) {
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const min = new BN(1).shln(bits - 1);
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const thirty = new BN(30);
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/*
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* We can avoid any multiples of 3 and 5 by looking at n mod 30
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* n mod 30 = 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29
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* the next possible prime is mod 30:
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* 1 7 7 7 7 7 7 11 11 11 11 13 13 17 17 17 17 19 19 23 23 23 23 29 29 29 29 29 29 1
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*/
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const adds = [1, 6, 5, 4, 3, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 2, 1, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 2];
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let n = await random.getRandomBN(min, min.shln(1));
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if (n.isEven()) {
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n.iaddn(1); // force odd
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}
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let i = n.mod(thirty).toNumber();
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// eslint-disable-next-line no-await-in-loop
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while (!await isProbablePrime(n, e, k)) {
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n.iaddn(2);
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// If reached the maximum, go back to the minimum.
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if (n.bitLength() > bits) {
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n = n.mod(min.shln(1)).iadd(min);
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}
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}
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do {
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n.iaddn(adds[i]);
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i = (i + adds[i]) % adds.length;
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// If reached the maximum, go back to the minimum.
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if (n.bitLength() > bits) {
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n = n.mod(min.shln(1)).iadd(min);
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}
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// eslint-disable-next-line no-await-in-loop
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} while (!await isProbablePrime(n, e, k));
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return n;
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}
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@ -67,10 +74,10 @@ async function isProbablePrime(n, e, k) {
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if (e && !n.subn(1).gcd(e).eqn(1)) {
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return false;
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}
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if (!fermat(n)) {
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if (!divisionTest(n)) {
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return false;
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}
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if (!await millerRabin(n, k, () => new BN(lowprimes[Math.random() * lowprimes.length | 0]))) {
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if (!fermat(n)) {
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return false;
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}
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if (!await millerRabin(n, k)) {
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@ -93,16 +100,94 @@ function fermat(n, b) {
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return b.toRed(BN.mont(n)).redPow(n.subn(1)).fromRed().cmpn(1) === 0;
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}
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const lowprimes = [
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2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71,
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73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173,
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179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281,
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283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409,
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419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541,
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547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659,
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661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809,
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811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941,
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947, 953, 967, 971, 977, 983, 991, 997];
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function divisionTest(n) {
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return small_primes.every(m => {
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return n.modn(m) !== 0;
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});
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}
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// https://github.com/gpg/libgcrypt/blob/master/cipher/primegen.c
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const small_primes = [
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7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43,
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47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101,
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103, 107, 109, 113, 127, 131, 137, 139, 149, 151,
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157, 163, 167, 173, 179, 181, 191, 193, 197, 199,
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211, 223, 227, 229, 233, 239, 241, 251, 257, 263,
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269, 271, 277, 281, 283, 293, 307, 311, 313, 317,
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331, 337, 347, 349, 353, 359, 367, 373, 379, 383,
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389, 397, 401, 409, 419, 421, 431, 433, 439, 443,
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449, 457, 461, 463, 467, 479, 487, 491, 499, 503,
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509, 521, 523, 541, 547, 557, 563, 569, 571, 577,
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587, 593, 599, 601, 607, 613, 617, 619, 631, 641,
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643, 647, 653, 659, 661, 673, 677, 683, 691, 701,
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709, 719, 727, 733, 739, 743, 751, 757, 761, 769,
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773, 787, 797, 809, 811, 821, 823, 827, 829, 839,
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853, 857, 859, 863, 877, 881, 883, 887, 907, 911,
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919, 929, 937, 941, 947, 953, 967, 971, 977, 983,
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991, 997, 1009, 1013, 1019, 1021, 1031, 1033,
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1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
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1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
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1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
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1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277,
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1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307,
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1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
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1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
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1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
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1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
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1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
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1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
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1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
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1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
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1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871,
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1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
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1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
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1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
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2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111,
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2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161,
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2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243,
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2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
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2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
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2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
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2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473,
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2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551,
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2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633,
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2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
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2689, 2693, 2699, 2707, 2711, 2713, 2719, 2729,
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2731, 2741, 2749, 2753, 2767, 2777, 2789, 2791,
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2797, 2801, 2803, 2819, 2833, 2837, 2843, 2851,
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2857, 2861, 2879, 2887, 2897, 2903, 2909, 2917,
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2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999,
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3001, 3011, 3019, 3023, 3037, 3041, 3049, 3061,
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3067, 3079, 3083, 3089, 3109, 3119, 3121, 3137,
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3163, 3167, 3169, 3181, 3187, 3191, 3203, 3209,
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3217, 3221, 3229, 3251, 3253, 3257, 3259, 3271,
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3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331,
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3343, 3347, 3359, 3361, 3371, 3373, 3389, 3391,
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3407, 3413, 3433, 3449, 3457, 3461, 3463, 3467,
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3469, 3491, 3499, 3511, 3517, 3527, 3529, 3533,
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3539, 3541, 3547, 3557, 3559, 3571, 3581, 3583,
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3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643,
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3659, 3671, 3673, 3677, 3691, 3697, 3701, 3709,
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3719, 3727, 3733, 3739, 3761, 3767, 3769, 3779,
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3793, 3797, 3803, 3821, 3823, 3833, 3847, 3851,
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3853, 3863, 3877, 3881, 3889, 3907, 3911, 3917,
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3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989,
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4001, 4003, 4007, 4013, 4019, 4021, 4027, 4049,
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4051, 4057, 4073, 4079, 4091, 4093, 4099, 4111,
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4127, 4129, 4133, 4139, 4153, 4157, 4159, 4177,
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4201, 4211, 4217, 4219, 4229, 4231, 4241, 4243,
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4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297,
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4327, 4337, 4339, 4349, 4357, 4363, 4373, 4391,
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4397, 4409, 4421, 4423, 4441, 4447, 4451, 4457,
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4463, 4481, 4483, 4493, 4507, 4513, 4517, 4519,
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4523, 4547, 4549, 4561, 4567, 4583, 4591, 4597,
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4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657,
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4663, 4673, 4679, 4691, 4703, 4721, 4723, 4729,
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4733, 4751, 4759, 4783, 4787, 4789, 4793, 4799,
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4801, 4813, 4817, 4831, 4861, 4871, 4877, 4889,
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4903, 4909, 4919, 4931, 4933, 4937, 4943, 4951,
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4957, 4967, 4969, 4973, 4987, 4993, 4999
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];
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// Miller-Rabin - Miller Rabin algorithm for primality test
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@ -131,6 +216,9 @@ const lowprimes = [
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// Adapted on Jan 2018 from version 4.0.1 at https://github.com/indutny/miller-rabin
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// Sample syntax for Fixed-Base Miller-Rabin:
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// millerRabin(n, k, () => new BN(small_primes[Math.random() * small_primes.length | 0]))
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/**
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* Tests whether n is probably prime or not using the Miller-Rabin test.
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* See HAC Remark 4.28.
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@ -144,8 +232,9 @@ async function millerRabin(n, k, rand) {
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const red = BN.mont(n);
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const rone = new BN(1).toRed(red);
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if (!k)
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if (!k) {
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k = Math.max(1, (len / 48) | 0);
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}
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const n1 = n.subn(1);
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const rn1 = n1.toRed(red);
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@ -157,25 +246,29 @@ async function millerRabin(n, k, rand) {
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for (; k > 0; k--) {
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// eslint-disable-next-line no-await-in-loop
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let a = rand ? rand() : await random.getRandomBN(new BN(2), n1);
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const a = rand ? rand() : await random.getRandomBN(new BN(2), n1);
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let x = a.toRed(red).redPow(d);
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if (x.eq(rone) || x.eq(rn1))
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if (x.eq(rone) || x.eq(rn1)) {
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continue;
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}
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let i;
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for (i = 1; i < s; i++) {
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x = x.redSqr();
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if (x.eq(rone))
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if (x.eq(rone)) {
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return false;
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if (x.eq(rn1))
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}
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if (x.eq(rn1)) {
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break;
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}
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}
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if (i === s)
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if (i === s) {
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return false;
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}
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}
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return true;
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};
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}
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