1 | var randomBytes = require('randombytes');
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2 | module.exports = findPrime;
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3 | findPrime.simpleSieve = simpleSieve;
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4 | findPrime.fermatTest = fermatTest;
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5 | var BN = require('bn.js');
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6 | var TWENTYFOUR = new BN(24);
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7 | var MillerRabin = require('miller-rabin');
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8 | var millerRabin = new MillerRabin();
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9 | var ONE = new BN(1);
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10 | var TWO = new BN(2);
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11 | var FIVE = new BN(5);
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12 | var SIXTEEN = new BN(16);
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13 | var EIGHT = new BN(8);
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14 | var TEN = new BN(10);
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15 | var THREE = new BN(3);
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16 | var SEVEN = new BN(7);
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17 | var ELEVEN = new BN(11);
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18 | var FOUR = new BN(4);
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19 | var TWELVE = new BN(12);
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20 | var primes = null;
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21 |
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22 | function _getPrimes() {
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23 | if (primes !== null)
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24 | return primes;
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25 |
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26 | var limit = 0x100000;
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27 | var res = [];
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28 | res[0] = 2;
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29 | for (var i = 1, k = 3; k < limit; k += 2) {
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30 | var sqrt = Math.ceil(Math.sqrt(k));
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31 | for (var j = 0; j < i && res[j] <= sqrt; j++)
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32 | if (k % res[j] === 0)
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33 | break;
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34 |
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35 | if (i !== j && res[j] <= sqrt)
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36 | continue;
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37 |
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38 | res[i++] = k;
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39 | }
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40 | primes = res;
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41 | return res;
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42 | }
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43 |
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44 | function simpleSieve(p) {
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45 | var primes = _getPrimes();
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46 |
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47 | for (var i = 0; i < primes.length; i++)
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48 | if (p.modn(primes[i]) === 0) {
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49 | if (p.cmpn(primes[i]) === 0) {
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50 | return true;
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51 | } else {
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52 | return false;
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53 | }
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54 | }
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55 |
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56 | return true;
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57 | }
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58 |
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59 | function fermatTest(p) {
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60 | var red = BN.mont(p);
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61 | return TWO.toRed(red).redPow(p.subn(1)).fromRed().cmpn(1) === 0;
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62 | }
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63 |
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64 | function findPrime(bits, gen) {
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65 | if (bits < 16) {
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66 |
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67 | if (gen === 2 || gen === 5) {
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68 | return new BN([0x8c, 0x7b]);
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69 | } else {
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70 | return new BN([0x8c, 0x27]);
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71 | }
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72 | }
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73 | gen = new BN(gen);
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74 |
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75 | var num, n2;
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76 |
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77 | while (true) {
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78 | num = new BN(randomBytes(Math.ceil(bits / 8)));
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79 | while (num.bitLength() > bits) {
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80 | num.ishrn(1);
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81 | }
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82 | if (num.isEven()) {
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83 | num.iadd(ONE);
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84 | }
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85 | if (!num.testn(1)) {
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86 | num.iadd(TWO);
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87 | }
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88 | if (!gen.cmp(TWO)) {
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89 | while (num.mod(TWENTYFOUR).cmp(ELEVEN)) {
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90 | num.iadd(FOUR);
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91 | }
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92 | } else if (!gen.cmp(FIVE)) {
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93 | while (num.mod(TEN).cmp(THREE)) {
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94 | num.iadd(FOUR);
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95 | }
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96 | }
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97 | n2 = num.shrn(1);
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98 | if (simpleSieve(n2) && simpleSieve(num) &&
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99 | fermatTest(n2) && fermatTest(num) &&
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100 | millerRabin.test(n2) && millerRabin.test(num)) {
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101 | return num;
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102 | }
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103 | }
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104 |
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105 | }
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