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