109 lines
2.2 KiB
JavaScript
109 lines
2.2 KiB
JavaScript
var randomBytes = require("./randombytes.js");
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module.exports = findPrime;
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findPrime.simpleSieve = simpleSieve;
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findPrime.fermatTest = fermatTest;
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var BN = require("./bn.js");
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var TWENTYFOUR = new BN(24);
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var MillerRabin = require("./miller-rabin.js");
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var millerRabin = new MillerRabin();
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var ONE = new BN(1);
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var TWO = new BN(2);
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var FIVE = new BN(5);
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var SIXTEEN = new BN(16);
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var EIGHT = new BN(8);
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var TEN = new BN(10);
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var THREE = new BN(3);
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var SEVEN = new BN(7);
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var ELEVEN = new BN(11);
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var FOUR = new BN(4);
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var TWELVE = new BN(12);
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var primes = null;
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function _getPrimes() {
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if (primes !== null) return primes;
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var limit = 0x100000;
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var res = [];
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res[0] = 2;
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for (var i = 1, k = 3; k < limit; k += 2) {
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var sqrt = Math.ceil(Math.sqrt(k));
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for (var j = 0; j < i && res[j] <= sqrt; j++) if (k % res[j] === 0) break;
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if (i !== j && res[j] <= sqrt) continue;
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res[i++] = k;
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}
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primes = res;
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return res;
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}
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function simpleSieve(p) {
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var primes = _getPrimes();
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for (var i = 0; i < primes.length; i++) if (p.modn(primes[i]) === 0) {
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if (p.cmpn(primes[i]) === 0) {
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return true;
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} else {
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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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function fermatTest(p) {
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var red = BN.mont(p);
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return TWO.toRed(red).redPow(p.subn(1)).fromRed().cmpn(1) === 0;
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}
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function findPrime(bits, gen) {
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if (bits < 16) {
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// this is what openssl does
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if (gen === 2 || gen === 5) {
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return new BN([0x8c, 0x7b]);
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} else {
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return new BN([0x8c, 0x27]);
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}
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}
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gen = new BN(gen);
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var num, n2;
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while (true) {
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num = new BN(randomBytes(Math.ceil(bits / 8)));
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while (num.bitLength() > bits) {
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num.ishrn(1);
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}
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if (num.isEven()) {
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num.iadd(ONE);
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}
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if (!num.testn(1)) {
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num.iadd(TWO);
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}
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if (!gen.cmp(TWO)) {
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while (num.mod(TWENTYFOUR).cmp(ELEVEN)) {
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num.iadd(FOUR);
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}
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} else if (!gen.cmp(FIVE)) {
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while (num.mod(TEN).cmp(THREE)) {
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num.iadd(FOUR);
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}
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}
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n2 = num.shrn(1);
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if (simpleSieve(n2) && simpleSieve(num) && fermatTest(n2) && fermatTest(num) && millerRabin.test(n2) && millerRabin.test(num)) {
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return num;
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}
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}
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} |