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