/**
* RSA Key Generation Worker.
*
* @author Dave Longley
*
* Copyright (c) 2013 Digital Bazaar, Inc.
*/
// worker is built using CommonJS syntax to include all code in one worker file
//importScripts('jsbn.js');
var forge = require('./forge');
require('./jsbn');
// prime constants
var LOW_PRIMES = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997];
var LP_LIMIT = (1 << 26) / LOW_PRIMES[LOW_PRIMES.length - 1];
var BigInteger = forge.jsbn.BigInteger;
var BIG_TWO = new BigInteger(null);
BIG_TWO.fromInt(2);
self.addEventListener('message', function(e) {
var result = findPrime(e.data);
self.postMessage(result);
});
// start receiving ranges to check
self.postMessage({found: false});
// primes are 30k+i for i = 1, 7, 11, 13, 17, 19, 23, 29
var GCD_30_DELTA = [6, 4, 2, 4, 2, 4, 6, 2];
function findPrime(data) {
// TODO: abstract based on data.algorithm (PRIMEINC vs. others)
// create BigInteger from given random bytes
var num = new BigInteger(data.hex, 16);
/* Note: All primes are of the form 30k+i for i < 30 and gcd(30, i)=1. The
number we are given is always aligned at 30k + 1. Each time the number is
determined not to be prime we add to get to the next 'i', eg: if the number
was at 30k + 1 we add 6. */
var deltaIdx = 0;
// find nearest prime
var workLoad = data.workLoad;
for(var i = 0; i < workLoad; ++i) {
// do primality test
if(isProbablePrime(num)) {
return {found: true, prime: num.toString(16)};
}
// get next potential prime
num.dAddOffset(GCD_30_DELTA[deltaIdx++ % 8], 0);
}
return {found: false};
}
function isProbablePrime(n) {
// divide by low primes, ignore even checks, etc (n alread aligned properly)
var i = 1;
while(i < LOW_PRIMES.length) {
var m = LOW_PRIMES[i];
var j = i + 1;
while(j < LOW_PRIMES.length && m < LP_LIMIT) {
m *= LOW_PRIMES[j++];
}
m = n.modInt(m);
while(i < j) {
if(m % LOW_PRIMES[i++] === 0) {
return false;
}
}
}
return runMillerRabin(n);
}
// HAC 4.24, Miller-Rabin
function runMillerRabin(n) {
// n1 = n - 1
var n1 = n.subtract(BigInteger.ONE);
// get s and d such that n1 = 2^s * d
var s = n1.getLowestSetBit();
if(s <= 0) {
return false;
}
var d = n1.shiftRight(s);
var k = _getMillerRabinTests(n.bitLength());
var prng = getPrng();
var a;
for(var i = 0; i < k; ++i) {
// select witness 'a' at random from between 1 and n - 1
do {
a = new BigInteger(n.bitLength(), prng);
} while(a.compareTo(BigInteger.ONE) <= 0 || a.compareTo(n1) >= 0);
/* See if 'a' is a composite witness. */
// x = a^d mod n
var x = a.modPow(d, n);
// probably prime
if(x.compareTo(BigInteger.ONE) === 0 || x.compareTo(n1) === 0) {
continue;
}
var j = s;
while(--j) {
// x = x^2 mod a
x = x.modPowInt(2, n);
// 'n' is composite because no previous x == -1 mod n
if(x.compareTo(BigInteger.ONE) === 0) {
return false;
}
// x == -1 mod n, so probably prime
if(x.compareTo(n1) === 0) {
break;
}
}
// 'x' is first_x^(n1/2) and is not +/- 1, so 'n' is not prime
if(j === 0) {
return false;
}
}
return true;
}
// get pseudo random number generator
function getPrng() {
// create prng with api that matches BigInteger secure random
return {
// x is an array to fill with bytes
nextBytes: function(x) {
for(var i = 0; i < x.length; ++i) {
x[i] = Math.floor(Math.random() * 0xFF);
}
}
};
}
/**
* Returns the required number of Miller-Rabin tests to generate a
* prime with an error probability of (1/2)^80.
*
* See Handbook of Applied Cryptography Chapter 4, Table 4.4.
*
* @param bits the bit size.
*
* @return the required number of iterations.
*/
function _getMillerRabinTests(bits) {
if(bits <= 100) return 27;
if(bits <= 150) return 18;
if(bits <= 200) return 15;
if(bits <= 250) return 12;
if(bits <= 300) return 9;
if(bits <= 350) return 8;
if(bits <= 400) return 7;
if(bits <= 500) return 6;
if(bits <= 600) return 5;
if(bits <= 800) return 4;
if(bits <= 1250) return 3;
return 2;
}