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168 lines
4.7 KiB
168 lines
4.7 KiB
/**
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* RSA Key Generation Worker.
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*
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* @author Dave Longley
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*
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* Copyright (c) 2013 Digital Bazaar, Inc.
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*/
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// worker is built using CommonJS syntax to include all code in one worker file
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//importScripts('jsbn.js');
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var forge = require('./forge');
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require('./jsbn');
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// prime constants
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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];
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var LP_LIMIT = (1 << 26) / LOW_PRIMES[LOW_PRIMES.length - 1];
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var BigInteger = forge.jsbn.BigInteger;
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var BIG_TWO = new BigInteger(null);
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BIG_TWO.fromInt(2);
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self.addEventListener('message', function(e) {
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var result = findPrime(e.data);
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self.postMessage(result);
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});
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// start receiving ranges to check
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self.postMessage({found: false});
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// primes are 30k+i for i = 1, 7, 11, 13, 17, 19, 23, 29
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var GCD_30_DELTA = [6, 4, 2, 4, 2, 4, 6, 2];
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function findPrime(data) {
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// TODO: abstract based on data.algorithm (PRIMEINC vs. others)
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// create BigInteger from given random bytes
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var num = new BigInteger(data.hex, 16);
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/* Note: All primes are of the form 30k+i for i < 30 and gcd(30, i)=1. The
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number we are given is always aligned at 30k + 1. Each time the number is
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determined not to be prime we add to get to the next 'i', eg: if the number
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was at 30k + 1 we add 6. */
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var deltaIdx = 0;
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// find nearest prime
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var workLoad = data.workLoad;
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for(var i = 0; i < workLoad; ++i) {
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// do primality test
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if(isProbablePrime(num)) {
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return {found: true, prime: num.toString(16)};
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}
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// get next potential prime
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num.dAddOffset(GCD_30_DELTA[deltaIdx++ % 8], 0);
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}
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return {found: false};
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}
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function isProbablePrime(n) {
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// divide by low primes, ignore even checks, etc (n alread aligned properly)
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var i = 1;
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while(i < LOW_PRIMES.length) {
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var m = LOW_PRIMES[i];
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var j = i + 1;
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while(j < LOW_PRIMES.length && m < LP_LIMIT) {
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m *= LOW_PRIMES[j++];
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}
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m = n.modInt(m);
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while(i < j) {
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if(m % LOW_PRIMES[i++] === 0) {
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return false;
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}
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}
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}
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return runMillerRabin(n);
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}
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// HAC 4.24, Miller-Rabin
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function runMillerRabin(n) {
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// n1 = n - 1
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var n1 = n.subtract(BigInteger.ONE);
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// get s and d such that n1 = 2^s * d
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var s = n1.getLowestSetBit();
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if(s <= 0) {
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return false;
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}
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var d = n1.shiftRight(s);
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var k = _getMillerRabinTests(n.bitLength());
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var prng = getPrng();
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var a;
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for(var i = 0; i < k; ++i) {
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// select witness 'a' at random from between 1 and n - 1
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do {
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a = new BigInteger(n.bitLength(), prng);
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} while(a.compareTo(BigInteger.ONE) <= 0 || a.compareTo(n1) >= 0);
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/* See if 'a' is a composite witness. */
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// x = a^d mod n
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var x = a.modPow(d, n);
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// probably prime
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if(x.compareTo(BigInteger.ONE) === 0 || x.compareTo(n1) === 0) {
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continue;
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}
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var j = s;
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while(--j) {
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// x = x^2 mod a
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x = x.modPowInt(2, n);
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// 'n' is composite because no previous x == -1 mod n
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if(x.compareTo(BigInteger.ONE) === 0) {
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return false;
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}
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// x == -1 mod n, so probably prime
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if(x.compareTo(n1) === 0) {
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break;
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}
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}
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// 'x' is first_x^(n1/2) and is not +/- 1, so 'n' is not prime
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if(j === 0) {
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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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// get pseudo random number generator
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function getPrng() {
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// create prng with api that matches BigInteger secure random
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return {
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// x is an array to fill with bytes
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nextBytes: function(x) {
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for(var i = 0; i < x.length; ++i) {
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x[i] = Math.floor(Math.random() * 0xFF);
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}
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}
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};
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}
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/**
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* Returns the required number of Miller-Rabin tests to generate a
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* prime with an error probability of (1/2)^80.
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*
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* See Handbook of Applied Cryptography Chapter 4, Table 4.4.
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*
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* @param bits the bit size.
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*
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* @return the required number of iterations.
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*/
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function _getMillerRabinTests(bits) {
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if(bits <= 100) return 27;
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if(bits <= 150) return 18;
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if(bits <= 200) return 15;
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if(bits <= 250) return 12;
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if(bits <= 300) return 9;
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if(bits <= 350) return 8;
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if(bits <= 400) return 7;
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if(bits <= 500) return 6;
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if(bits <= 600) return 5;
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if(bits <= 800) return 4;
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if(bits <= 1250) return 3;
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return 2;
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}
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