| /** |
| * RSA Key Generation Worker. |
| * |
| * @author Dave Longley |
| * |
| * Copyright (c) 2013 Digital Bazaar, Inc. |
| */ |
| importScripts('jsbn.js'); |
| |
| // 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; |
| } |