/**
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* Prime number generation API.
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*
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* @author Dave Longley
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*
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* Copyright (c) 2014 Digital Bazaar, Inc.
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*/
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var forge = require('./forge');
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require('./util');
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require('./jsbn');
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require('./random');
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(function() {
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// forge.prime already defined
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if(forge.prime) {
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module.exports = forge.prime;
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return;
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}
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/* PRIME API */
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var prime = module.exports = forge.prime = forge.prime || {};
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var BigInteger = forge.jsbn.BigInteger;
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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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var THIRTY = new BigInteger(null);
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THIRTY.fromInt(30);
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var op_or = function(x, y) {return x|y;};
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/**
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* Generates a random probable prime with the given number of bits.
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*
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* Alternative algorithms can be specified by name as a string or as an
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* object with custom options like so:
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*
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* {
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* name: 'PRIMEINC',
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* options: {
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* maxBlockTime: <the maximum amount of time to block the main
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* thread before allowing I/O other JS to run>,
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* millerRabinTests: <the number of miller-rabin tests to run>,
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* workerScript: <the worker script URL>,
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* workers: <the number of web workers (if supported) to use,
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* -1 to use estimated cores minus one>.
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* workLoad: the size of the work load, ie: number of possible prime
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* numbers for each web worker to check per work assignment,
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* (default: 100).
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* }
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* }
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*
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* @param bits the number of bits for the prime number.
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* @param options the options to use.
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* [algorithm] the algorithm to use (default: 'PRIMEINC').
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* [prng] a custom crypto-secure pseudo-random number generator to use,
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* that must define "getBytesSync".
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*
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* @return callback(err, num) called once the operation completes.
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*/
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prime.generateProbablePrime = function(bits, options, callback) {
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if(typeof options === 'function') {
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callback = options;
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options = {};
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}
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options = options || {};
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// default to PRIMEINC algorithm
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var algorithm = options.algorithm || 'PRIMEINC';
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if(typeof algorithm === 'string') {
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algorithm = {name: algorithm};
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}
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algorithm.options = algorithm.options || {};
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// create prng with api that matches BigInteger secure random
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var prng = options.prng || forge.random;
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var rng = {
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// x is an array to fill with bytes
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nextBytes: function(x) {
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var b = prng.getBytesSync(x.length);
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for(var i = 0; i < x.length; ++i) {
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x[i] = b.charCodeAt(i);
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}
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}
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};
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if(algorithm.name === 'PRIMEINC') {
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return primeincFindPrime(bits, rng, algorithm.options, callback);
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}
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throw new Error('Invalid prime generation algorithm: ' + algorithm.name);
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};
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function primeincFindPrime(bits, rng, options, callback) {
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if('workers' in options) {
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return primeincFindPrimeWithWorkers(bits, rng, options, callback);
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}
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return primeincFindPrimeWithoutWorkers(bits, rng, options, callback);
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}
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function primeincFindPrimeWithoutWorkers(bits, rng, options, callback) {
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// initialize random number
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var num = generateRandom(bits, rng);
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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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// get required number of MR tests
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var mrTests = getMillerRabinTests(num.bitLength());
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if('millerRabinTests' in options) {
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mrTests = options.millerRabinTests;
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}
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// find prime nearest to 'num' for maxBlockTime ms
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// 10 ms gives 5ms of leeway for other calculations before dropping
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// below 60fps (1000/60 == 16.67), but in reality, the number will
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// likely be higher due to an 'atomic' big int modPow
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var maxBlockTime = 10;
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if('maxBlockTime' in options) {
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maxBlockTime = options.maxBlockTime;
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}
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_primeinc(num, bits, rng, deltaIdx, mrTests, maxBlockTime, callback);
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}
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function _primeinc(num, bits, rng, deltaIdx, mrTests, maxBlockTime, callback) {
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var start = +new Date();
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do {
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// overflow, regenerate random number
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if(num.bitLength() > bits) {
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num = generateRandom(bits, rng);
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}
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// do primality test
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if(num.isProbablePrime(mrTests)) {
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return callback(null, num);
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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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} while(maxBlockTime < 0 || (+new Date() - start < maxBlockTime));
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// keep trying later
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forge.util.setImmediate(function() {
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_primeinc(num, bits, rng, deltaIdx, mrTests, maxBlockTime, callback);
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});
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}
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// NOTE: This algorithm is indeterminate in nature because workers
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// run in parallel looking at different segments of numbers. Even if this
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// algorithm is run twice with the same input from a predictable RNG, it
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// may produce different outputs.
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function primeincFindPrimeWithWorkers(bits, rng, options, callback) {
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// web workers unavailable
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if(typeof Worker === 'undefined') {
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return primeincFindPrimeWithoutWorkers(bits, rng, options, callback);
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}
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// initialize random number
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var num = generateRandom(bits, rng);
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// use web workers to generate keys
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var numWorkers = options.workers;
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var workLoad = options.workLoad || 100;
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var range = workLoad * 30 / 8;
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var workerScript = options.workerScript || 'forge/prime.worker.js';
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if(numWorkers === -1) {
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return forge.util.estimateCores(function(err, cores) {
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if(err) {
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// default to 2
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cores = 2;
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}
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numWorkers = cores - 1;
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generate();
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});
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}
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generate();
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function generate() {
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// require at least 1 worker
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numWorkers = Math.max(1, numWorkers);
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// TODO: consider optimizing by starting workers outside getPrime() ...
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// note that in order to clean up they will have to be made internally
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// asynchronous which may actually be slower
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// start workers immediately
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var workers = [];
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for(var i = 0; i < numWorkers; ++i) {
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// FIXME: fix path or use blob URLs
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workers[i] = new Worker(workerScript);
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}
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var running = numWorkers;
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// listen for requests from workers and assign ranges to find prime
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for(var i = 0; i < numWorkers; ++i) {
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workers[i].addEventListener('message', workerMessage);
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}
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/* Note: The distribution of random numbers is unknown. Therefore, each
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web worker is continuously allocated a range of numbers to check for a
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random number until one is found.
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Every 30 numbers will be checked just 8 times, because prime numbers
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have the form:
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30k+i, for i < 30 and gcd(30, i)=1 (there are 8 values of i for this)
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Therefore, if we want a web worker to run N checks before asking for
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a new range of numbers, each range must contain N*30/8 numbers.
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For 100 checks (workLoad), this is a range of 375. */
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var found = false;
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function workerMessage(e) {
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// ignore message, prime already found
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if(found) {
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return;
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}
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--running;
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var data = e.data;
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if(data.found) {
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// terminate all workers
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for(var i = 0; i < workers.length; ++i) {
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workers[i].terminate();
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}
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found = true;
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return callback(null, new BigInteger(data.prime, 16));
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}
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// overflow, regenerate random number
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if(num.bitLength() > bits) {
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num = generateRandom(bits, rng);
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}
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// assign new range to check
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var hex = num.toString(16);
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// start prime search
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e.target.postMessage({
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hex: hex,
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workLoad: workLoad
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});
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num.dAddOffset(range, 0);
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}
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}
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}
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/**
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* Generates a random number using the given number of bits and RNG.
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*
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* @param bits the number of bits for the number.
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* @param rng the random number generator to use.
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*
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* @return the random number.
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*/
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function generateRandom(bits, rng) {
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var num = new BigInteger(bits, rng);
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// force MSB set
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var bits1 = bits - 1;
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if(!num.testBit(bits1)) {
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num.bitwiseTo(BigInteger.ONE.shiftLeft(bits1), op_or, num);
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}
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// align number on 30k+1 boundary
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num.dAddOffset(31 - num.mod(THIRTY).byteValue(), 0);
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return num;
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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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})();
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