709 lines
17 KiB
JavaScript
709 lines
17 KiB
JavaScript
'use strict'
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Object.defineProperty(exports, '__esModule', { value: true })
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var bigintModArith = require('bigint-mod-arith')
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/**
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* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
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* iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
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*
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* @param {number | bigint} w An integer to be tested for primality
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* @param {number} [iterations = 16] The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
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*
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* @returns {Promise<boolean>} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
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*/
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function isProbablyPrime (w, iterations = 16) {
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if (typeof w === 'number') {
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w = BigInt(w)
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}
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/* eslint-disable no-lone-blocks */
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{ // Node.js
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if (_useWorkers) {
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const { Worker } = require('worker_threads')
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return new Promise((resolve, reject) => {
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const worker = new Worker(__filename)
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worker.on('message', (data) => {
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worker.terminate()
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resolve(data.isPrime)
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})
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worker.on('error', reject)
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worker.postMessage({
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rnd: w,
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iterations: iterations,
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id: 0
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})
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})
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} else {
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return new Promise((resolve) => {
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resolve(_isProbablyPrime(w, iterations))
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})
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}
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}
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/* eslint-enable no-lone-blocks */
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}
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/**
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* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
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* The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI
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* main process, and it can be much faster (if several cores or cpu are available).
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* The node version can also use worker_threads if they are available (enabled by default with Node 11 and
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* and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).
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*
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* @param {number} bitLength The required bit length for the generated prime
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* @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
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*
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* @returns {Promise<bigint>} A promise that resolves to a bigint probable prime of bitLength bits.
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*/
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function prime (bitLength, iterations = 16) {
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if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
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if (!_useWorkers) {
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let rnd = 0n
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do {
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rnd = fromBuffer(randBitsSync(bitLength, true))
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} while (!_isProbablyPrime(rnd, iterations))
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return new Promise((resolve) => { resolve(rnd) })
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}
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return new Promise((resolve) => {
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const workerList = []
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const _onmessage = (msg, newWorker) => {
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if (msg.isPrime) {
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// if a prime number has been found, stop all the workers, and return it
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for (let j = 0; j < workerList.length; j++) {
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workerList[j].terminate()
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}
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while (workerList.length) {
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workerList.pop()
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}
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resolve(msg.value)
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} else { // if a composite is found, make the worker test another random number
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const buf = randBitsSync(bitLength, true)
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const rnd = fromBuffer(buf)
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try {
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newWorker.postMessage({
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rnd: rnd,
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iterations: iterations,
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id: msg.id
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})
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} catch (error) {
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// The worker has already terminated. There is nothing to handle here
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}
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}
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}
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/* eslint-disable no-lone-blocks */
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{ // Node.js
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const { cpus } = require('os')
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const { Worker } = require('worker_threads')
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for (let i = 0; i < cpus().length - 1; i++) {
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const newWorker = new Worker(__filename)
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newWorker.on('message', (msg) => _onmessage(msg, newWorker))
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workerList.push(newWorker)
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}
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}
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/* eslint-enable no-lone-blocks */
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for (let i = 0; i < workerList.length; i++) {
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const buf = randBitsSync(bitLength, true)
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const rnd = fromBuffer(buf)
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workerList[i].postMessage({
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rnd: rnd,
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iterations: iterations,
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id: i
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})
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}
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})
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}
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/**
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* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
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* The sync version is NOT RECOMMENDED since it won't use workers and thus it'll be slower and may freeze thw window in browser's javascript. Please consider using prime() instead.
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*
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* @param {number} bitLength The required bit length for the generated prime
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* @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
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*
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* @returns {bigint} A bigint probable prime of bitLength bits.
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*/
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function primeSync (bitLength, iterations = 16) {
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if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
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let rnd = 0n
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do {
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rnd = fromBuffer(randBitsSync(bitLength, true))
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} while (!_isProbablyPrime(rnd, iterations))
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return rnd
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}
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/**
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* Returns a cryptographically secure random integer between [min,max]
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* @param {bigint} max Returned value will be <= max
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* @param {bigint} [min = BigInt(1)] Returned value will be >= min
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*
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* @returns {bigint} A cryptographically secure random bigint between [min,max]
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*/
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function randBetween (max, min = 1n) {
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if (max <= min) throw new Error('max must be > min')
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const interval = max - min
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const bitLen = bigintModArith.bitLength(interval)
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let rnd
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do {
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const buf = randBitsSync(bitLen)
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rnd = fromBuffer(buf)
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} while (rnd > interval)
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return rnd + min
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}
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/**
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* Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* Since version 3.0.0 this is an async function and a new randBitsSync function has been added. If you are migrating from version 2 call randBitsSync instead.
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* @since 3.0.0
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* @param {number} bitLength The desired number of random bits
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* @param {boolean} [forceLength = false] If we want to force the output to have a specific bit length. It basically forces the msb to be 1
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*
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* @returns {Promise<Buffer | Uint8Array>} A Promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
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*/
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async function randBits (bitLength, forceLength = false) {
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if (bitLength < 1) {
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throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`)
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}
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const byteLength = Math.ceil(bitLength / 8)
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const bitLengthMod8 = bitLength % 8
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const rndBytes = await randBytes(byteLength, false)
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if (bitLengthMod8) {
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// Fill with 0's the extra bits
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rndBytes[0] = rndBytes[0] & (2 ** bitLengthMod8 - 1)
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}
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if (forceLength) {
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const mask = bitLengthMod8 ? 2 ** (bitLengthMod8 - 1) : 128
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rndBytes[0] = rndBytes[0] | mask
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}
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return rndBytes
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}
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/**
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* Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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* @since 3.0.0
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* @param {number} bitLength The desired number of random bits
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* @param {boolean} [forceLength = false] If we want to force the output to have a specific bit length. It basically forces the msb to be 1
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*
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* @returns {Buffer | Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
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*/
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function randBitsSync (bitLength, forceLength = false) {
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if (bitLength < 1) {
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throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`)
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}
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const byteLength = Math.ceil(bitLength / 8)
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const rndBytes = randBytesSync(byteLength, false)
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const bitLengthMod8 = bitLength % 8
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if (bitLengthMod8) {
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// Fill with 0's the extra bits
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rndBytes[0] = rndBytes[0] & (2 ** bitLengthMod8 - 1)
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}
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if (forceLength) {
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const mask = bitLengthMod8 ? 2 ** (bitLengthMod8 - 1) : 128
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rndBytes[0] = rndBytes[0] | mask
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}
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return rndBytes
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}
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/**
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* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param {number} byteLength The desired number of random bytes
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* @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
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*
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* @returns {Promise<Buffer | Uint8Array>} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
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*/
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function randBytes (byteLength, forceLength = false) {
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if (byteLength < 1) { throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`) }
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/* eslint-disable no-lone-blocks */
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{ // node
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const crypto = require('crypto')
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const buf = Buffer.alloc(byteLength)
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return crypto.randomFill(buf, function (resolve) {
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// If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
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if (forceLength) { buf[0] = buf[0] | 128 }
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resolve(buf)
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})
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}
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/* eslint-enable no-lone-blocks */
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}
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/**
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* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param {number} byteLength The desired number of random bytes
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* @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
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*
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* @returns {Buffer | Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
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*/
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function randBytesSync (byteLength, forceLength = false) {
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if (byteLength < 1) { throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`) }
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/* eslint-disable no-lone-blocks */
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{ // node
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const crypto = require('crypto')
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const buf = Buffer.alloc(byteLength)
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crypto.randomFillSync(buf)
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// If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
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if (forceLength) { buf[0] = buf[0] | 128 }
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return buf
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}
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/* eslint-enable no-lone-blocks */
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}
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/* HELPER FUNCTIONS */
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function fromBuffer (buf) {
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let ret = 0n
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for (const i of buf.values()) {
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const bi = BigInt(i)
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ret = (ret << BigInt(8)) + bi
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}
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return ret
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}
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function _isProbablyPrime (w, iterations = 16) {
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/*
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PREFILTERING. Even values but 2 are not primes, so don't test.
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1 is not a prime and the M-R algorithm needs w>1.
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*/
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if (w === 2n) { return true } else if ((w & 1n) === 0n || w === 1n) { return false }
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/*
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Test if any of the first 250 small primes are a factor of w. 2 is not tested because it was already tested above.
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*/
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const firstPrimes = [
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3n,
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5n,
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7n,
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11n,
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13n,
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17n,
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19n,
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23n,
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29n,
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31n,
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37n,
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41n,
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43n,
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47n,
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53n,
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59n,
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61n,
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67n,
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71n,
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73n,
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79n,
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83n,
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89n,
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97n,
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101n,
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103n,
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107n,
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109n,
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113n,
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127n,
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131n,
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137n,
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139n,
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149n,
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151n,
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157n,
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163n,
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167n,
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173n,
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179n,
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181n,
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191n,
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193n,
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197n,
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199n,
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211n,
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223n,
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227n,
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229n,
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233n,
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239n,
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241n,
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251n,
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257n,
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263n,
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269n,
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271n,
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277n,
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281n,
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283n,
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293n,
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307n,
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311n,
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313n,
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317n,
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331n,
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337n,
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347n,
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349n,
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353n,
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359n,
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367n,
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373n,
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379n,
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383n,
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389n,
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397n,
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401n,
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409n,
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419n,
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421n,
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431n,
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433n,
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439n,
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443n,
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449n,
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457n,
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461n,
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463n,
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467n,
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479n,
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487n,
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491n,
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499n,
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503n,
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509n,
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521n,
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523n,
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541n,
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547n,
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557n,
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563n,
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569n,
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571n,
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577n,
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587n,
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593n,
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599n,
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601n,
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607n,
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613n,
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617n,
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619n,
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631n,
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641n,
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643n,
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647n,
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653n,
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659n,
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661n,
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673n,
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677n,
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683n,
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691n,
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701n,
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709n,
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719n,
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727n,
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733n,
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739n,
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743n,
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751n,
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757n,
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761n,
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769n,
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773n,
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787n,
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797n,
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809n,
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811n,
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821n,
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823n,
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827n,
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829n,
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839n,
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853n,
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857n,
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859n,
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863n,
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877n,
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881n,
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883n,
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887n,
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907n,
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911n,
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919n,
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929n,
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937n,
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941n,
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947n,
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953n,
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967n,
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971n,
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977n,
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983n,
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991n,
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997n,
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1009n,
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1013n,
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1019n,
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1021n,
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1031n,
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1033n,
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1039n,
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1049n,
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1051n,
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1061n,
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1063n,
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1069n,
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1087n,
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1091n,
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1093n,
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1097n,
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1103n,
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1109n,
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1117n,
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1123n,
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1129n,
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1151n,
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1153n,
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1163n,
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1171n,
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1181n,
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1187n,
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1193n,
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1201n,
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1213n,
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1217n,
|
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1223n,
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1229n,
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1231n,
|
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1237n,
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1249n,
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1259n,
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1277n,
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1279n,
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1283n,
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1289n,
|
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1291n,
|
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1297n,
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1301n,
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1303n,
|
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1307n,
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1319n,
|
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1321n,
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1327n,
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1361n,
|
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1367n,
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1373n,
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1381n,
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1399n,
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1409n,
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1423n,
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1427n,
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1429n,
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1433n,
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1439n,
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1447n,
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1451n,
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1453n,
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1459n,
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1471n,
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1481n,
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1483n,
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1487n,
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1489n,
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1493n,
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1499n,
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1511n,
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1523n,
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1531n,
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1543n,
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1549n,
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1553n,
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1559n,
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1567n,
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1571n,
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1579n,
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1583n,
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1597n
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]
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for (let i = 0; i < firstPrimes.length && (firstPrimes[i] <= w); i++) {
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const p = firstPrimes[i]
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if (w === p) {
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return true
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} else if (w % p === 0n) {
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return false
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}
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}
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/*
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1. Let a be the largest integer such that 2**a divides w−1.
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2. m = (w−1) / 2**a.
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3. wlen = len (w).
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4. For i = 1 to iterations do
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4.1 Obtain a string b of wlen bits from an RBG.
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Comment: Ensure that 1 < b < w−1.
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4.2 If ((b ≤ 1) or (b ≥ w−1)), then go to step 4.1.
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4.3 z = b**m mod w.
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4.4 If ((z = 1) or (z = w − 1)), then go to step 4.7.
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4.5 For j = 1 to a − 1 do.
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4.5.1 z = z**2 mod w.
|
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4.5.2 If (z = w−1), then go to step 4.7.
|
||
4.5.3 If (z = 1), then go to step 4.6.
|
||
4.6 Return COMPOSITE.
|
||
4.7 Continue.
|
||
Comment: Increment i for the do-loop in step 4.
|
||
5. Return PROBABLY PRIME.
|
||
*/
|
||
let a = 0n
|
||
const d = w - 1n
|
||
let aux = d
|
||
while (aux % 2n === 0n) {
|
||
aux /= 2n
|
||
++a
|
||
}
|
||
|
||
const m = d / (2n ** a)
|
||
|
||
// /* eslint-disable no-labels */
|
||
// loop: do {
|
||
// const b = randBetween(w - 1n, 2n)
|
||
// let z = modPow(b, m, w)
|
||
// if (z === 1n || z === w - 1n) { continue }
|
||
// for (let j = 1; j < a; j++) {
|
||
// z = modPow(z, 2n, w)
|
||
// if (z === w - 1n) { continue loop }
|
||
// if (z === 1n) { break }
|
||
// }
|
||
// return false
|
||
// } while (--iterations)
|
||
// /* eslint-enable no-labels */
|
||
|
||
// return true
|
||
|
||
do {
|
||
const b = randBetween(d, 2n)
|
||
let z = bigintModArith.modPow(b, m, w)
|
||
if (z === 1n || z === d) { continue }
|
||
let j = 1
|
||
while (j < a) {
|
||
z = bigintModArith.modPow(z, 2n, w)
|
||
if (z === d) { break }
|
||
if (z === 1n) { return false }
|
||
j++
|
||
}
|
||
if (z !== d) {
|
||
return false
|
||
}
|
||
} while (--iterations)
|
||
return true
|
||
}
|
||
|
||
let _useWorkers = true // The following is just to check whether Node.js can use workers
|
||
/* eslint-disable no-lone-blocks */
|
||
{ // Node.js
|
||
_useWorkers = (function _workers () {
|
||
try {
|
||
require.resolve('worker_threads')
|
||
return true
|
||
} catch (e) {
|
||
console.log(`[bigint-crypto-utils] WARNING:
|
||
This node version doesn't support worker_threads. You should enable them in order to greatly speedup the generation of big prime numbers.
|
||
· With Node >=11 it is enabled by default (consider upgrading).
|
||
· With Node 10, starting with 10.5.0, you can enable worker_threads at runtime executing node --experimental-worker `)
|
||
return false
|
||
}
|
||
})()
|
||
}
|
||
/* eslint-enable no-lone-blocks */
|
||
|
||
if (_useWorkers) { // node.js with support for workers
|
||
const { parentPort, isMainThread } = require('worker_threads')
|
||
if (!isMainThread) { // worker
|
||
parentPort.on('message', function (data) { // Let's start once we are called
|
||
// data = {rnd: <bigint>, iterations: <number>}
|
||
const isPrime = _isProbablyPrime(data.rnd, data.iterations)
|
||
parentPort.postMessage({
|
||
isPrime: isPrime,
|
||
value: data.rnd,
|
||
id: data.id
|
||
})
|
||
})
|
||
}
|
||
}
|
||
|
||
Object.defineProperty(exports, 'abs', {
|
||
enumerable: true,
|
||
get: function () {
|
||
return bigintModArith.abs
|
||
}
|
||
})
|
||
Object.defineProperty(exports, 'bitLength', {
|
||
enumerable: true,
|
||
get: function () {
|
||
return bigintModArith.bitLength
|
||
}
|
||
})
|
||
Object.defineProperty(exports, 'eGcd', {
|
||
enumerable: true,
|
||
get: function () {
|
||
return bigintModArith.eGcd
|
||
}
|
||
})
|
||
Object.defineProperty(exports, 'gcd', {
|
||
enumerable: true,
|
||
get: function () {
|
||
return bigintModArith.gcd
|
||
}
|
||
})
|
||
Object.defineProperty(exports, 'lcm', {
|
||
enumerable: true,
|
||
get: function () {
|
||
return bigintModArith.lcm
|
||
}
|
||
})
|
||
Object.defineProperty(exports, 'max', {
|
||
enumerable: true,
|
||
get: function () {
|
||
return bigintModArith.max
|
||
}
|
||
})
|
||
Object.defineProperty(exports, 'min', {
|
||
enumerable: true,
|
||
get: function () {
|
||
return bigintModArith.min
|
||
}
|
||
})
|
||
Object.defineProperty(exports, 'modInv', {
|
||
enumerable: true,
|
||
get: function () {
|
||
return bigintModArith.modInv
|
||
}
|
||
})
|
||
Object.defineProperty(exports, 'modPow', {
|
||
enumerable: true,
|
||
get: function () {
|
||
return bigintModArith.modPow
|
||
}
|
||
})
|
||
Object.defineProperty(exports, 'toZn', {
|
||
enumerable: true,
|
||
get: function () {
|
||
return bigintModArith.toZn
|
||
}
|
||
})
|
||
exports.isProbablyPrime = isProbablyPrime
|
||
exports.prime = prime
|
||
exports.primeSync = primeSync
|
||
exports.randBetween = randBetween
|
||
exports.randBits = randBits
|
||
exports.randBitsSync = randBitsSync
|
||
exports.randBytes = randBytes
|
||
exports.randBytesSync = randBytesSync
|