627 lines
32 KiB
JavaScript
627 lines
32 KiB
JavaScript
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import { bitLength, eGcd, modInv, modPow, toZn } from 'bigint-mod-arith';
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export { abs, bitLength, eGcd, gcd, lcm, max, min, modInv, modPow, toZn } from 'bigint-mod-arith';
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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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/**
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* Secure random bytes for both node and browsers. Node version uses crypto.randomBytes() and browser one self.crypto.getRandomValues()
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*
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* @param byteLength - The desired number of random bytes
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* @param forceLength - 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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* @throws {RangeError}
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* byteLength MUST be > 0
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*
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* @returns A promise that resolves to a UInt8Array/Buffer (Browser/Node.js) 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)
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throw new RangeError('byteLength MUST be > 0');
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return new Promise(function (resolve, reject) {
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{ // browser
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const buf = new Uint8Array(byteLength);
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self.crypto.getRandomValues(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)
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buf[0] = buf[0] | 128;
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resolve(buf);
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}
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});
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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 byteLength - The desired number of random bytes
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* @param forceLength - 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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* @throws {RangeError}
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* byteLength MUST be > 0
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*
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* @returns A UInt8Array/Buffer (Browser/Node.js) 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)
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throw new RangeError('byteLength MUST be > 0');
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/* eslint-disable no-lone-blocks */
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{ // browser
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const buf = new Uint8Array(byteLength);
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self.crypto.getRandomValues(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)
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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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/**
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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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* @param bitLength - The desired number of random bits
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* @param forceLength - 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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* @throws {RangeError}
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* bitLength MUST be > 0
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*
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* @returns A Promise that resolves to a UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bits
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*/
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function randBits(bitLength, forceLength = false) {
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if (bitLength < 1)
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throw new RangeError('bitLength MUST be > 0');
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const byteLength = Math.ceil(bitLength / 8);
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const bitLengthMod8 = bitLength % 8;
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return new Promise((resolve, reject) => {
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randBytes(byteLength, false).then(function (rndBytes) {
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if (bitLengthMod8 !== 0) {
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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 !== 0) ? 2 ** (bitLengthMod8 - 1) : 128;
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rndBytes[0] = rndBytes[0] | mask;
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}
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resolve(rndBytes);
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});
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});
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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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* @param bitLength - The desired number of random bits
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* @param forceLength - 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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* @throws {RangeError}
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* bitLength MUST be > 0
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*
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* @returns A Uint8Array/Buffer (Browser/Node.js) 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');
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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 !== 0) {
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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 !== 0) ? 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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* Returns a cryptographically secure random integer between [min,max]. Both numbers must be >=0
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* @param max Returned value will be <= max
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* @param min Returned value will be >= min
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*
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* @throws {RangeError}
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* Arguments MUST be: max > 0 && min >=0 && max > min
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*
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* @returns 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 <= 0n || min < 0n || max <= min)
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throw new RangeError('Arguments MUST be: max > 0 && min >=0 && max > min');
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const interval = max - min;
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const bitLen = 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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function _workerUrl(workerCode) {
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workerCode = `(() => {${workerCode}})()`; // encapsulate IIFE
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const _blob = new Blob([workerCode], { type: 'text/javascript' });
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return window.URL.createObjectURL(_blob);
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}
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let _useWorkers = false; // The following is just to check whether we can use workers
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/* eslint-disable no-lone-blocks */
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{ // Native JS
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if (self.Worker !== undefined)
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_useWorkers = true;
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}
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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 w - A positive integer to be tested for primality
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* @param iterations - 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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* @param disableWorkers - Disable the use of workers for the primality test
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*
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* @throws {RangeError}
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* w MUST be >= 0
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*
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* @returns 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, disableWorkers = false) {
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if (typeof w === 'number') {
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w = BigInt(w);
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}
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if (w < 0n)
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throw RangeError('w MUST be >= 0');
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{ // browser
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return new Promise((resolve, reject) => {
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const worker = new Worker(_isProbablyPrimeWorkerUrl());
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worker.onmessage = (event) => {
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worker.terminate();
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resolve(event.data.isPrime);
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};
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worker.onmessageerror = (event) => {
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reject(event);
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};
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const msg = {
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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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worker.postMessage(msg);
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});
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}
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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)
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return true;
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else if ((w & 1n) === 0n || w === 1n)
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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,
|
|||
|
|
1061n,
|
|||
|
|
1063n,
|
|||
|
|
1069n,
|
|||
|
|
1087n,
|
|||
|
|
1091n,
|
|||
|
|
1093n,
|
|||
|
|
1097n,
|
|||
|
|
1103n,
|
|||
|
|
1109n,
|
|||
|
|
1117n,
|
|||
|
|
1123n,
|
|||
|
|
1129n,
|
|||
|
|
1151n,
|
|||
|
|
1153n,
|
|||
|
|
1163n,
|
|||
|
|
1171n,
|
|||
|
|
1181n,
|
|||
|
|
1187n,
|
|||
|
|
1193n,
|
|||
|
|
1201n,
|
|||
|
|
1213n,
|
|||
|
|
1217n,
|
|||
|
|
1223n,
|
|||
|
|
1229n,
|
|||
|
|
1231n,
|
|||
|
|
1237n,
|
|||
|
|
1249n,
|
|||
|
|
1259n,
|
|||
|
|
1277n,
|
|||
|
|
1279n,
|
|||
|
|
1283n,
|
|||
|
|
1289n,
|
|||
|
|
1291n,
|
|||
|
|
1297n,
|
|||
|
|
1301n,
|
|||
|
|
1303n,
|
|||
|
|
1307n,
|
|||
|
|
1319n,
|
|||
|
|
1321n,
|
|||
|
|
1327n,
|
|||
|
|
1361n,
|
|||
|
|
1367n,
|
|||
|
|
1373n,
|
|||
|
|
1381n,
|
|||
|
|
1399n,
|
|||
|
|
1409n,
|
|||
|
|
1423n,
|
|||
|
|
1427n,
|
|||
|
|
1429n,
|
|||
|
|
1433n,
|
|||
|
|
1439n,
|
|||
|
|
1447n,
|
|||
|
|
1451n,
|
|||
|
|
1453n,
|
|||
|
|
1459n,
|
|||
|
|
1471n,
|
|||
|
|
1481n,
|
|||
|
|
1483n,
|
|||
|
|
1487n,
|
|||
|
|
1489n,
|
|||
|
|
1493n,
|
|||
|
|
1499n,
|
|||
|
|
1511n,
|
|||
|
|
1523n,
|
|||
|
|
1531n,
|
|||
|
|
1543n,
|
|||
|
|
1549n,
|
|||
|
|
1553n,
|
|||
|
|
1559n,
|
|||
|
|
1567n,
|
|||
|
|
1571n,
|
|||
|
|
1579n,
|
|||
|
|
1583n,
|
|||
|
|
1597n
|
|||
|
|
];
|
|||
|
|
for (let i = 0; i < firstPrimes.length && (firstPrimes[i] <= w); i++) {
|
|||
|
|
const p = firstPrimes[i];
|
|||
|
|
if (w === p)
|
|||
|
|
return true;
|
|||
|
|
else if (w % p === 0n)
|
|||
|
|
return false;
|
|||
|
|
}
|
|||
|
|
/*
|
|||
|
|
1. Let a be the largest integer such that 2**a divides w−1.
|
|||
|
|
2. m = (w−1) / 2**a.
|
|||
|
|
3. wlen = len (w).
|
|||
|
|
4. For i = 1 to iterations do
|
|||
|
|
4.1 Obtain a string b of wlen bits from an RBG.
|
|||
|
|
Comment: Ensure that 1 < b < w−1.
|
|||
|
|
4.2 If ((b ≤ 1) or (b ≥ w−1)), then go to step 4.1.
|
|||
|
|
4.3 z = b**m mod w.
|
|||
|
|
4.4 If ((z = 1) or (z = w − 1)), then go to step 4.7.
|
|||
|
|
4.5 For j = 1 to a − 1 do.
|
|||
|
|
4.5.1 z = z**2 mod w.
|
|||
|
|
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);
|
|||
|
|
do {
|
|||
|
|
const b = randBetween(d, 2n);
|
|||
|
|
let z = modPow(b, m, w);
|
|||
|
|
if (z === 1n || z === d)
|
|||
|
|
continue;
|
|||
|
|
let j = 1;
|
|||
|
|
while (j < a) {
|
|||
|
|
z = modPow(z, 2n, w);
|
|||
|
|
if (z === d)
|
|||
|
|
break;
|
|||
|
|
if (z === 1n)
|
|||
|
|
return false;
|
|||
|
|
j++;
|
|||
|
|
}
|
|||
|
|
if (z !== d)
|
|||
|
|
return false;
|
|||
|
|
} while (--iterations !== 0);
|
|||
|
|
return true;
|
|||
|
|
}
|
|||
|
|
function _isProbablyPrimeWorkerUrl() {
|
|||
|
|
// Let's us first add all the required functions
|
|||
|
|
let workerCode = `'use strict';const ${eGcd.name}=${eGcd.toString()};const ${modInv.name}=${modInv.toString()};const ${modPow.name}=${modPow.toString()};const ${toZn.name}=${toZn.toString()};const ${randBitsSync.name}=${randBitsSync.toString()};const ${randBytesSync.name}=${randBytesSync.toString()};const ${randBetween.name}=${randBetween.toString()};const ${isProbablyPrime.name}=${_isProbablyPrime.toString()};${bitLength.toString()};${fromBuffer.toString()};`;
|
|||
|
|
const onmessage = async function (event) {
|
|||
|
|
// event.data = {rnd: <bigint>, iterations: <number>}
|
|||
|
|
const isPrime = await isProbablyPrime(event.data.rnd, event.data.iterations);
|
|||
|
|
const msg = {
|
|||
|
|
isPrime: isPrime,
|
|||
|
|
value: event.data.rnd,
|
|||
|
|
id: event.data.id
|
|||
|
|
};
|
|||
|
|
postMessage(msg);
|
|||
|
|
};
|
|||
|
|
workerCode += `onmessage = ${onmessage.toString()};`;
|
|||
|
|
return _workerUrl(workerCode);
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
/**
|
|||
|
|
* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
|
|||
|
|
* The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI
|
|||
|
|
* main process, and it can be much faster (if several cores or cpu are available).
|
|||
|
|
* The node version can also use worker_threads if they are available (enabled by default with Node 11 and
|
|||
|
|
* and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).
|
|||
|
|
*
|
|||
|
|
* @param bitLength - The required bit length for the generated prime
|
|||
|
|
* @param iterations - The number of iterations for the Miller-Rabin Probabilistic Primality Test
|
|||
|
|
*
|
|||
|
|
* @throws {RangeError}
|
|||
|
|
* bitLength MUST be > 0
|
|||
|
|
*
|
|||
|
|
* @returns A promise that resolves to a bigint probable prime of bitLength bits.
|
|||
|
|
*/
|
|||
|
|
function prime(bitLength, iterations = 16) {
|
|||
|
|
if (bitLength < 1)
|
|||
|
|
throw new RangeError('bitLength MUST be > 0');
|
|||
|
|
/* istanbul ignore if */
|
|||
|
|
if (!_useWorkers) { // If there is no support for workers
|
|||
|
|
let rnd = 0n;
|
|||
|
|
do {
|
|||
|
|
rnd = fromBuffer(randBitsSync(bitLength, true));
|
|||
|
|
} while (!_isProbablyPrime(rnd, iterations));
|
|||
|
|
return new Promise((resolve) => { resolve(rnd); });
|
|||
|
|
}
|
|||
|
|
return new Promise((resolve, reject) => {
|
|||
|
|
const workerList = [];
|
|||
|
|
const _onmessage = (msg, newWorker) => {
|
|||
|
|
if (msg.isPrime) {
|
|||
|
|
// if a prime number has been found, stop all the workers, and return it
|
|||
|
|
for (let j = 0; j < workerList.length; j++) {
|
|||
|
|
workerList[j].terminate();
|
|||
|
|
}
|
|||
|
|
while (workerList.length > 0) {
|
|||
|
|
workerList.pop();
|
|||
|
|
}
|
|||
|
|
resolve(msg.value);
|
|||
|
|
}
|
|||
|
|
else { // if a composite is found, make the worker test another random number
|
|||
|
|
const buf = randBitsSync(bitLength, true);
|
|||
|
|
const rnd = fromBuffer(buf);
|
|||
|
|
try {
|
|||
|
|
const msgToWorker = {
|
|||
|
|
rnd: rnd,
|
|||
|
|
iterations: iterations,
|
|||
|
|
id: msg.id
|
|||
|
|
};
|
|||
|
|
newWorker.postMessage(msgToWorker);
|
|||
|
|
}
|
|||
|
|
catch (error) {
|
|||
|
|
// The worker has already terminated. There is nothing to handle here
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
};
|
|||
|
|
{ // browser
|
|||
|
|
const workerURL = _isProbablyPrimeWorkerUrl();
|
|||
|
|
for (let i = 0; i < self.navigator.hardwareConcurrency - 1; i++) {
|
|||
|
|
const newWorker = new Worker(workerURL);
|
|||
|
|
newWorker.onmessage = (event) => _onmessage(event.data, newWorker);
|
|||
|
|
workerList.push(newWorker);
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
for (let i = 0; i < workerList.length; i++) {
|
|||
|
|
randBits(bitLength, true).then(function (buf) {
|
|||
|
|
const rnd = fromBuffer(buf);
|
|||
|
|
workerList[i].postMessage({
|
|||
|
|
rnd: rnd,
|
|||
|
|
iterations: iterations,
|
|||
|
|
id: i
|
|||
|
|
});
|
|||
|
|
}).catch(reject);
|
|||
|
|
}
|
|||
|
|
});
|
|||
|
|
}
|
|||
|
|
/**
|
|||
|
|
* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
|
|||
|
|
* 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.
|
|||
|
|
*
|
|||
|
|
* @param bitLength - The required bit length for the generated prime
|
|||
|
|
* @param iterations - The number of iterations for the Miller-Rabin Probabilistic Primality Test
|
|||
|
|
*
|
|||
|
|
* @throws {RangeError}
|
|||
|
|
* bitLength MUST be > 0
|
|||
|
|
*
|
|||
|
|
* @returns A bigint probable prime of bitLength bits.
|
|||
|
|
*/
|
|||
|
|
function primeSync(bitLength, iterations = 16) {
|
|||
|
|
if (bitLength < 1)
|
|||
|
|
throw new RangeError('bitLength MUST be > 0');
|
|||
|
|
let rnd = 0n;
|
|||
|
|
do {
|
|||
|
|
rnd = fromBuffer(randBitsSync(bitLength, true));
|
|||
|
|
} while (!_isProbablyPrime(rnd, iterations));
|
|||
|
|
return rnd;
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
export { isProbablyPrime, prime, primeSync, randBetween, randBits, randBitsSync, randBytes, randBytesSync };
|
|||
|
|
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