Working!
This commit is contained in:
Juan Hernández Serrano
parent
788bcd219f
commit
066352b391
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@ -1,4 +1,4 @@
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var bigintUtils = (function (exports) {
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var bigintCryptoUtils = (function (exports) {
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'use strict';
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'use strict';
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/**
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/**
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@ -13,64 +13,6 @@ var bigintUtils = (function (exports) {
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return (a >= BigInt(0)) ? a : -a;
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return (a >= BigInt(0)) ? a : -a;
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};
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};
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/**
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* Greatest-common divisor of two integers based on the iterative binary algorithm.
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*
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* @param {number|bigint} a
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* @param {number|bigint} b
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*
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* @returns {bigint} The greatest common divisor of a and b
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*/
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const gcd = function (a, b) {
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a = abs(a);
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b = abs(b);
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let shift = BigInt(0);
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while (!((a | b) & BigInt(1))) {
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a >>= BigInt(1);
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b >>= BigInt(1);
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shift++;
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}
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while (!(a & BigInt(1))) a >>= BigInt(1);
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do {
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while (!(b & BigInt(1))) b >>= BigInt(1);
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if (a > b) {
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let x = a;
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a = b;
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b = x;
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}
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b -= a;
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} while (b);
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// rescale
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return a << shift;
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};
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/**
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* The least common multiple computed as abs(a*b)/gcd(a,b)
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* @param {number|bigint} a
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* @param {number|bigint} b
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*
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* @returns {bigint} The least common multiple of a and b
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*/
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const lcm = function (a, b) {
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a = BigInt(a);
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b = BigInt(b);
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return abs(a * b) / gcd(a, b);
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};
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/**
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* Finds the smallest positive element that is congruent to a in modulo n
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* @param {number|bigint} a An integer
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* @param {number|bigint} n The modulo
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*
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* @returns {bigint} The smallest positive representation of a in modulo n
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*/
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const toZn = function (a, n) {
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n = BigInt(n);
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a = BigInt(a) % n;
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return (a < 0) ? a + n : a;
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};
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/**
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/**
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* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
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* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
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* @property {bigint} g
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* @property {bigint} g
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@ -113,6 +55,77 @@ var bigintUtils = (function (exports) {
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};
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};
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};
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};
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/**
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* Greatest-common divisor of two integers based on the iterative binary algorithm.
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*
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* @param {number|bigint} a
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* @param {number|bigint} b
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*
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* @returns {bigint} The greatest common divisor of a and b
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*/
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const gcd = function (a, b) {
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a = abs(a);
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b = abs(b);
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let shift = BigInt(0);
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while (!((a | b) & BigInt(1))) {
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a >>= BigInt(1);
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b >>= BigInt(1);
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shift++;
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}
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while (!(a & BigInt(1))) a >>= BigInt(1);
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do {
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while (!(b & BigInt(1))) b >>= BigInt(1);
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if (a > b) {
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let x = a;
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a = b;
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b = x;
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}
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b -= a;
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} while (b);
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// rescale
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return a << shift;
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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 iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
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*
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* @param {bigint} w An integer to be tested for primality
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* @param {number} 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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*
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* @return {Promise} A promise that resolve to a boolean that is either true (a probably prime number) or false (definitely composite)
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*/
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const isProbablyPrime = async function (w, iterations = 16) {
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{
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return new Promise(resolve => {
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let worker = _isProbablyPrimeWorker();
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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.postMessage({
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'rnd': w,
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'iterations': iterations
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});
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});
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}
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};
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/**
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* The least common multiple computed as abs(a*b)/gcd(a,b)
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* @param {number|bigint} a
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* @param {number|bigint} b
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*
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* @returns {bigint} The least common multiple of a and b
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*/
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const lcm = function (a, b) {
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a = BigInt(a);
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b = BigInt(b);
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return abs(a * b) / gcd(a, b);
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};
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/**
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/**
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* Modular inverse.
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* Modular inverse.
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*
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*
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@ -162,29 +175,56 @@ var bigintUtils = (function (exports) {
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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. Browser implementation uses WebWorkers in order to not lock the main process
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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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*
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*
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* @param {number} byteLength The desired number of random bytes
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* @param {number} bitLength The required bit length for the generated prime
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* @param {boolean} 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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* @param {number} iterations The number of iterations for the Miller-Rabin Probabilistic Primality Test
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*
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*
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* @returns {Promise} A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes
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* @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits
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*/
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*/
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const randBytes = async function (byteLength, forceLength = false) {
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const prime = async function (bitLength, iterations = 16) {
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return new Promise((resolve) => {
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return new Promise(async (resolve) => {
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let buf;
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{
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let workerList = [];
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for (let i = 0; i < self.navigator.hardwareConcurrency; i++) {
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let newWorker = _isProbablyPrimeWorker();
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newWorker.onmessage = async (event) => {
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if (event.data.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(event.data.value);
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} else { // if a composite is found, make the worker test another random number
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let rnd = BigInt(0);
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rnd = fromBuffer(await randBytes(bitLength / 8, true));
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newWorker.postMessage({
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'rnd': rnd,
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'iterations': iterations
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});
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}
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};
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workerList.push(newWorker);
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}
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for (const worker of workerList) {
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let rnd = BigInt(0);
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rnd = fromBuffer(await randBytes(bitLength / 8, true));
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worker.postMessage({
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'rnd': rnd,
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'iterations': iterations
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});
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}
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{ // browser
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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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};
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};
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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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* 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} max Returned value will be <= max
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};
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};
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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 iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
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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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*
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* @param {bigint} w An integer to be tested for primality
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* @param {number} byteLength The desired number of random bytes
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* @param {number} 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 {boolean} 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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*
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* @return {Promise} A promise that resolve to a boolean that is either true (a probably prime number) or false (definitely composite)
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* @returns {Promise} A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes
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*/
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*/
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const isProbablyPrime = async function (w, iterations = 16) {
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const randBytes = async function (byteLength, forceLength = false) {
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{
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return new Promise((resolve) => {
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return new Promise(resolve => {
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let buf;
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let worker = _isProbablyPrimeWorker();
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worker.onmessage = (event) => {
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{ // browser
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resolve(event.data.isPrime);
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buf = new Uint8Array(byteLength);
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};
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self.crypto.getRandomValues(buf);
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worker.postMessage({
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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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'rnd': w,
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if (forceLength)
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'iterations': iterations
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buf[0] = buf[0] | 128;
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});
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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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};
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};
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/**
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* Finds the smallest positive element that is congruent to a in modulo n
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* @param {number|bigint} a An integer
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* @param {number|bigint} n The modulo
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*
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* @returns {bigint} The smallest positive representation of a in modulo n
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*/
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const toZn = function (a, n) {
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n = BigInt(n);
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a = BigInt(a) % n;
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return (a < 0) ? a + n : a;
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};
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/* HELPER FUNCTIONS */
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function fromBuffer(buf) {
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let ret = BigInt(0);
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for (let i of buf.values()) {
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let 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 bitLength(a) {
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let bits = 1;
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do {
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bits++;
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} while ((a >>= BigInt(1)) > BigInt(1));
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return bits;
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}
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function _isProbablyPrimeWorker() {
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function _isProbablyPrimeWorker() {
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async function _onmessage(event) { // Let's start once we are called
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async function _onmessage(event) { // Let's start once we are called
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// event.data = {rnd: <bigint>, iterations: <number>}
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// event.data = {rnd: <bigint>, iterations: <number>}
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const isPrime = await isProbablyPrime(event.data.rnd, event.data.iterations, false);
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const isPrime = await isProbablyPrime(event.data.rnd, event.data.iterations);
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postMessage({
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postMessage({
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'isPrime': isPrime,
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'isPrime': isPrime,
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'value': event.data.rnd
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'value': event.data.rnd
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});
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});
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}
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}
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let workerCode = `(() => {
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let workerCode = `(() => {'use strict';const eGcd = ${eGcd.toString()};const modInv = ${modInv.toString()};const modPow = ${modPow.toString()};const toZn = ${toZn.toString()};const randBytes = ${randBytes.toString()};const randBetween = ${randBetween.toString()};const isProbablyPrime = ${_isProbablyPrime.toString()};${bitLength.toString()}${fromBuffer.toString()}onmessage = ${_onmessage.toString()};})()`;
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'use strict';
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const eGcd = ${eGcd.toString()};
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const modInv = ${modInv.toString()};
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const modPow = ${modPow.toString()};
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const toZn = ${toZn.toString()};
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const randBytes = ${randBytes.toString()};
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const randBetween = ${randBetween.toString()};
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const isProbablyPrime = ${_isProbablyPrime.toString()};
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${bitLength.toString()}
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${fromBuffer.toString()}
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onmessage = ${_onmessage.toString()};
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})()`;
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var _blob = new Blob([workerCode], { type: 'text/javascript' });
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var _blob = new Blob([workerCode], { type: 'text/javascript' });
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return new Worker(window.URL.createObjectURL(_blob));
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return new Worker(window.URL.createObjectURL(_blob));
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@ -585,77 +646,6 @@ var bigintUtils = (function (exports) {
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return true;
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return true;
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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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*
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* @param {number} bitLength The required bit length for the generated prime
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* @param {number} iterations The number of iterations for the Miller-Rabin Probabilistic Primality Test
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*
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* @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits
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*/
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const prime = async function (bitLength, iterations = 16) {
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return new Promise(async (resolve) => {
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{
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let workerList = [];
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for (let i = 0; i < self.navigator.hardwareConcurrency; i++) {
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let newWorker = _isProbablyPrimeWorker();
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newWorker.onmessage = async (event) => {
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if (event.data.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(event.data.value);
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} else { // if a composite is found, make the worker test another random number
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let rnd = BigInt(0);
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rnd = fromBuffer(await randBytes(bitLength / 8, true));
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newWorker.postMessage({
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'rnd': rnd,
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'iterations': iterations
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});
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}
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};
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workerList.push(newWorker);
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}
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for (const worker of workerList) {
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let rnd = BigInt(0);
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rnd = fromBuffer(await randBytes(bitLength / 8, true));
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worker.postMessage({
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'rnd': rnd,
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'iterations': iterations
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});
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}
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}
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});
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};
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/* HELPER FUNCTIONS */
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function fromBuffer(buf) {
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let ret = BigInt(0);
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for (let i of buf.values()) {
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||||||
let bi = BigInt(i);
|
|
||||||
ret = (ret << BigInt(8)) + bi;
|
|
||||||
}
|
|
||||||
return ret;
|
|
||||||
}
|
|
||||||
|
|
||||||
function bitLength(a) {
|
|
||||||
let bits = 1;
|
|
||||||
do {
|
|
||||||
bits++;
|
|
||||||
} while ((a >>= BigInt(1)) > BigInt(1));
|
|
||||||
return bits;
|
|
||||||
}
|
|
||||||
|
|
||||||
exports.abs = abs;
|
exports.abs = abs;
|
||||||
exports.eGcd = eGcd;
|
exports.eGcd = eGcd;
|
||||||
exports.gcd = gcd;
|
exports.gcd = gcd;
|
||||||
|
|
@ -0,0 +1 @@
|
||||||
|
var bigintCryptoUtils=function(a){'use strict';function b(a){let b=BigInt(0);for(let c of a.values()){let a=BigInt(c);b=(b<<BigInt(8))+a}return b}function c(b){let c=1;do c++;while((b>>=BigInt(1))>BigInt(1));return c}function d(){let a=`(() => {'use strict';const eGcd = ${g.toString()};const modInv = ${j.toString()};const modPow = ${k.toString()};const toZn = ${o.toString()};const randBytes = ${m.toString()};const randBetween = ${l.toString()};const isProbablyPrime = ${e.toString()};${c.toString()}${b.toString()}onmessage = ${async function(a){const b=await i(a.data.rnd,a.data.iterations);postMessage({isPrime:b,value:a.data.rnd})}.toString()};})()`;var d=new Blob([a],{type:"text/javascript"});return new Worker(window.URL.createObjectURL(d))}async function e(c,b=16){if(c===BigInt(2))return!0;if((c&BigInt(1))===BigInt(0)||c===BigInt(1))return!1;const e=[3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597];for(let a=0;a<e.length&&BigInt(e[a])<=c;a++){const b=BigInt(e[a]);if(c===b)return!0;if(c%b===BigInt(0))return!1}let f=BigInt(0),g=c-BigInt(1);for(;g%BigInt(2)===BigInt(0);)g/=BigInt(2),++f;let h=(c-BigInt(1))/BigInt(2)**f;loop:do{let a=await l(c-BigInt(1),2),b=k(a,h,c);if(b===BigInt(1)||b===c-BigInt(1))continue;for(let a=1;a<f;a++){if(b=k(b,BigInt(2),c),b===c-BigInt(1))continue loop;if(b===BigInt(1))break}return!1}while(--b);return!0}const f=function(b){return b=BigInt(b),b>=BigInt(0)?b:-b},g=function(c,d){c=BigInt(c),d=BigInt(d);let e=BigInt(0),f=BigInt(1),g=BigInt(1),h=BigInt(0);for(;c!==BigInt(0);){let a=d/c,b=d%c,i=e-g*a,j=f-h*a;d=c,c=b,e=g,f=h,g=i,h=j}return{b:d,x:e,y:f}},h=function(c,d){c=f(c),d=f(d);let e=BigInt(0);for(;!((c|d)&BigInt(1));)c>>=BigInt(1),d>>=BigInt(1),e++;for(;!(c&BigInt(1));)c>>=BigInt(1);do{for(;!(d&BigInt(1));)d>>=BigInt(1);if(c>d){let a=c;c=d,d=a}d-=c}while(d);return c<<e},i=async function(a,b=16){return new Promise(c=>{let e=d();e.onmessage=a=>{e.terminate(),c(a.data.isPrime)},e.postMessage({rnd:a,iterations:b})})},j=function(b,a){let c=g(b,a);return c.b===BigInt(1)?o(c.x,a):null},k=function(c,d,e){if(e=BigInt(e),c=o(c,e),d=BigInt(d),d<BigInt(0))return j(k(c,f(d),e),e);let g=BigInt(1),h=c;for(;0<d;){var i=d%BigInt(2);d/=BigInt(2),i==BigInt(1)&&(g*=h,g%=e),h*=h,h%=e}return g},l=async function(a,d=1){let e,f=c(a),g=f>>3,h=f-8*g;0<h&&(g++,e=2**h-1);let i;do{let a=await m(g);0<h&&(a[0]&=e),i=b(a)}while(i>a||i<d);return i},m=async function(a,b=!1){return new Promise(c=>{let d;d=new Uint8Array(a),self.crypto.getRandomValues(d),b&&(d[0]|=128),c(d)})},o=function(b,c){return c=BigInt(c),b=BigInt(b)%c,0>b?b+c:b};return a.abs=f,a.eGcd=g,a.gcd=h,a.isProbablyPrime=i,a.lcm=function(c,d){return c=BigInt(c),d=BigInt(d),f(c*d)/h(c,d)},a.modInv=j,a.modPow=k,a.prime=async function(a,c=16){return new Promise(async e=>{{let f=[];for(let g,h=0;h<self.navigator.hardwareConcurrency;h++)g=d(),g.onmessage=async d=>{if(d.data.isPrime){for(let a=0;a<f.length;a++)f[a].terminate();for(;f.length;)f.pop();e(d.data.value)}else{let d=BigInt(0);d=b((await m(a/8,!0))),g.postMessage({rnd:d,iterations:c})}},f.push(g);for(const d of f){let e=BigInt(0);e=b((await m(a/8,!0))),d.postMessage({rnd:e,iterations:c})}}})},a.randBetween=l,a.randBytes=m,a.toZn=o,a}({});
|
||||||
|
|
@ -10,64 +10,6 @@ const abs = function (a) {
|
||||||
return (a >= BigInt(0)) ? a : -a;
|
return (a >= BigInt(0)) ? a : -a;
|
||||||
};
|
};
|
||||||
|
|
||||||
/**
|
|
||||||
* Greatest-common divisor of two integers based on the iterative binary algorithm.
|
|
||||||
*
|
|
||||||
* @param {number|bigint} a
|
|
||||||
* @param {number|bigint} b
|
|
||||||
*
|
|
||||||
* @returns {bigint} The greatest common divisor of a and b
|
|
||||||
*/
|
|
||||||
const gcd = function (a, b) {
|
|
||||||
a = abs(a);
|
|
||||||
b = abs(b);
|
|
||||||
let shift = BigInt(0);
|
|
||||||
while (!((a | b) & BigInt(1))) {
|
|
||||||
a >>= BigInt(1);
|
|
||||||
b >>= BigInt(1);
|
|
||||||
shift++;
|
|
||||||
}
|
|
||||||
while (!(a & BigInt(1))) a >>= BigInt(1);
|
|
||||||
do {
|
|
||||||
while (!(b & BigInt(1))) b >>= BigInt(1);
|
|
||||||
if (a > b) {
|
|
||||||
let x = a;
|
|
||||||
a = b;
|
|
||||||
b = x;
|
|
||||||
}
|
|
||||||
b -= a;
|
|
||||||
} while (b);
|
|
||||||
|
|
||||||
// rescale
|
|
||||||
return a << shift;
|
|
||||||
};
|
|
||||||
|
|
||||||
/**
|
|
||||||
* The least common multiple computed as abs(a*b)/gcd(a,b)
|
|
||||||
* @param {number|bigint} a
|
|
||||||
* @param {number|bigint} b
|
|
||||||
*
|
|
||||||
* @returns {bigint} The least common multiple of a and b
|
|
||||||
*/
|
|
||||||
const lcm = function (a, b) {
|
|
||||||
a = BigInt(a);
|
|
||||||
b = BigInt(b);
|
|
||||||
return abs(a * b) / gcd(a, b);
|
|
||||||
};
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Finds the smallest positive element that is congruent to a in modulo n
|
|
||||||
* @param {number|bigint} a An integer
|
|
||||||
* @param {number|bigint} n The modulo
|
|
||||||
*
|
|
||||||
* @returns {bigint} The smallest positive representation of a in modulo n
|
|
||||||
*/
|
|
||||||
const toZn = function (a, n) {
|
|
||||||
n = BigInt(n);
|
|
||||||
a = BigInt(a) % n;
|
|
||||||
return (a < 0) ? a + n : a;
|
|
||||||
};
|
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
|
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
|
||||||
* @property {bigint} g
|
* @property {bigint} g
|
||||||
|
|
@ -110,6 +52,77 @@ const eGcd = function (a, b) {
|
||||||
};
|
};
|
||||||
};
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Greatest-common divisor of two integers based on the iterative binary algorithm.
|
||||||
|
*
|
||||||
|
* @param {number|bigint} a
|
||||||
|
* @param {number|bigint} b
|
||||||
|
*
|
||||||
|
* @returns {bigint} The greatest common divisor of a and b
|
||||||
|
*/
|
||||||
|
const gcd = function (a, b) {
|
||||||
|
a = abs(a);
|
||||||
|
b = abs(b);
|
||||||
|
let shift = BigInt(0);
|
||||||
|
while (!((a | b) & BigInt(1))) {
|
||||||
|
a >>= BigInt(1);
|
||||||
|
b >>= BigInt(1);
|
||||||
|
shift++;
|
||||||
|
}
|
||||||
|
while (!(a & BigInt(1))) a >>= BigInt(1);
|
||||||
|
do {
|
||||||
|
while (!(b & BigInt(1))) b >>= BigInt(1);
|
||||||
|
if (a > b) {
|
||||||
|
let x = a;
|
||||||
|
a = b;
|
||||||
|
b = x;
|
||||||
|
}
|
||||||
|
b -= a;
|
||||||
|
} while (b);
|
||||||
|
|
||||||
|
// rescale
|
||||||
|
return a << shift;
|
||||||
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
|
||||||
|
*
|
||||||
|
* @param {bigint} w An integer to be tested for primality
|
||||||
|
* @param {number} iterations The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
|
||||||
|
*
|
||||||
|
* @return {Promise} A promise that resolve to a boolean that is either true (a probably prime number) or false (definitely composite)
|
||||||
|
*/
|
||||||
|
const isProbablyPrime = async function (w, iterations = 16) {
|
||||||
|
{
|
||||||
|
return new Promise(resolve => {
|
||||||
|
let worker = _isProbablyPrimeWorker();
|
||||||
|
|
||||||
|
worker.onmessage = (event) => {
|
||||||
|
worker.terminate();
|
||||||
|
resolve(event.data.isPrime);
|
||||||
|
};
|
||||||
|
|
||||||
|
worker.postMessage({
|
||||||
|
'rnd': w,
|
||||||
|
'iterations': iterations
|
||||||
|
});
|
||||||
|
});
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* The least common multiple computed as abs(a*b)/gcd(a,b)
|
||||||
|
* @param {number|bigint} a
|
||||||
|
* @param {number|bigint} b
|
||||||
|
*
|
||||||
|
* @returns {bigint} The least common multiple of a and b
|
||||||
|
*/
|
||||||
|
const lcm = function (a, b) {
|
||||||
|
a = BigInt(a);
|
||||||
|
b = BigInt(b);
|
||||||
|
return abs(a * b) / gcd(a, b);
|
||||||
|
};
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Modular inverse.
|
* Modular inverse.
|
||||||
*
|
*
|
||||||
|
|
@ -159,29 +172,56 @@ const modPow = function (a, b, n) {
|
||||||
};
|
};
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process
|
* 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).
|
||||||
*
|
*
|
||||||
* @param {number} byteLength The desired number of random bytes
|
* @param {number} bitLength The required bit length for the generated prime
|
||||||
* @param {boolean} forceLength If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
|
* @param {number} iterations The number of iterations for the Miller-Rabin Probabilistic Primality Test
|
||||||
*
|
*
|
||||||
* @returns {Promise} A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes
|
* @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits
|
||||||
*/
|
*/
|
||||||
const randBytes = async function (byteLength, forceLength = false) {
|
const prime = async function (bitLength, iterations = 16) {
|
||||||
return new Promise((resolve) => {
|
return new Promise(async (resolve) => {
|
||||||
let buf;
|
{
|
||||||
|
let workerList = [];
|
||||||
|
for (let i = 0; i < self.navigator.hardwareConcurrency; i++) {
|
||||||
|
let newWorker = _isProbablyPrimeWorker();
|
||||||
|
newWorker.onmessage = async (event) => {
|
||||||
|
if (event.data.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) {
|
||||||
|
workerList.pop();
|
||||||
|
}
|
||||||
|
resolve(event.data.value);
|
||||||
|
} else { // if a composite is found, make the worker test another random number
|
||||||
|
let rnd = BigInt(0);
|
||||||
|
rnd = fromBuffer(await randBytes(bitLength / 8, true));
|
||||||
|
newWorker.postMessage({
|
||||||
|
'rnd': rnd,
|
||||||
|
'iterations': iterations
|
||||||
|
});
|
||||||
|
}
|
||||||
|
};
|
||||||
|
workerList.push(newWorker);
|
||||||
|
}
|
||||||
|
|
||||||
|
for (const worker of workerList) {
|
||||||
|
let rnd = BigInt(0);
|
||||||
|
rnd = fromBuffer(await randBytes(bitLength / 8, true));
|
||||||
|
worker.postMessage({
|
||||||
|
'rnd': rnd,
|
||||||
|
'iterations': iterations
|
||||||
|
});
|
||||||
|
}
|
||||||
|
|
||||||
{ // browser
|
|
||||||
buf = new Uint8Array(byteLength);
|
|
||||||
self.crypto.getRandomValues(buf);
|
|
||||||
// If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
|
|
||||||
if (forceLength)
|
|
||||||
buf[0] = buf[0] | 128;
|
|
||||||
resolve(buf);
|
|
||||||
}
|
}
|
||||||
});
|
});
|
||||||
};
|
};
|
||||||
|
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Returns a cryptographically secure random integer between [min,max]
|
* Returns a cryptographically secure random integer between [min,max]
|
||||||
* @param {bigint} max Returned value will be <= max
|
* @param {bigint} max Returned value will be <= max
|
||||||
|
|
@ -211,53 +251,74 @@ const randBetween = async function (max, min = 1) {
|
||||||
};
|
};
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
|
* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
|
||||||
*
|
*
|
||||||
* @param {bigint} w An integer to be tested for primality
|
* @param {number} byteLength The desired number of random bytes
|
||||||
* @param {number} iterations The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
|
* @param {boolean} forceLength If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
|
||||||
*
|
*
|
||||||
* @return {Promise} A promise that resolve to a boolean that is either true (a probably prime number) or false (definitely composite)
|
* @returns {Promise} A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes
|
||||||
*/
|
*/
|
||||||
const isProbablyPrime = async function (w, iterations = 16) {
|
const randBytes = async function (byteLength, forceLength = false) {
|
||||||
{
|
return new Promise((resolve) => {
|
||||||
return new Promise(resolve => {
|
let buf;
|
||||||
let worker = _isProbablyPrimeWorker();
|
|
||||||
|
|
||||||
worker.onmessage = (event) => {
|
{ // browser
|
||||||
resolve(event.data.isPrime);
|
buf = new Uint8Array(byteLength);
|
||||||
};
|
self.crypto.getRandomValues(buf);
|
||||||
worker.postMessage({
|
// If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
|
||||||
'rnd': w,
|
if (forceLength)
|
||||||
'iterations': iterations
|
buf[0] = buf[0] | 128;
|
||||||
});
|
resolve(buf);
|
||||||
});
|
}
|
||||||
}
|
});
|
||||||
};
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Finds the smallest positive element that is congruent to a in modulo n
|
||||||
|
* @param {number|bigint} a An integer
|
||||||
|
* @param {number|bigint} n The modulo
|
||||||
|
*
|
||||||
|
* @returns {bigint} The smallest positive representation of a in modulo n
|
||||||
|
*/
|
||||||
|
const toZn = function (a, n) {
|
||||||
|
n = BigInt(n);
|
||||||
|
a = BigInt(a) % n;
|
||||||
|
return (a < 0) ? a + n : a;
|
||||||
|
};
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
/* HELPER FUNCTIONS */
|
||||||
|
|
||||||
|
function fromBuffer(buf) {
|
||||||
|
let ret = BigInt(0);
|
||||||
|
for (let i of buf.values()) {
|
||||||
|
let bi = BigInt(i);
|
||||||
|
ret = (ret << BigInt(8)) + bi;
|
||||||
|
}
|
||||||
|
return ret;
|
||||||
|
}
|
||||||
|
|
||||||
|
function bitLength(a) {
|
||||||
|
let bits = 1;
|
||||||
|
do {
|
||||||
|
bits++;
|
||||||
|
} while ((a >>= BigInt(1)) > BigInt(1));
|
||||||
|
return bits;
|
||||||
|
}
|
||||||
|
|
||||||
function _isProbablyPrimeWorker() {
|
function _isProbablyPrimeWorker() {
|
||||||
async function _onmessage(event) { // Let's start once we are called
|
async function _onmessage(event) { // Let's start once we are called
|
||||||
// event.data = {rnd: <bigint>, iterations: <number>}
|
// event.data = {rnd: <bigint>, iterations: <number>}
|
||||||
const isPrime = await isProbablyPrime(event.data.rnd, event.data.iterations, false);
|
const isPrime = await isProbablyPrime(event.data.rnd, event.data.iterations);
|
||||||
postMessage({
|
postMessage({
|
||||||
'isPrime': isPrime,
|
'isPrime': isPrime,
|
||||||
'value': event.data.rnd
|
'value': event.data.rnd
|
||||||
});
|
});
|
||||||
}
|
}
|
||||||
|
|
||||||
let workerCode = `(() => {
|
let workerCode = `(() => {'use strict';const eGcd = ${eGcd.toString()};const modInv = ${modInv.toString()};const modPow = ${modPow.toString()};const toZn = ${toZn.toString()};const randBytes = ${randBytes.toString()};const randBetween = ${randBetween.toString()};const isProbablyPrime = ${_isProbablyPrime.toString()};${bitLength.toString()}${fromBuffer.toString()}onmessage = ${_onmessage.toString()};})()`;
|
||||||
'use strict';
|
|
||||||
|
|
||||||
const eGcd = ${eGcd.toString()};
|
|
||||||
const modInv = ${modInv.toString()};
|
|
||||||
const modPow = ${modPow.toString()};
|
|
||||||
const toZn = ${toZn.toString()};
|
|
||||||
const randBytes = ${randBytes.toString()};
|
|
||||||
const randBetween = ${randBetween.toString()};
|
|
||||||
const isProbablyPrime = ${_isProbablyPrime.toString()};
|
|
||||||
${bitLength.toString()}
|
|
||||||
${fromBuffer.toString()}
|
|
||||||
|
|
||||||
onmessage = ${_onmessage.toString()};
|
|
||||||
})()`;
|
|
||||||
var _blob = new Blob([workerCode], { type: 'text/javascript' });
|
var _blob = new Blob([workerCode], { type: 'text/javascript' });
|
||||||
|
|
||||||
return new Worker(window.URL.createObjectURL(_blob));
|
return new Worker(window.URL.createObjectURL(_blob));
|
||||||
|
|
@ -582,75 +643,4 @@ async function _isProbablyPrime(w, iterations = 16) {
|
||||||
return true;
|
return true;
|
||||||
}
|
}
|
||||||
|
|
||||||
/**
|
|
||||||
* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator
|
|
||||||
*
|
|
||||||
* @param {number} bitLength The required bit length for the generated prime
|
|
||||||
* @param {number} iterations The number of iterations for the Miller-Rabin Probabilistic Primality Test
|
|
||||||
*
|
|
||||||
* @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits
|
|
||||||
*/
|
|
||||||
const prime = async function (bitLength, iterations = 16) {
|
|
||||||
return new Promise(async (resolve) => {
|
|
||||||
{
|
|
||||||
let workerList = [];
|
|
||||||
for (let i = 0; i < self.navigator.hardwareConcurrency; i++) {
|
|
||||||
let newWorker = _isProbablyPrimeWorker();
|
|
||||||
newWorker.onmessage = async (event) => {
|
|
||||||
if (event.data.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) {
|
|
||||||
workerList.pop();
|
|
||||||
}
|
|
||||||
resolve(event.data.value);
|
|
||||||
} else { // if a composite is found, make the worker test another random number
|
|
||||||
let rnd = BigInt(0);
|
|
||||||
rnd = fromBuffer(await randBytes(bitLength / 8, true));
|
|
||||||
newWorker.postMessage({
|
|
||||||
'rnd': rnd,
|
|
||||||
'iterations': iterations
|
|
||||||
});
|
|
||||||
}
|
|
||||||
};
|
|
||||||
workerList.push(newWorker);
|
|
||||||
}
|
|
||||||
|
|
||||||
for (const worker of workerList) {
|
|
||||||
let rnd = BigInt(0);
|
|
||||||
rnd = fromBuffer(await randBytes(bitLength / 8, true));
|
|
||||||
worker.postMessage({
|
|
||||||
'rnd': rnd,
|
|
||||||
'iterations': iterations
|
|
||||||
});
|
|
||||||
}
|
|
||||||
|
|
||||||
}
|
|
||||||
});
|
|
||||||
};
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
/* HELPER FUNCTIONS */
|
|
||||||
|
|
||||||
function fromBuffer(buf) {
|
|
||||||
let ret = BigInt(0);
|
|
||||||
for (let i of buf.values()) {
|
|
||||||
let bi = BigInt(i);
|
|
||||||
ret = (ret << BigInt(8)) + bi;
|
|
||||||
}
|
|
||||||
return ret;
|
|
||||||
}
|
|
||||||
|
|
||||||
function bitLength(a) {
|
|
||||||
let bits = 1;
|
|
||||||
do {
|
|
||||||
bits++;
|
|
||||||
} while ((a >>= BigInt(1)) > BigInt(1));
|
|
||||||
return bits;
|
|
||||||
}
|
|
||||||
|
|
||||||
export { abs, eGcd, gcd, isProbablyPrime, lcm, modInv, modPow, prime, randBetween, randBytes, toZn };
|
export { abs, eGcd, gcd, isProbablyPrime, lcm, modInv, modPow, prime, randBetween, randBytes, toZn };
|
||||||
|
|
@ -0,0 +1 @@
|
||||||
|
const abs=function(b){return b=BigInt(b),b>=BigInt(0)?b:-b},eGcd=function(c,d){c=BigInt(c),d=BigInt(d);let e=BigInt(0),f=BigInt(1),g=BigInt(1),h=BigInt(0);for(;c!==BigInt(0);){let a=d/c,b=d%c,i=e-g*a,j=f-h*a;d=c,c=b,e=g,f=h,g=i,h=j}return{b:d,x:e,y:f}},gcd=function(c,d){c=abs(c),d=abs(d);let e=BigInt(0);for(;!((c|d)&BigInt(1));)c>>=BigInt(1),d>>=BigInt(1),e++;for(;!(c&BigInt(1));)c>>=BigInt(1);do{for(;!(d&BigInt(1));)d>>=BigInt(1);if(c>d){let a=c;c=d,d=a}d-=c}while(d);return c<<e},isProbablyPrime=async function(a,b=16){return new Promise(c=>{let d=_isProbablyPrimeWorker();d.onmessage=a=>{d.terminate(),c(a.data.isPrime)},d.postMessage({rnd:a,iterations:b})})},lcm=function(c,d){return c=BigInt(c),d=BigInt(d),abs(c*d)/gcd(c,d)},modInv=function(b,a){let c=eGcd(b,a);return c.b===BigInt(1)?toZn(c.x,a):null},modPow=function(c,d,e){if(e=BigInt(e),c=toZn(c,e),d=BigInt(d),d<BigInt(0))return modInv(modPow(c,abs(d),e),e);let f=BigInt(1),g=c;for(;0<d;){var h=d%BigInt(2);d/=BigInt(2),h==BigInt(1)&&(f*=g,f%=e),g*=g,g%=e}return f},prime=async function(a,b=16){return new Promise(async c=>{{let d=[];for(let e,f=0;f<self.navigator.hardwareConcurrency;f++)e=_isProbablyPrimeWorker(),e.onmessage=async f=>{if(f.data.isPrime){for(let a=0;a<d.length;a++)d[a].terminate();for(;d.length;)d.pop();c(f.data.value)}else{let c=BigInt(0);c=fromBuffer((await randBytes(a/8,!0))),e.postMessage({rnd:c,iterations:b})}},d.push(e);for(const c of d){let d=BigInt(0);d=fromBuffer((await randBytes(a/8,!0))),c.postMessage({rnd:d,iterations:b})}}})},randBetween=async function(a,b=1){let c,d=bitLength(a),e=d>>3,f=d-8*e;0<f&&(e++,c=2**f-1);let g;do{let a=await randBytes(e);0<f&&(a[0]&=c),g=fromBuffer(a)}while(g>a||g<b);return g},randBytes=async function(a,b=!1){return new Promise(c=>{let d;d=new Uint8Array(a),self.crypto.getRandomValues(d),b&&(d[0]|=128),c(d)})},toZn=function(b,c){return c=BigInt(c),b=BigInt(b)%c,0>b?b+c:b};function fromBuffer(a){let b=BigInt(0);for(let c of a.values()){let a=BigInt(c);b=(b<<BigInt(8))+a}return b}function bitLength(b){let c=1;do c++;while((b>>=BigInt(1))>BigInt(1));return c}function _isProbablyPrimeWorker(){let a=`(() => {'use strict';const eGcd = ${eGcd.toString()};const modInv = ${modInv.toString()};const modPow = ${modPow.toString()};const toZn = ${toZn.toString()};const randBytes = ${randBytes.toString()};const randBetween = ${randBetween.toString()};const isProbablyPrime = ${_isProbablyPrime.toString()};${bitLength.toString()}${fromBuffer.toString()}onmessage = ${async function(a){const b=await isProbablyPrime(a.data.rnd,a.data.iterations);postMessage({isPrime:b,value:a.data.rnd})}.toString()};})()`;var b=new Blob([a],{type:"text/javascript"});return new Worker(window.URL.createObjectURL(b))}async function _isProbablyPrime(c,b=16){if(c===BigInt(2))return!0;if((c&BigInt(1))===BigInt(0)||c===BigInt(1))return!1;const e=[3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597];for(let a=0;a<e.length&&BigInt(e[a])<=c;a++){const b=BigInt(e[a]);if(c===b)return!0;if(c%b===BigInt(0))return!1}let f=BigInt(0),g=c-BigInt(1);for(;g%BigInt(2)===BigInt(0);)g/=BigInt(2),++f;let h=(c-BigInt(1))/BigInt(2)**f;loop:do{let a=await randBetween(c-BigInt(1),2),b=modPow(a,h,c);if(b===BigInt(1)||b===c-BigInt(1))continue;for(let a=1;a<f;a++){if(b=modPow(b,BigInt(2),c),b===c-BigInt(1))continue loop;if(b===BigInt(1))break}return!1}while(--b);return!0}export{abs,eGcd,gcd,isProbablyPrime,lcm,modInv,modPow,prime,randBetween,randBytes,toZn};
|
||||||
|
|
@ -14,64 +14,6 @@ const abs = function (a) {
|
||||||
return (a >= BigInt(0)) ? a : -a;
|
return (a >= BigInt(0)) ? a : -a;
|
||||||
};
|
};
|
||||||
|
|
||||||
/**
|
|
||||||
* Greatest-common divisor of two integers based on the iterative binary algorithm.
|
|
||||||
*
|
|
||||||
* @param {number|bigint} a
|
|
||||||
* @param {number|bigint} b
|
|
||||||
*
|
|
||||||
* @returns {bigint} The greatest common divisor of a and b
|
|
||||||
*/
|
|
||||||
const gcd = function (a, b) {
|
|
||||||
a = abs(a);
|
|
||||||
b = abs(b);
|
|
||||||
let shift = BigInt(0);
|
|
||||||
while (!((a | b) & BigInt(1))) {
|
|
||||||
a >>= BigInt(1);
|
|
||||||
b >>= BigInt(1);
|
|
||||||
shift++;
|
|
||||||
}
|
|
||||||
while (!(a & BigInt(1))) a >>= BigInt(1);
|
|
||||||
do {
|
|
||||||
while (!(b & BigInt(1))) b >>= BigInt(1);
|
|
||||||
if (a > b) {
|
|
||||||
let x = a;
|
|
||||||
a = b;
|
|
||||||
b = x;
|
|
||||||
}
|
|
||||||
b -= a;
|
|
||||||
} while (b);
|
|
||||||
|
|
||||||
// rescale
|
|
||||||
return a << shift;
|
|
||||||
};
|
|
||||||
|
|
||||||
/**
|
|
||||||
* The least common multiple computed as abs(a*b)/gcd(a,b)
|
|
||||||
* @param {number|bigint} a
|
|
||||||
* @param {number|bigint} b
|
|
||||||
*
|
|
||||||
* @returns {bigint} The least common multiple of a and b
|
|
||||||
*/
|
|
||||||
const lcm = function (a, b) {
|
|
||||||
a = BigInt(a);
|
|
||||||
b = BigInt(b);
|
|
||||||
return abs(a * b) / gcd(a, b);
|
|
||||||
};
|
|
||||||
|
|
||||||
/**
|
|
||||||
* Finds the smallest positive element that is congruent to a in modulo n
|
|
||||||
* @param {number|bigint} a An integer
|
|
||||||
* @param {number|bigint} n The modulo
|
|
||||||
*
|
|
||||||
* @returns {bigint} The smallest positive representation of a in modulo n
|
|
||||||
*/
|
|
||||||
const toZn = function (a, n) {
|
|
||||||
n = BigInt(n);
|
|
||||||
a = BigInt(a) % n;
|
|
||||||
return (a < 0) ? a + n : a;
|
|
||||||
};
|
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
|
* @typedef {Object} egcdReturn A triple (g, x, y), such that ax + by = g = gcd(a, b).
|
||||||
* @property {bigint} g
|
* @property {bigint} g
|
||||||
|
|
@ -114,6 +56,65 @@ const eGcd = function (a, b) {
|
||||||
};
|
};
|
||||||
};
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Greatest-common divisor of two integers based on the iterative binary algorithm.
|
||||||
|
*
|
||||||
|
* @param {number|bigint} a
|
||||||
|
* @param {number|bigint} b
|
||||||
|
*
|
||||||
|
* @returns {bigint} The greatest common divisor of a and b
|
||||||
|
*/
|
||||||
|
const gcd = function (a, b) {
|
||||||
|
a = abs(a);
|
||||||
|
b = abs(b);
|
||||||
|
let shift = BigInt(0);
|
||||||
|
while (!((a | b) & BigInt(1))) {
|
||||||
|
a >>= BigInt(1);
|
||||||
|
b >>= BigInt(1);
|
||||||
|
shift++;
|
||||||
|
}
|
||||||
|
while (!(a & BigInt(1))) a >>= BigInt(1);
|
||||||
|
do {
|
||||||
|
while (!(b & BigInt(1))) b >>= BigInt(1);
|
||||||
|
if (a > b) {
|
||||||
|
let x = a;
|
||||||
|
a = b;
|
||||||
|
b = x;
|
||||||
|
}
|
||||||
|
b -= a;
|
||||||
|
} while (b);
|
||||||
|
|
||||||
|
// rescale
|
||||||
|
return a << shift;
|
||||||
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
|
||||||
|
*
|
||||||
|
* @param {bigint} w An integer to be tested for primality
|
||||||
|
* @param {number} iterations The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
|
||||||
|
*
|
||||||
|
* @return {Promise} A promise that resolve to a boolean that is either true (a probably prime number) or false (definitely composite)
|
||||||
|
*/
|
||||||
|
const isProbablyPrime = async function (w, iterations = 16) {
|
||||||
|
{
|
||||||
|
return _isProbablyPrime(w, iterations);
|
||||||
|
}
|
||||||
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* The least common multiple computed as abs(a*b)/gcd(a,b)
|
||||||
|
* @param {number|bigint} a
|
||||||
|
* @param {number|bigint} b
|
||||||
|
*
|
||||||
|
* @returns {bigint} The least common multiple of a and b
|
||||||
|
*/
|
||||||
|
const lcm = function (a, b) {
|
||||||
|
a = BigInt(a);
|
||||||
|
b = BigInt(b);
|
||||||
|
return abs(a * b) / gcd(a, b);
|
||||||
|
};
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Modular inverse.
|
* Modular inverse.
|
||||||
*
|
*
|
||||||
|
|
@ -163,32 +164,27 @@ const modPow = function (a, b, n) {
|
||||||
};
|
};
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process
|
* 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).
|
||||||
*
|
*
|
||||||
* @param {number} byteLength The desired number of random bytes
|
* @param {number} bitLength The required bit length for the generated prime
|
||||||
* @param {boolean} forceLength If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
|
* @param {number} iterations The number of iterations for the Miller-Rabin Probabilistic Primality Test
|
||||||
*
|
*
|
||||||
* @returns {Promise} A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes
|
* @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits
|
||||||
*/
|
*/
|
||||||
const randBytes = async function (byteLength, forceLength = false) {
|
const prime = async function (bitLength, iterations = 16) {
|
||||||
return new Promise((resolve) => {
|
return new Promise(async (resolve) => {
|
||||||
let buf;
|
{
|
||||||
|
let rnd = BigInt(0);
|
||||||
{ // node
|
do {
|
||||||
const crypto = require('crypto');
|
rnd = fromBuffer(await randBytes(bitLength / 8, true));
|
||||||
buf = Buffer.alloc(byteLength);
|
} while (! await isProbablyPrime(rnd, iterations));
|
||||||
crypto.randomFill(buf, (err, buf) => {
|
resolve(rnd);
|
||||||
// If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
|
|
||||||
if (forceLength)
|
|
||||||
buf[0] = buf[0] | 128;
|
|
||||||
|
|
||||||
resolve(buf);
|
|
||||||
});
|
|
||||||
}
|
}
|
||||||
});
|
});
|
||||||
};
|
};
|
||||||
|
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* Returns a cryptographically secure random integer between [min,max]
|
* Returns a cryptographically secure random integer between [min,max]
|
||||||
* @param {bigint} max Returned value will be <= max
|
* @param {bigint} max Returned value will be <= max
|
||||||
|
|
@ -218,19 +214,65 @@ const randBetween = async function (max, min = 1) {
|
||||||
};
|
};
|
||||||
|
|
||||||
/**
|
/**
|
||||||
* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
|
* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
|
||||||
*
|
*
|
||||||
* @param {bigint} w An integer to be tested for primality
|
* @param {number} byteLength The desired number of random bytes
|
||||||
* @param {number} iterations The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
|
* @param {boolean} forceLength If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
|
||||||
*
|
*
|
||||||
* @return {Promise} A promise that resolve to a boolean that is either true (a probably prime number) or false (definitely composite)
|
* @returns {Promise} A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes
|
||||||
*/
|
*/
|
||||||
const isProbablyPrime = async function (w, iterations = 16) {
|
const randBytes = async function (byteLength, forceLength = false) {
|
||||||
{
|
return new Promise((resolve) => {
|
||||||
return _isProbablyPrime(w, iterations);
|
let buf;
|
||||||
}
|
|
||||||
|
{ // node
|
||||||
|
const crypto = require('crypto');
|
||||||
|
buf = Buffer.alloc(byteLength);
|
||||||
|
crypto.randomFill(buf, (err, buf) => {
|
||||||
|
// If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
|
||||||
|
if (forceLength)
|
||||||
|
buf[0] = buf[0] | 128;
|
||||||
|
|
||||||
|
resolve(buf);
|
||||||
|
});
|
||||||
|
}
|
||||||
|
});
|
||||||
};
|
};
|
||||||
|
|
||||||
|
/**
|
||||||
|
* Finds the smallest positive element that is congruent to a in modulo n
|
||||||
|
* @param {number|bigint} a An integer
|
||||||
|
* @param {number|bigint} n The modulo
|
||||||
|
*
|
||||||
|
* @returns {bigint} The smallest positive representation of a in modulo n
|
||||||
|
*/
|
||||||
|
const toZn = function (a, n) {
|
||||||
|
n = BigInt(n);
|
||||||
|
a = BigInt(a) % n;
|
||||||
|
return (a < 0) ? a + n : a;
|
||||||
|
};
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
/* HELPER FUNCTIONS */
|
||||||
|
|
||||||
|
function fromBuffer(buf) {
|
||||||
|
let ret = BigInt(0);
|
||||||
|
for (let i of buf.values()) {
|
||||||
|
let bi = BigInt(i);
|
||||||
|
ret = (ret << BigInt(8)) + bi;
|
||||||
|
}
|
||||||
|
return ret;
|
||||||
|
}
|
||||||
|
|
||||||
|
function bitLength(a) {
|
||||||
|
let bits = 1;
|
||||||
|
do {
|
||||||
|
bits++;
|
||||||
|
} while ((a >>= BigInt(1)) > BigInt(1));
|
||||||
|
return bits;
|
||||||
|
}
|
||||||
|
|
||||||
async function _isProbablyPrime(w, iterations = 16) {
|
async function _isProbablyPrime(w, iterations = 16) {
|
||||||
/*
|
/*
|
||||||
PREFILTERING. Even values but 2 are not primes, so don't test.
|
PREFILTERING. Even values but 2 are not primes, so don't test.
|
||||||
|
|
@ -550,48 +592,6 @@ async function _isProbablyPrime(w, iterations = 16) {
|
||||||
return true;
|
return true;
|
||||||
}
|
}
|
||||||
|
|
||||||
/**
|
|
||||||
* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator
|
|
||||||
*
|
|
||||||
* @param {number} bitLength The required bit length for the generated prime
|
|
||||||
* @param {number} iterations The number of iterations for the Miller-Rabin Probabilistic Primality Test
|
|
||||||
*
|
|
||||||
* @returns {Promise} A promise that resolves to a bigint probable prime of bitLength bits
|
|
||||||
*/
|
|
||||||
const prime = async function (bitLength, iterations = 16) {
|
|
||||||
return new Promise(async (resolve) => {
|
|
||||||
{
|
|
||||||
let rnd = BigInt(0);
|
|
||||||
do {
|
|
||||||
rnd = fromBuffer(await randBytes(bitLength / 8, true));
|
|
||||||
} while (! await isProbablyPrime(rnd, iterations));
|
|
||||||
resolve(rnd);
|
|
||||||
}
|
|
||||||
});
|
|
||||||
};
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
|
|
||||||
/* HELPER FUNCTIONS */
|
|
||||||
|
|
||||||
function fromBuffer(buf) {
|
|
||||||
let ret = BigInt(0);
|
|
||||||
for (let i of buf.values()) {
|
|
||||||
let bi = BigInt(i);
|
|
||||||
ret = (ret << BigInt(8)) + bi;
|
|
||||||
}
|
|
||||||
return ret;
|
|
||||||
}
|
|
||||||
|
|
||||||
function bitLength(a) {
|
|
||||||
let bits = 1;
|
|
||||||
do {
|
|
||||||
bits++;
|
|
||||||
} while ((a >>= BigInt(1)) > BigInt(1));
|
|
||||||
return bits;
|
|
||||||
}
|
|
||||||
|
|
||||||
exports.abs = abs;
|
exports.abs = abs;
|
||||||
exports.eGcd = eGcd;
|
exports.eGcd = eGcd;
|
||||||
exports.gcd = gcd;
|
exports.gcd = gcd;
|
||||||
|
|
@ -1,15 +0,0 @@
|
||||||
var bigintUtils=function(a){'use strict';function b(){let a=`(() => {
|
|
||||||
'use strict';
|
|
||||||
|
|
||||||
const eGcd = ${i.toString()};
|
|
||||||
const modInv = ${j.toString()};
|
|
||||||
const modPow = ${k.toString()};
|
|
||||||
const toZn = ${h.toString()};
|
|
||||||
const randBytes = ${l.toString()};
|
|
||||||
const randBetween = ${n.toString()};
|
|
||||||
const isProbablyPrime = ${c.toString()};
|
|
||||||
${e.toString()}
|
|
||||||
${d.toString()}
|
|
||||||
|
|
||||||
onmessage = ${async function(a){const b=await o(a.data.rnd,a.data.iterations,!1);postMessage({isPrime:b,value:a.data.rnd})}.toString()};
|
|
||||||
})()`;var b=new Blob([a],{type:"text/javascript"});return new Worker(window.URL.createObjectURL(b))}async function c(c,b=16){if(c===BigInt(2))return!0;if((c&BigInt(1))===BigInt(0)||c===BigInt(1))return!1;const e=[3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597];for(let a=0;a<e.length&&BigInt(e[a])<=c;a++){const b=BigInt(e[a]);if(c===b)return!0;if(c%b===BigInt(0))return!1}let f=BigInt(0),g=c-BigInt(1);for(;g%BigInt(2)===BigInt(0);)g/=BigInt(2),++f;let h=(c-BigInt(1))/BigInt(2)**f;loop:do{let a=await n(c-BigInt(1),2),b=k(a,h,c);if(b===BigInt(1)||b===c-BigInt(1))continue;for(let a=1;a<f;a++){if(b=k(b,BigInt(2),c),b===c-BigInt(1))continue loop;if(b===BigInt(1))break}return!1}while(--b);return!0}function d(a){let b=BigInt(0);for(let c of a.values()){let a=BigInt(c);b=(b<<BigInt(8))+a}return b}function e(b){let c=1;do c++;while((b>>=BigInt(1))>BigInt(1));return c}const f=function(b){return b=BigInt(b),b>=BigInt(0)?b:-b},g=function(c,d){c=f(c),d=f(d);let e=BigInt(0);for(;!((c|d)&BigInt(1));)c>>=BigInt(1),d>>=BigInt(1),e++;for(;!(c&BigInt(1));)c>>=BigInt(1);do{for(;!(d&BigInt(1));)d>>=BigInt(1);if(c>d){let a=c;c=d,d=a}d-=c}while(d);return c<<e},h=function(b,c){return c=BigInt(c),b=BigInt(b)%c,0>b?b+c:b},i=function(c,d){c=BigInt(c),d=BigInt(d);let e=BigInt(0),f=BigInt(1),g=BigInt(1),h=BigInt(0);for(;c!==BigInt(0);){let a=d/c,b=d%c,i=e-g*a,j=f-h*a;d=c,c=b,e=g,f=h,g=i,h=j}return{b:d,x:e,y:f}},j=function(b,a){let c=i(b,a);return c.b===BigInt(1)?h(c.x,a):null},k=function(c,d,e){if(e=BigInt(e),c=h(c,e),d=BigInt(d),d<BigInt(0))return j(k(c,f(d),e),e);let g=BigInt(1),i=c;for(;0<d;){var l=d%BigInt(2);d/=BigInt(2),l==BigInt(1)&&(g*=i,g%=e),i*=i,i%=e}return g},l=async function(a,b=!1){return new Promise(c=>{let d;d=new Uint8Array(a),self.crypto.getRandomValues(d),b&&(d[0]|=128),c(d)})},n=async function(a,b=1){let c,f=e(a),g=f>>3,h=f-8*g;0<h&&(g++,c=2**h-1);let i;do{let a=await l(g);0<h&&(a[0]&=c),i=d(a)}while(i>a||i<b);return i},o=async function(a,c=16){return new Promise(d=>{let e=b();e.onmessage=a=>{d(a.data.isPrime)},e.postMessage({rnd:a,iterations:c})})};return a.abs=f,a.eGcd=i,a.gcd=g,a.isProbablyPrime=o,a.lcm=function(c,d){return c=BigInt(c),d=BigInt(d),f(c*d)/g(c,d)},a.modInv=j,a.modPow=k,a.prime=async function(a,c=16){return new Promise(async e=>{{let f=[];for(let g,h=0;h<self.navigator.hardwareConcurrency;h++)g=b(),g.onmessage=async b=>{if(b.data.isPrime){for(let a=0;a<f.length;a++)f[a].terminate();for(;f.length;)f.pop();e(b.data.value)}else{let b=BigInt(0);b=d((await l(a/8,!0))),g.postMessage({rnd:b,iterations:c})}},f.push(g);for(const b of f){let e=BigInt(0);e=d((await l(a/8,!0))),b.postMessage({rnd:e,iterations:c})}}})},a.randBetween=n,a.randBytes=l,a.toZn=h,a}({});
|
|
||||||
|
|
@ -1,15 +0,0 @@
|
||||||
const abs=function(b){return b=BigInt(b),b>=BigInt(0)?b:-b},gcd=function(c,d){c=abs(c),d=abs(d);let e=BigInt(0);for(;!((c|d)&BigInt(1));)c>>=BigInt(1),d>>=BigInt(1),e++;for(;!(c&BigInt(1));)c>>=BigInt(1);do{for(;!(d&BigInt(1));)d>>=BigInt(1);if(c>d){let a=c;c=d,d=a}d-=c}while(d);return c<<e},lcm=function(c,d){return c=BigInt(c),d=BigInt(d),abs(c*d)/gcd(c,d)},toZn=function(b,c){return c=BigInt(c),b=BigInt(b)%c,0>b?b+c:b},eGcd=function(c,d){c=BigInt(c),d=BigInt(d);let e=BigInt(0),f=BigInt(1),g=BigInt(1),h=BigInt(0);for(;c!==BigInt(0);){let a=d/c,b=d%c,i=e-g*a,j=f-h*a;d=c,c=b,e=g,f=h,g=i,h=j}return{b:d,x:e,y:f}},modInv=function(b,a){let c=eGcd(b,a);return c.b===BigInt(1)?toZn(c.x,a):null},modPow=function(c,d,e){if(e=BigInt(e),c=toZn(c,e),d=BigInt(d),d<BigInt(0))return modInv(modPow(c,abs(d),e),e);let f=BigInt(1),g=c;for(;0<d;){var h=d%BigInt(2);d/=BigInt(2),h==BigInt(1)&&(f*=g,f%=e),g*=g,g%=e}return f},randBytes=async function(a,b=!1){return new Promise(c=>{let d;d=new Uint8Array(a),self.crypto.getRandomValues(d),b&&(d[0]|=128),c(d)})},randBetween=async function(a,b=1){let c,d=bitLength(a),e=d>>3,f=d-8*e;0<f&&(e++,c=2**f-1);let g;do{let a=await randBytes(e);0<f&&(a[0]&=c),g=fromBuffer(a)}while(g>a||g<b);return g},isProbablyPrime=async function(a,b=16){return new Promise(c=>{let d=_isProbablyPrimeWorker();d.onmessage=a=>{c(a.data.isPrime)},d.postMessage({rnd:a,iterations:b})})};function _isProbablyPrimeWorker(){let a=`(() => {
|
|
||||||
'use strict';
|
|
||||||
|
|
||||||
const eGcd = ${eGcd.toString()};
|
|
||||||
const modInv = ${modInv.toString()};
|
|
||||||
const modPow = ${modPow.toString()};
|
|
||||||
const toZn = ${toZn.toString()};
|
|
||||||
const randBytes = ${randBytes.toString()};
|
|
||||||
const randBetween = ${randBetween.toString()};
|
|
||||||
const isProbablyPrime = ${_isProbablyPrime.toString()};
|
|
||||||
${bitLength.toString()}
|
|
||||||
${fromBuffer.toString()}
|
|
||||||
|
|
||||||
onmessage = ${async function(a){const b=await isProbablyPrime(a.data.rnd,a.data.iterations,!1);postMessage({isPrime:b,value:a.data.rnd})}.toString()};
|
|
||||||
})()`;var b=new Blob([a],{type:"text/javascript"});return new Worker(window.URL.createObjectURL(b))}async function _isProbablyPrime(c,b=16){if(c===BigInt(2))return!0;if((c&BigInt(1))===BigInt(0)||c===BigInt(1))return!1;const e=[3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597];for(let a=0;a<e.length&&BigInt(e[a])<=c;a++){const b=BigInt(e[a]);if(c===b)return!0;if(c%b===BigInt(0))return!1}let f=BigInt(0),g=c-BigInt(1);for(;g%BigInt(2)===BigInt(0);)g/=BigInt(2),++f;let h=(c-BigInt(1))/BigInt(2)**f;loop:do{let a=await randBetween(c-BigInt(1),2),b=modPow(a,h,c);if(b===BigInt(1)||b===c-BigInt(1))continue;for(let a=1;a<f;a++){if(b=modPow(b,BigInt(2),c),b===c-BigInt(1))continue loop;if(b===BigInt(1))break}return!1}while(--b);return!0}const prime=async function(a,b=16){return new Promise(async c=>{{let d=[];for(let e,f=0;f<self.navigator.hardwareConcurrency;f++)e=_isProbablyPrimeWorker(),e.onmessage=async f=>{if(f.data.isPrime){for(let a=0;a<d.length;a++)d[a].terminate();for(;d.length;)d.pop();c(f.data.value)}else{let c=BigInt(0);c=fromBuffer((await randBytes(a/8,!0))),e.postMessage({rnd:c,iterations:b})}},d.push(e);for(const c of d){let d=BigInt(0);d=fromBuffer((await randBytes(a/8,!0))),c.postMessage({rnd:d,iterations:b})}}})};function fromBuffer(a){let b=BigInt(0);for(let c of a.values()){let a=BigInt(c);b=(b<<BigInt(8))+a}return b}function bitLength(b){let c=1;do c++;while((b>>=BigInt(1))>BigInt(1));return c}export{abs,eGcd,gcd,isProbablyPrime,lcm,modInv,modPow,prime,randBetween,randBytes,toZn};
|
|
||||||
Loading…
Reference in New Issue