794 lines
18 KiB
JavaScript
794 lines
18 KiB
JavaScript
/**
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* Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
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*
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* @param {number|bigint} a
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*
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* @returns {bigint} the absolute value of a
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*/
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function abs (a) {
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a = BigInt(a)
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return (a >= 0n) ? a : -a
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}
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/**
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* Returns the bitlength of a number
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*
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* @param {number|bigint} a
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* @returns {number} - the bit length
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*/
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function bitLength (a) {
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a = BigInt(a)
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if (a === 1n) { return 1 }
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let bits = 1
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do {
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bits++
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} while ((a >>= 1n) > 1n)
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return bits
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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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* @property {bigint} g
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* @property {bigint} x
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* @property {bigint} y
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*/
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/**
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* An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
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* Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
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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 {egcdReturn} A triple (g, x, y), such that ax + by = g = gcd(a, b).
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*/
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function eGcd (a, b) {
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a = BigInt(a)
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b = BigInt(b)
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if (a <= 0n | b <= 0n) { return NaN } // a and b MUST be positive
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let x = 0n
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let y = 1n
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let u = 1n
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let v = 0n
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while (a !== 0n) {
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const q = b / a
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const r = b % a
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const m = x - (u * q)
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const n = y - (v * q)
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b = a
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a = r
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x = u
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y = v
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u = m
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v = n
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}
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return {
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b: b,
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x: x,
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y: y
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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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function gcd (a, b) {
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a = abs(a)
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b = abs(b)
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if (a === 0n) { return b } else if (b === 0n) { return a }
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let shift = 0n
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while (!((a | b) & 1n)) {
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a >>= 1n
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b >>= 1n
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shift++
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}
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while (!(a & 1n)) a >>= 1n
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do {
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while (!(b & 1n)) b >>= 1n
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if (a > b) {
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const 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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function lcm (a, b) {
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a = BigInt(a)
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b = BigInt(b)
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if (a === 0n && b === 0n) { return 0n }
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return abs(a * b) / gcd(a, b)
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}
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/**
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* Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
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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} maximum of numbers a and b
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*/
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function max (a, b) {
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a = BigInt(a)
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b = BigInt(b)
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return (a >= b) ? a : b
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}
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/**
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* Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
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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} minimum of numbers a and b
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*/
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function min (a, b) {
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a = BigInt(a)
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b = BigInt(b)
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return (a >= b) ? b : a
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}
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/**
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* Modular inverse.
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*
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* @param {number|bigint} a The number to find an inverse for
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* @param {number|bigint} n The modulo
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*
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* @returns {bigint} the inverse modulo n or NaN if it does not exist
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*/
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function modInv (a, n) {
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const egcd = eGcd(toZn(a, n), n)
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if (egcd.b !== 1n) {
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return NaN // modular inverse does not exist
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} else {
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return toZn(egcd.x, n)
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}
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}
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/**
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* Modular exponentiation b**e mod n. Currently using the right-to-left binary method
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*
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* @param {number|bigint} b base
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* @param {number|bigint} e exponent
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* @param {number|bigint} n modulo
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*
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* @returns {bigint} b**e mod n
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*/
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function modPow (b, e, n) {
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n = BigInt(n)
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if (n === 0n) { return NaN } else if (n === 1n) { return 0n }
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b = toZn(b, n)
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e = BigInt(e)
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if (e < 0n) {
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return modInv(modPow(b, abs(e), n), n)
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}
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let r = 1n
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while (e > 0) {
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if ((e % 2n) === 1n) {
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r = (r * b) % n
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}
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e = e / 2n
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b = b ** 2n % n
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}
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return r
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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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function toZn (a, n) {
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n = BigInt(n)
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if (n <= 0) { return NaN }
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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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* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
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* iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
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*
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* @param {number | bigint} w An integer to be tested for primality
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* @param {number} [iterations = 16] The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
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*
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* @return {Promise<boolean>} A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
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*/
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async function isProbablyPrime (w, iterations = 16) {
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if (typeof w === 'number') {
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w = BigInt(w)
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}
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/* eslint-disable no-lone-blocks */
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{ // 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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worker.postMessage({
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rnd: w,
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iterations: iterations,
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id: 0
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})
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})
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}
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/* eslint-enable no-lone-blocks */
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}
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/**
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* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
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* The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI
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* main process, and it can be much faster (if several cores or cpu are available).
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* The node version can also use worker_threads if they are available (enabled by default with Node 11 and
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* and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).
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*
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* @param {number} bitLength The required bit length for the generated prime
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* @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
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*
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* @returns {Promise<bigint>} A promise that resolves to a bigint probable prime of bitLength bits.
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*/
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function prime (bitLength, iterations = 16) {
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if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
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return new Promise((resolve) => {
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const workerList = []
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const _onmessage = (msg, newWorker) => {
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if (msg.isPrime) {
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// if a prime number has been found, stop all the workers, and return it
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for (let j = 0; j < workerList.length; j++) {
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workerList[j].terminate()
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}
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while (workerList.length) {
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workerList.pop()
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}
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resolve(msg.value)
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} else { // if a composite is found, make the worker test another random number
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const buf = randBits(bitLength, true)
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const rnd = fromBuffer(buf)
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try {
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newWorker.postMessage({
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rnd: rnd,
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iterations: iterations,
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id: msg.id
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})
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} catch (error) {
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// The worker has already terminated. There is nothing to handle here
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}
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}
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}
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/* eslint-disable no-lone-blocks */
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{ // browser
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const workerURL = _isProbablyPrimeWorkerUrl()
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for (let i = 0; i < self.navigator.hardwareConcurrency - 1; i++) {
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const newWorker = new Worker(workerURL)
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newWorker.onmessage = (event) => _onmessage(event.data, newWorker)
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workerList.push(newWorker)
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}
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}
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/* eslint-enable no-lone-blocks */
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for (let i = 0; i < workerList.length; i++) {
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const buf = randBits(bitLength, true)
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const rnd = fromBuffer(buf)
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workerList[i].postMessage({
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rnd: rnd,
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iterations: iterations,
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id: i
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})
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}
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})
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}
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/**
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* A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
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* The sync version is NOT RECOMMENDED since it won't use workers and thus it'll be slower and may freeze thw window in browser's javascript. Please consider using prime() instead.
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*
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* @param {number} bitLength The required bit length for the generated prime
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* @param {number} [iterations = 16] The number of iterations for the Miller-Rabin Probabilistic Primality Test
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*
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* @returns {bigint} A bigint probable prime of bitLength bits.
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*/
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function primeSync (bitLength, iterations = 16) {
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if (bitLength < 1) { throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`) }
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let rnd = 0n
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do {
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rnd = fromBuffer(randBits(bitLength, true))
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} while (!_isProbablyPrime(rnd, iterations))
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return rnd
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}
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/**
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* Returns a cryptographically secure random integer between [min,max]
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* @param {bigint} max Returned value will be <= max
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* @param {bigint} [min = BigInt(1)] Returned value will be >= min
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*
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* @returns {bigint} A cryptographically secure random bigint between [min,max]
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*/
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function randBetween (max, min = 1n) {
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if (max <= min) throw new Error('max must be > min')
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const interval = max - min
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const bitLen = bitLength(interval)
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let rnd
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do {
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const buf = randBits(bitLen)
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rnd = fromBuffer(buf)
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} while (rnd > interval)
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return rnd + min
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}
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/**
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* Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param {number} bitLength The desired number of random bits
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* @param {boolean} [forceLength = false] If we want to force the output to have a specific bit length. It basically forces the msb to be 1
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*
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* @returns {Buffer | Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
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*/
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function randBits (bitLength, forceLength = false) {
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if (bitLength < 1) {
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throw new RangeError(`bitLength MUST be > 0 and it is ${bitLength}`)
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}
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const byteLength = Math.ceil(bitLength / 8)
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const rndBytes = randBytesSync(byteLength, false)
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const bitLengthMod8 = bitLength % 8
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if (bitLengthMod8) {
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// Fill with 0's the extra bits
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rndBytes[0] = rndBytes[0] & (2 ** bitLengthMod8 - 1)
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}
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if (forceLength) {
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const mask = bitLengthMod8 ? 2 ** (bitLengthMod8 - 1) : 128
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rndBytes[0] = rndBytes[0] | mask
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}
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return rndBytes
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}
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/**
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* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param {number} byteLength The desired number of random bytes
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* @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
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*
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* @returns {Promise<Buffer | Uint8Array>} A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
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*/
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function randBytes (byteLength, forceLength = false) {
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if (byteLength < 1) { throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`) }
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/* eslint-disable no-lone-blocks */
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{ // browser
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return new Promise(function (resolve) {
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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) { buf[0] = buf[0] | 128 }
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resolve(buf)
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})
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}
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/* eslint-enable no-lone-blocks */
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}
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/**
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* Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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*
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* @param {number} byteLength The desired number of random bytes
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* @param {boolean} [forceLength = false] If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1
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*
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* @returns {Buffer | Uint8Array} A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
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*/
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function randBytesSync (byteLength, forceLength = false) {
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if (byteLength < 1) { throw new RangeError(`byteLength MUST be > 0 and it is ${byteLength}`) }
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let buf
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/* eslint-disable no-lone-blocks */
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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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}
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/* eslint-enable no-lone-blocks */
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// If fixed length is required we put the first bit to 1 -> to get the necessary bitLength
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if (forceLength) { buf[0] = buf[0] | 128 }
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return buf
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}
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/* HELPER FUNCTIONS */
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function fromBuffer (buf) {
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let ret = 0n
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for (const i of buf.values()) {
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const bi = BigInt(i)
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ret = (ret << BigInt(8)) + bi
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}
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return ret
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}
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function _isProbablyPrimeWorkerUrl () {
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// Let's us first add all the required functions
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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 ${randBits.name}=${randBits.toString()};const ${randBytesSync.name}=${randBytesSync.toString()};const ${randBetween.name}=${randBetween.toString()};const ${isProbablyPrime.name}=${_isProbablyPrime.toString()};${bitLength.toString()}${fromBuffer.toString()}`
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const onmessage = async function (event) { // Let's start once we are called
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// event.data = {rnd: <bigint>, iterations: <number>}
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const isPrime = await isProbablyPrime(event.data.rnd, event.data.iterations)
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postMessage({
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isPrime: isPrime,
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value: event.data.rnd,
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id: event.data.id
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})
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}
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workerCode += `onmessage = ${onmessage.toString()};`
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return _workerUrl(workerCode)
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}
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function _workerUrl (workerCode) {
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workerCode = `(() => {${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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function _isProbablyPrime (w, iterations = 16) {
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/*
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PREFILTERING. Even values but 2 are not primes, so don't test.
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1 is not a prime and the M-R algorithm needs w>1.
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*/
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if (w === 2n) { return true } else if ((w & 1n) === 0n || w === 1n) { return false }
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/*
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Test if any of the first 250 small primes are a factor of w. 2 is not tested because it was already tested above.
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*/
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const firstPrimes = [
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3n,
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5n,
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7n,
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11n,
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13n,
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17n,
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19n,
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23n,
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29n,
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31n,
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37n,
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41n,
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43n,
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47n,
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53n,
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59n,
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61n,
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67n,
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71n,
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73n,
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79n,
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83n,
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89n,
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97n,
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101n,
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103n,
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107n,
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109n,
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113n,
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127n,
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131n,
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137n,
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139n,
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149n,
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151n,
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157n,
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163n,
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167n,
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173n,
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179n,
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181n,
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191n,
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193n,
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197n,
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199n,
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211n,
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223n,
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227n,
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229n,
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233n,
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239n,
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241n,
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251n,
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257n,
|
||
263n,
|
||
269n,
|
||
271n,
|
||
277n,
|
||
281n,
|
||
283n,
|
||
293n,
|
||
307n,
|
||
311n,
|
||
313n,
|
||
317n,
|
||
331n,
|
||
337n,
|
||
347n,
|
||
349n,
|
||
353n,
|
||
359n,
|
||
367n,
|
||
373n,
|
||
379n,
|
||
383n,
|
||
389n,
|
||
397n,
|
||
401n,
|
||
409n,
|
||
419n,
|
||
421n,
|
||
431n,
|
||
433n,
|
||
439n,
|
||
443n,
|
||
449n,
|
||
457n,
|
||
461n,
|
||
463n,
|
||
467n,
|
||
479n,
|
||
487n,
|
||
491n,
|
||
499n,
|
||
503n,
|
||
509n,
|
||
521n,
|
||
523n,
|
||
541n,
|
||
547n,
|
||
557n,
|
||
563n,
|
||
569n,
|
||
571n,
|
||
577n,
|
||
587n,
|
||
593n,
|
||
599n,
|
||
601n,
|
||
607n,
|
||
613n,
|
||
617n,
|
||
619n,
|
||
631n,
|
||
641n,
|
||
643n,
|
||
647n,
|
||
653n,
|
||
659n,
|
||
661n,
|
||
673n,
|
||
677n,
|
||
683n,
|
||
691n,
|
||
701n,
|
||
709n,
|
||
719n,
|
||
727n,
|
||
733n,
|
||
739n,
|
||
743n,
|
||
751n,
|
||
757n,
|
||
761n,
|
||
769n,
|
||
773n,
|
||
787n,
|
||
797n,
|
||
809n,
|
||
811n,
|
||
821n,
|
||
823n,
|
||
827n,
|
||
829n,
|
||
839n,
|
||
853n,
|
||
857n,
|
||
859n,
|
||
863n,
|
||
877n,
|
||
881n,
|
||
883n,
|
||
887n,
|
||
907n,
|
||
911n,
|
||
919n,
|
||
929n,
|
||
937n,
|
||
941n,
|
||
947n,
|
||
953n,
|
||
967n,
|
||
971n,
|
||
977n,
|
||
983n,
|
||
991n,
|
||
997n,
|
||
1009n,
|
||
1013n,
|
||
1019n,
|
||
1021n,
|
||
1031n,
|
||
1033n,
|
||
1039n,
|
||
1049n,
|
||
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)
|
||
|
||
// /* eslint-disable no-labels */
|
||
// loop: do {
|
||
// const b = randBetween(w - 1n, 2n)
|
||
// let z = modPow(b, m, w)
|
||
// if (z === 1n || z === w - 1n) { continue }
|
||
// for (let j = 1; j < a; j++) {
|
||
// z = modPow(z, 2n, w)
|
||
// if (z === w - 1n) { continue loop }
|
||
// if (z === 1n) { break }
|
||
// }
|
||
// return false
|
||
// } while (--iterations)
|
||
// /* eslint-enable no-labels */
|
||
|
||
// return true
|
||
|
||
do {
|
||
const b = randBetween(d, 2n)
|
||
let z = 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)
|
||
return true
|
||
}
|
||
|
||
export { abs, bitLength, eGcd, gcd, isProbablyPrime, lcm, max, min, modInv, modPow, prime, primeSync, randBetween, randBits, randBytes, randBytesSync, toZn }
|