/** * Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0 * * @param a * * @returns The absolute value of a */ function abs(a) { return (a >= 0) ? a : -a; } /** * Returns the bitlength of a number * * @param a * @returns The bit length */ function bitLength(a) { if (typeof a === 'number') a = BigInt(a); if (a === 1n) { return 1; } let bits = 1; do { bits++; } while ((a >>= 1n) > 1n); return bits; } /** * An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm. * Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b). * * @param a * @param b * * @throws {RangeError} * This excepction is thrown if a or b are less than 0 * * @returns A triple (g, x, y), such that ax + by = g = gcd(a, b). */ function eGcd(a, b) { if (typeof a === 'number') a = BigInt(a); if (typeof b === 'number') b = BigInt(b); if (a <= 0n || b <= 0n) throw new RangeError('a and b MUST be > 0'); // a and b MUST be positive let x = 0n; let y = 1n; let u = 1n; let v = 0n; while (a !== 0n) { const q = b / a; const r = b % a; const m = x - (u * q); const n = y - (v * q); b = a; a = r; x = u; y = v; u = m; v = n; } return { g: b, x: x, y: y }; } /** * Greatest-common divisor of two integers based on the iterative binary algorithm. * * @param a * @param b * * @returns The greatest common divisor of a and b */ function gcd(a, b) { let aAbs = (typeof a === 'number') ? BigInt(abs(a)) : abs(a); let bAbs = (typeof b === 'number') ? BigInt(abs(b)) : abs(b); if (aAbs === 0n) { return bAbs; } else if (bAbs === 0n) { return aAbs; } let shift = 0n; while (((aAbs | bAbs) & 1n) === 0n) { aAbs >>= 1n; bAbs >>= 1n; shift++; } while ((aAbs & 1n) === 0n) aAbs >>= 1n; do { while ((bAbs & 1n) === 0n) bAbs >>= 1n; if (aAbs > bAbs) { const x = aAbs; aAbs = bAbs; bAbs = x; } bAbs -= aAbs; } while (bAbs !== 0n); // rescale return aAbs << shift; } /** * The least common multiple computed as abs(a*b)/gcd(a,b) * @param a * @param b * * @returns The least common multiple of a and b */ function lcm(a, b) { if (typeof a === 'number') a = BigInt(a); if (typeof b === 'number') b = BigInt(b); if (a === 0n && b === 0n) return BigInt(0); // return abs(a * b) as bigint / gcd(a, b) return abs((a / gcd(a, b)) * b); } /** * Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b * * @param a * @param b * * @returns Maximum of numbers a and b */ function max(a, b) { return (a >= b) ? a : b; } /** * Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b * * @param a * @param b * * @returns Minimum of numbers a and b */ function min(a, b) { return (a >= b) ? b : a; } /** * Finds the smallest positive element that is congruent to a in modulo n * * @remarks * a and b must be the same type, either number or bigint * * @param a - An integer * @param n - The modulo * * @throws {RangeError} * Excpeption thrown when n is not > 0 * * @returns A bigint with the smallest positive representation of a modulo n */ function toZn(a, n) { if (typeof a === 'number') a = BigInt(a); if (typeof n === 'number') n = BigInt(n); if (n <= 0n) { throw new RangeError('n must be > 0'); } const aZn = a % n; return (aZn < 0n) ? aZn + n : aZn; } /** * Modular inverse. * * @param a The number to find an inverse for * @param n The modulo * * @throws {RangeError} * Excpeption thorwn when a does not have inverse modulo n * * @returns The inverse modulo n */ function modInv(a, n) { const egcd = eGcd(toZn(a, n), n); if (egcd.g !== 1n) { throw new RangeError(`${a.toString()} does not have inverse modulo ${n.toString()}`); // modular inverse does not exist } else { return toZn(egcd.x, n); } } /** * Modular exponentiation b**e mod n. Currently using the right-to-left binary method * * @param b base * @param e exponent * @param n modulo * * @throws {RangeError} * Excpeption thrown when n is not > 0 * * @returns b**e mod n */ function modPow(b, e, n) { if (typeof b === 'number') b = BigInt(b); if (typeof e === 'number') e = BigInt(e); if (typeof n === 'number') n = BigInt(n); if (n <= 0n) { throw new RangeError('n must be > 0'); } else if (n === 1n) { return 0n; } b = toZn(b, n); if (e < 0n) { return modInv(modPow(b, abs(e), n), n); } let r = 1n; while (e > 0) { if ((e % 2n) === 1n) { r = r * b % n; } e = e / 2n; b = b ** 2n % n; } return r; } function fromBuffer(buf) { let ret = 0n; for (const i of buf.values()) { const bi = BigInt(i); ret = (ret << 8n) + bi; } return ret; } /** * Secure random bytes for both node and browsers. Node version uses crypto.randomBytes() and browser one self.crypto.getRandomValues() * * @param byteLength - The desired number of random bytes * @param forceLength - If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1 * * @throws {RangeError} * byteLength MUST be > 0 * * @returns A promise that resolves to a UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bytes */ function randBytes(byteLength, forceLength = false) { if (byteLength < 1) throw new RangeError('byteLength MUST be > 0'); return new Promise(function (resolve, reject) { { // browser const 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); } }); } /** * Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues() * * @param byteLength - The desired number of random bytes * @param forceLength - If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1 * * @throws {RangeError} * byteLength MUST be > 0 * * @returns A UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bytes */ function randBytesSync(byteLength, forceLength = false) { if (byteLength < 1) throw new RangeError('byteLength MUST be > 0'); /* eslint-disable no-lone-blocks */ { // browser const 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; return buf; } /* eslint-enable no-lone-blocks */ } /** * Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues() * * @param bitLength - The desired number of random bits * @param forceLength - If we want to force the output to have a specific bit length. It basically forces the msb to be 1 * * @throws {RangeError} * bitLength MUST be > 0 * * @returns A Promise that resolves to a UInt8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bits */ function randBits(bitLength, forceLength = false) { if (bitLength < 1) throw new RangeError('bitLength MUST be > 0'); const byteLength = Math.ceil(bitLength / 8); const bitLengthMod8 = bitLength % 8; return new Promise((resolve, reject) => { randBytes(byteLength, false).then(function (rndBytes) { if (bitLengthMod8 !== 0) { // Fill with 0's the extra bits rndBytes[0] = rndBytes[0] & (2 ** bitLengthMod8 - 1); } if (forceLength) { const mask = (bitLengthMod8 !== 0) ? 2 ** (bitLengthMod8 - 1) : 128; rndBytes[0] = rndBytes[0] | mask; } resolve(rndBytes); }); }); } /** * Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues() * @param bitLength - The desired number of random bits * @param forceLength - If we want to force the output to have a specific bit length. It basically forces the msb to be 1 * * @throws {RangeError} * bitLength MUST be > 0 * * @returns A Uint8Array/Buffer (Browser/Node.js) filled with cryptographically secure random bits */ function randBitsSync(bitLength, forceLength = false) { if (bitLength < 1) throw new RangeError('bitLength MUST be > 0'); const byteLength = Math.ceil(bitLength / 8); const rndBytes = randBytesSync(byteLength, false); const bitLengthMod8 = bitLength % 8; if (bitLengthMod8 !== 0) { // Fill with 0's the extra bits rndBytes[0] = rndBytes[0] & (2 ** bitLengthMod8 - 1); } if (forceLength) { const mask = (bitLengthMod8 !== 0) ? 2 ** (bitLengthMod8 - 1) : 128; rndBytes[0] = rndBytes[0] | mask; } return rndBytes; } /** * Returns a cryptographically secure random integer between [min,max]. * @param max Returned value will be <= max * @param min Returned value will be >= min * * @throws {RangeError} * Arguments MUST be: max > min * * @returns A cryptographically secure random bigint between [min,max] */ function randBetween(max, min = 1n) { if (max <= min) throw new RangeError('Arguments MUST be: max > min'); const interval = max - min; const bitLen = bitLength(interval); let rnd; do { const buf = randBitsSync(bitLen); rnd = fromBuffer(buf); } while (rnd > interval); return rnd + min; } function _workerUrl(workerCode) { workerCode = `(() => {${workerCode}})()`; // encapsulate IIFE const _blob = new Blob([workerCode], { type: 'text/javascript' }); return window.URL.createObjectURL(_blob); } let _useWorkers = false; // The following is just to check whether we can use workers /* eslint-disable no-lone-blocks */ { // Native JS if (self.Worker !== undefined) _useWorkers = true; } /** * 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 w - A positive integer to be tested for primality * @param iterations - The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3 * @param disableWorkers - Disable the use of workers for the primality test * * @throws {RangeError} * w MUST be >= 0 * * @returns A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite) */ function isProbablyPrime(w, iterations = 16, disableWorkers = false) { if (typeof w === 'number') { w = BigInt(w); } if (w < 0n) throw RangeError('w MUST be >= 0'); { // browser return new Promise((resolve, reject) => { const worker = new Worker(_isProbablyPrimeWorkerUrl()); worker.onmessage = (event) => { worker.terminate(); resolve(event.data.isPrime); }; worker.onmessageerror = (event) => { reject(event); }; const msg = { rnd: w, iterations: iterations, id: 0 }; worker.postMessage(msg); }); } } function _isProbablyPrime(w, iterations) { /* PREFILTERING. Even values but 2 are not primes, so don't test. 1 is not a prime and the M-R algorithm needs w>1. */ if (w === 2n) return true; else if ((w & 1n) === 0n || w === 1n) return false; /* Test if any of the first 250 small primes are a factor of w. 2 is not tested because it was already tested above. */ const firstPrimes = [ 3n, 5n, 7n, 11n, 13n, 17n, 19n, 23n, 29n, 31n, 37n, 41n, 43n, 47n, 53n, 59n, 61n, 67n, 71n, 73n, 79n, 83n, 89n, 97n, 101n, 103n, 107n, 109n, 113n, 127n, 131n, 137n, 139n, 149n, 151n, 157n, 163n, 167n, 173n, 179n, 181n, 191n, 193n, 197n, 199n, 211n, 223n, 227n, 229n, 233n, 239n, 241n, 251n, 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); do { const b = randBetween(d, 2n); let z = modPow(b, m, w); if (z === 1n || z === d) continue; let j = 1; while (j < a) { z = modPow(z, 2n, w); if (z === d) break; if (z === 1n) return false; j++; } if (z !== d) return false; } while (--iterations !== 0); return true; } function _isProbablyPrimeWorkerUrl() { // Let's us first add all the required functions let workerCode = `'use strict';const ${eGcd.name}=${eGcd.toString()};const ${modInv.name}=${modInv.toString()};const ${modPow.name}=${modPow.toString()};const ${toZn.name}=${toZn.toString()};const ${randBitsSync.name}=${randBitsSync.toString()};const ${randBytesSync.name}=${randBytesSync.toString()};const ${randBetween.name}=${randBetween.toString()};const ${isProbablyPrime.name}=${_isProbablyPrime.toString()};${bitLength.toString()};${fromBuffer.toString()};`; workerCode += `onmessage=async function(_e){const _m={isPrime:await ${isProbablyPrime.name}(_e.data.rnd,_e.data.iterations),value:_e.data.rnd,id:_e.data.id};postMessage(_m);}`; return _workerUrl(workerCode); } /** * A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator. * The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI * main process, and it can be much faster (if several cores or cpu are available). * The node version can also use worker_threads if they are available (enabled by default with Node 11 and * and can be enabled at runtime executing node --experimental-worker with node >=10.5.0). * * @param bitLength - The required bit length for the generated prime * @param iterations - The number of iterations for the Miller-Rabin Probabilistic Primality Test * * @throws {RangeError} * bitLength MUST be > 0 * * @returns A promise that resolves to a bigint probable prime of bitLength bits. */ function prime(bitLength, iterations = 16) { if (bitLength < 1) throw new RangeError('bitLength MUST be > 0'); /* istanbul ignore if */ if (!_useWorkers) { // If there is no support for workers let rnd = 0n; do { rnd = fromBuffer(randBitsSync(bitLength, true)); } while (!_isProbablyPrime(rnd, iterations)); return new Promise((resolve) => { resolve(rnd); }); } return new Promise((resolve, reject) => { const workerList = []; const _onmessage = (msg, newWorker) => { if (msg.isPrime) { // if a prime number has been found, stop all the workers, and return it for (let j = 0; j < workerList.length; j++) { workerList[j].terminate(); // eslint-disable-line @typescript-eslint/no-floating-promises } while (workerList.length > 0) { workerList.pop(); } resolve(msg.value); } else { // if a composite is found, make the worker test another random number const buf = randBitsSync(bitLength, true); const rnd = fromBuffer(buf); try { const msgToWorker = { rnd: rnd, iterations: iterations, id: msg.id }; newWorker.postMessage(msgToWorker); } catch (error) { // The worker has already terminated. There is nothing to handle here } } }; { // browser const workerURL = _isProbablyPrimeWorkerUrl(); for (let i = 0; i < self.navigator.hardwareConcurrency - 1; i++) { const newWorker = new Worker(workerURL); newWorker.onmessage = (event) => _onmessage(event.data, newWorker); workerList.push(newWorker); } } for (let i = 0; i < workerList.length; i++) { randBits(bitLength, true).then(function (buf) { const rnd = fromBuffer(buf); workerList[i].postMessage({ rnd: rnd, iterations: iterations, id: i }); }).catch(reject); } }); } /** * A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator. * The sync version is NOT RECOMMENDED since it won't use workers and thus it'll be slower and may freeze thw window in browser's javascript. Please consider using prime() instead. * * @param bitLength - The required bit length for the generated prime * @param iterations - The number of iterations for the Miller-Rabin Probabilistic Primality Test * * @throws {RangeError} * bitLength MUST be > 0 * * @returns A bigint probable prime of bitLength bits. */ function primeSync(bitLength, iterations = 16) { if (bitLength < 1) throw new RangeError('bitLength MUST be > 0'); let rnd = 0n; do { rnd = fromBuffer(randBitsSync(bitLength, true)); } while (!_isProbablyPrime(rnd, iterations)); return rnd; } export { abs, bitLength, eGcd, gcd, isProbablyPrime, lcm, max, min, modInv, modPow, prime, primeSync, randBetween, randBits, randBitsSync, randBytes, randBytesSync, toZn }; //# 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