417 lines
8.0 KiB
TypeScript
417 lines
8.0 KiB
TypeScript
import { eGcd, modInv, modPow, toZn, bitLength } from 'bigint-mod-arith'
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import { fromBuffer } from './fromBuffer'
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import { randBetween } from './randBetween'
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import { randBitsSync } from './randBits'
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import { randBytesSync } from './randBytes'
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import { _useWorkers, _workerUrl, WorkerToMainMsg, MainToWorkerMsg } from './workerUtils'
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/**
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* The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
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* iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
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*
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* @param w - A positive integer to be tested for primality
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* @param iterations - The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3
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* @param disableWorkers - Disable the use of workers for the primality test
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*
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* @throws {RangeError}
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* w MUST be >= 0
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*
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* @returns A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
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*/
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export function isProbablyPrime (w: number|bigint, iterations: number = 16, disableWorkers: boolean = false): Promise<boolean> { // eslint-disable-line
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if (typeof w === 'number') {
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w = BigInt(w)
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}
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if (w < 0n) throw RangeError('w MUST be >= 0')
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if (!IS_BROWSER) { // Node.js
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/* istanbul ignore else */
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if (!disableWorkers && _useWorkers) {
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const { Worker } = require('worker_threads') // eslint-disable-line
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return new Promise((resolve, reject) => {
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const worker = new Worker(__filename)
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worker.on('message', (data: WorkerToMainMsg) => {
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worker.terminate()
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resolve(data.isPrime)
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})
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worker.on('error', reject)
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const msg: MainToWorkerMsg = {
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rnd: w as bigint,
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iterations: iterations,
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id: 0
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}
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worker.postMessage(msg)
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})
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} else {
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return new Promise((resolve) => {
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resolve(_isProbablyPrime(w as bigint, iterations))
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})
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}
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} else { // browser
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return new Promise((resolve, reject) => {
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const worker = new Worker(_isProbablyPrimeWorkerUrl())
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worker.onmessage = (event) => {
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worker.terminate()
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resolve(event.data.isPrime)
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}
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worker.onmessageerror = (event) => {
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reject(event)
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}
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const msg: MainToWorkerMsg = {
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rnd: w as bigint,
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iterations: iterations,
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id: 0
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}
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worker.postMessage(msg)
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})
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}
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}
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export function _isProbablyPrime (w: bigint, iterations: number): boolean {
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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
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else if ((w & 1n) === 0n || w === 1n) return false
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/*
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Test if any of the first 250 small primes are a factor of w. 2 is not tested because it was already tested above.
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*/
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const firstPrimes = [
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3n,
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5n,
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7n,
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11n,
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13n,
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17n,
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19n,
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23n,
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29n,
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31n,
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37n,
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41n,
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43n,
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47n,
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53n,
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59n,
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61n,
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67n,
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71n,
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73n,
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79n,
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83n,
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89n,
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97n,
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101n,
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103n,
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107n,
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109n,
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113n,
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127n,
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131n,
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137n,
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139n,
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149n,
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151n,
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157n,
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163n,
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167n,
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173n,
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179n,
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181n,
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191n,
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193n,
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197n,
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199n,
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211n,
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223n,
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227n,
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229n,
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233n,
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239n,
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241n,
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251n,
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257n,
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263n,
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269n,
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271n,
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277n,
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281n,
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283n,
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293n,
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307n,
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311n,
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313n,
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317n,
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331n,
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337n,
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347n,
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349n,
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353n,
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359n,
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367n,
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373n,
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379n,
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383n,
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389n,
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397n,
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401n,
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409n,
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419n,
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421n,
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431n,
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433n,
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439n,
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443n,
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449n,
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457n,
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461n,
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463n,
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467n,
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479n,
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487n,
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491n,
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499n,
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503n,
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509n,
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521n,
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523n,
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541n,
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547n,
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557n,
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563n,
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569n,
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571n,
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577n,
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587n,
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593n,
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599n,
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601n,
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607n,
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613n,
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617n,
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619n,
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631n,
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641n,
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643n,
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647n,
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653n,
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659n,
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661n,
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673n,
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677n,
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683n,
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691n,
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701n,
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709n,
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719n,
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727n,
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733n,
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739n,
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743n,
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751n,
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757n,
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761n,
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769n,
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773n,
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787n,
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797n,
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809n,
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811n,
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821n,
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823n,
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827n,
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829n,
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839n,
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853n,
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857n,
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859n,
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863n,
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877n,
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881n,
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883n,
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887n,
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907n,
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911n,
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919n,
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929n,
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937n,
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941n,
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947n,
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953n,
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967n,
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971n,
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977n,
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983n,
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991n,
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997n,
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1009n,
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1013n,
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1019n,
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1021n,
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1031n,
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1033n,
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1039n,
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1049n,
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1051n,
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1061n,
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1063n,
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1069n,
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1087n,
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1091n,
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1093n,
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1097n,
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1103n,
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1109n,
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1117n,
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1123n,
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1129n,
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1151n,
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1153n,
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1163n,
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1171n,
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1181n,
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1187n,
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1193n,
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1201n,
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1213n,
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1217n,
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1223n,
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1229n,
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1231n,
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1237n,
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1249n,
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1259n,
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1277n,
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1279n,
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1283n,
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1289n,
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1291n,
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1297n,
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1301n,
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1303n,
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1307n,
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1319n,
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1321n,
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1327n,
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1361n,
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1367n,
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1373n,
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1381n,
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1399n,
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1409n,
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1423n,
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1427n,
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1429n,
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1433n,
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1439n,
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1447n,
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1451n,
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1453n,
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1459n,
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1471n,
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1481n,
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1483n,
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1487n,
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1489n,
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1493n,
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1499n,
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1511n,
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1523n,
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1531n,
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1543n,
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1549n,
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1553n,
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1559n,
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1567n,
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1571n,
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1579n,
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1583n,
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1597n
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]
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for (let i = 0; i < firstPrimes.length && (firstPrimes[i] <= w); i++) {
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const p = firstPrimes[i]
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if (w === p) return true
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else if (w % p === 0n) return false
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}
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/*
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1. Let a be the largest integer such that 2**a divides w−1.
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2. m = (w−1) / 2**a.
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3. wlen = len (w).
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4. For i = 1 to iterations do
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4.1 Obtain a string b of wlen bits from an RBG.
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Comment: Ensure that 1 < b < w−1.
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4.2 If ((b ≤ 1) or (b ≥ w−1)), then go to step 4.1.
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4.3 z = b**m mod w.
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4.4 If ((z = 1) or (z = w − 1)), then go to step 4.7.
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4.5 For j = 1 to a − 1 do.
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4.5.1 z = z**2 mod w.
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4.5.2 If (z = w−1), then go to step 4.7.
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4.5.3 If (z = 1), then go to step 4.6.
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4.6 Return COMPOSITE.
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4.7 Continue.
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Comment: Increment i for the do-loop in step 4.
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5. Return PROBABLY PRIME.
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*/
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let a = 0n
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const d = w - 1n
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let aux = d
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while (aux % 2n === 0n) {
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aux /= 2n
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++a
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}
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const m = d / (2n ** a)
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do {
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const b = randBetween(d, 2n)
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let z = modPow(b, m, w)
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if (z === 1n || z === d) continue
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let j = 1
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while (j < a) {
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z = modPow(z, 2n, w)
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if (z === d) break
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if (z === 1n) return false
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j++
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}
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if (z !== d) return false
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} while (--iterations !== 0)
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return true
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}
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export function _isProbablyPrimeWorkerUrl (): string {
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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 ${randBitsSync.name}=${randBitsSync.toString()};const ${randBytesSync.name}=${randBytesSync.toString()};const ${randBetween.name}=${randBetween.toString()};const ${isProbablyPrime.name}=${_isProbablyPrime.toString()};${bitLength.toString()};${fromBuffer.toString()};`
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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);}`
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return _workerUrl(workerCode)
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}
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if (!IS_BROWSER && _useWorkers) { // node.js with support for workers
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const { parentPort, isMainThread } = require('worker_threads') // eslint-disable-line
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const isWorker = !(isMainThread as boolean)
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/* istanbul ignore if */
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if (isWorker) { // worker
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parentPort.on('message', function (data: MainToWorkerMsg) { // Let's start once we are called
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const isPrime = _isProbablyPrime(data.rnd, data.iterations)
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const msg: WorkerToMainMsg = {
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isPrime: isPrime,
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value: data.rnd,
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id: data.id
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}
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parentPort.postMessage(msg)
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})
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}
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}
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