From faefecc21d9806ce70471922b87b495655cec835 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Juan=20Hern=C3=A1ndez=20Serrano?= Date: Fri, 19 Apr 2019 09:42:28 +0200 Subject: [PATCH] working with worker file --- .eslintrc.json | 36 + LICENSE | 21 + README.hbs | 87 + README.md | 290 ++ build/build.browser.tests.js | 89 + build/build.rollup.js | 135 + dist/bigint-utils-latest.browser.js | 629 ++++ dist/bigint-utils-latest.browser.min.js | 1 + dist/bigint-utils-latest.browser.mod.js | 612 ++++ dist/bigint-utils-latest.browser.mod.min.js | 1 + dist/bigint-utils-latest.node.js | 599 ++++ dist/workerPrimalityTest.js | 14 + package-lock.json | 3515 +++++++++++++++++++ package.json | 46 + src/browser-test-template.html | 15 + src/main.js | 628 ++++ src/workerPrimalityTest.js | 14 + test/01_PrimeValidation.js | 60 + test/02_PrimeGeneration.js | 31 + test/browser/index.html | 22 + test/browser/tests.js | 88 + 21 files changed, 6933 insertions(+) create mode 100644 .eslintrc.json create mode 100644 LICENSE create mode 100644 README.hbs create mode 100644 README.md create mode 100644 build/build.browser.tests.js create mode 100644 build/build.rollup.js create mode 100644 dist/bigint-utils-latest.browser.js create mode 100644 dist/bigint-utils-latest.browser.min.js create mode 100644 dist/bigint-utils-latest.browser.mod.js create mode 100644 dist/bigint-utils-latest.browser.mod.min.js create mode 100644 dist/bigint-utils-latest.node.js create mode 100644 dist/workerPrimalityTest.js create mode 100644 package-lock.json create mode 100644 package.json create mode 100644 src/browser-test-template.html create mode 100644 src/main.js create mode 100644 src/workerPrimalityTest.js create mode 100644 test/01_PrimeValidation.js create mode 100644 test/02_PrimeGeneration.js create mode 100644 test/browser/index.html create mode 100644 test/browser/tests.js diff --git a/.eslintrc.json b/.eslintrc.json new file mode 100644 index 0000000..9bb7d2e --- /dev/null +++ b/.eslintrc.json @@ -0,0 +1,36 @@ +{ + "env": { + "node": true, + "mocha": true, + "worker": true + }, + "parserOptions": { + "ecmaVersion": 2017, + "sourceType": "module" + }, + "extends": "eslint:recommended", + "rules": { + "no-console": 0, + "indent": [ + "error", + 4 + ], + "linebreak-style": [ + "error", + "unix" + ], + "quotes": [ + "error", + "single" + ], + "semi": [ + "error", + "always" + ] + }, + "globals": { + "BigInt": "readonly", + "window": "readonly", + "Uint8Array": "readonly" + } +} \ No newline at end of file diff --git a/LICENSE b/LICENSE new file mode 100644 index 0000000..b76dbea --- /dev/null +++ b/LICENSE @@ -0,0 +1,21 @@ +MIT License + +Copyright (c) 2018 Juan Hernández Serrano + +Permission is hereby granted, free of charge, to any person obtaining a copy +of this software and associated documentation files (the "Software"), to deal +in the Software without restriction, including without limitation the rights +to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +copies of the Software, and to permit persons to whom the Software is +furnished to do so, subject to the following conditions: + +The above copyright notice and this permission notice shall be included in all +copies or substantial portions of the Software. + +THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +SOFTWARE. diff --git a/README.hbs b/README.hbs new file mode 100644 index 0000000..e7de3ab --- /dev/null +++ b/README.hbs @@ -0,0 +1,87 @@ +# bigint-utils + +Some extra functions to work with modular arithmetics along with secure random numbers and probable prime (Miller-Rabin primality test) generation/testing using native JS (stage 3) implementation of BigInt. It can be used with Node.js (>=10.4.0) and [Web Browsers supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility). + +_The operations supported on BigInts are not constant time. BigInt can be therefore **[unsuitable for use in cryptography](https://www.chosenplaintext.ca/articles/beginners-guide-constant-time-cryptography.html)**_ + +Many platforms provide native support for cryptography, such as [webcrypto](https://w3c.github.io/webcrypto/Overview.html) or [node crypto](https://nodejs.org/dist/latest/docs/api/crypto.html). + +## Installation +bigint-utils is distributed as both an ES6 and a CJS module. + +The ES6 module is built for any [web browser supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility). The module only uses native javascript implementations and no polyfills had been applied. + +The CJS module is built as a standard node module. + +bigint-utils can be imported to your project with `npm`: +```bash +npm install bigint-utils +``` + +For web browsers, you can also [download the bundle from GitHub](https://raw.githubusercontent.com/juanelas/bigint-utils/master/dist/bigint-utils-latest.browser.mod.min.js). + +## Usage example + +With node js: +```javascript +const bigintUtils = require('bigint-utils'); + +// Stage 3 BigInts with value 666 can be declared as BigInt('666') +// or the shorter new no-so-linter-friendly syntax 666n +let a = BigInt('5'); +let b = BigInt('2'); +let n = BigInt('19'); + +console.log(bigintModArith.modPow(a, b, n)); // prints 6 + +console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3 + +console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2 + +// Generation of a probable prime of 2048 bits +const prime = await bigintUtils.prime(2048); + +// Testing if a prime is a probable prime (Miller-Rabin) +if ( await bigintUtils.isProbablyPrime(prime) ) + // code if is prime + +// Get a cryptographically secure random number between 1 and 2**256 bits. +const rnd = bigintUtils.randBetween(BigInt(2)**256); + +``` + +From a browser, you can just load the module in a html page as: +```html + +``` + +# bigint-utils JS Doc + +{{>main}} + +* * * diff --git a/README.md b/README.md new file mode 100644 index 0000000..c021819 --- /dev/null +++ b/README.md @@ -0,0 +1,290 @@ +# bigint-utils + +Some extra functions to work with modular arithmetics along with secure random numbers and probable prime (Miller-Rabin primality test) generation/testing using native JS (stage 3) implementation of BigInt. It can be used with Node.js (>=10.4.0) and [Web Browsers supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility). + +_The operations supported on BigInts are not constant time. BigInt can be therefore **[unsuitable for use in cryptography](https://www.chosenplaintext.ca/articles/beginners-guide-constant-time-cryptography.html)**_ + +Many platforms provide native support for cryptography, such as [webcrypto](https://w3c.github.io/webcrypto/Overview.html) or [node crypto](https://nodejs.org/dist/latest/docs/api/crypto.html). + +## Installation +bigint-utils is distributed as both an ES6 and a CJS module. + +The ES6 module is built for any [web browser supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility). The module only uses native javascript implementations and no polyfills had been applied. + +The CJS module is built as a standard node module. + +bigint-utils can be imported to your project with `npm`: +```bash +npm install bigint-utils +``` + +For web browsers, you can also [download the bundle from GitHub](https://raw.githubusercontent.com/juanelas/bigint-utils/master/dist/bigint-utils-latest.browser.mod.min.js). + +## Usage example + +With node js: +```javascript +const bigintUtils = require('bigint-utils'); + +// Stage 3 BigInts with value 666 can be declared as BigInt('666') +// or the shorter new no-so-linter-friendly syntax 666n +let a = BigInt('5'); +let b = BigInt('2'); +let n = BigInt('19'); + +console.log(bigintModArith.modPow(a, b, n)); // prints 6 + +console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3 + +console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2 + +// Generation of a probable prime of 2048 bits +const prime = await bigintUtils.prime(2048); + +// Testing if a prime is a probable prime (Miller-Rabin) +if ( await bigintUtils.isProbablyPrime(prime) ) + // code if is prime + +// Get a cryptographically secure random number between 1 and 2**256 bits. +const rnd = bigintUtils.randBetween(BigInt(2)**256); + +``` + +From a browser, you can just load the module in a html page as: +```html + +``` + +# bigint-utils JS Doc + +## Constants + +
+
abs ⇒ bigint
+

Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0

+
+
gcd ⇒ bigint
+

Greatest-common divisor of two integers based on the iterative binary algorithm.

+
+
lcm ⇒ bigint
+

The least common multiple computed as abs(a*b)/gcd(a,b)

+
+
toZn ⇒ bigint
+

Finds the smallest positive element that is congruent to a in modulo n

+
+
eGcd ⇒ egcdReturn
+

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).

+
+
modInv ⇒ bigint
+

Modular inverse.

+
+
modPow ⇒ bigint
+

Modular exponentiation a**b mod n

+
+
randBytes ⇒ Promise
+

Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process

+
+
randBetween ⇒ Promise
+

Returns a cryptographically secure random integer between [min,max]

+
+
isProbablyPrime ⇒ Promise
+

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)

+
+
prime ⇒ Promise
+

A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator

+
+
+ +## Typedefs + +
+
egcdReturn : Object
+

A triple (g, x, y), such that ax + by = g = gcd(a, b).

+
+
+ + + +## abs ⇒ bigint +Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0 + +**Kind**: global constant +**Returns**: bigint - the absolute value of a + +| Param | Type | +| --- | --- | +| a | number \| bigint | + + + +## gcd ⇒ bigint +Greatest-common divisor of two integers based on the iterative binary algorithm. + +**Kind**: global constant +**Returns**: bigint - The greatest common divisor of a and b + +| Param | Type | +| --- | --- | +| a | number \| bigint | +| b | number \| bigint | + + + +## lcm ⇒ bigint +The least common multiple computed as abs(a*b)/gcd(a,b) + +**Kind**: global constant +**Returns**: bigint - The least common multiple of a and b + +| Param | Type | +| --- | --- | +| a | number \| bigint | +| b | number \| bigint | + + + +## toZn ⇒ bigint +Finds the smallest positive element that is congruent to a in modulo n + +**Kind**: global constant +**Returns**: bigint - The smallest positive representation of a in modulo n + +| Param | Type | Description | +| --- | --- | --- | +| a | number \| bigint | An integer | +| n | number \| bigint | The modulo | + + + +## eGcd ⇒ [egcdReturn](#egcdReturn) +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). + +**Kind**: global constant + +| Param | Type | +| --- | --- | +| a | number \| bigint | +| b | number \| bigint | + + + +## modInv ⇒ bigint +Modular inverse. + +**Kind**: global constant +**Returns**: bigint - the inverse modulo n + +| Param | Type | Description | +| --- | --- | --- | +| a | number \| bigint | The number to find an inverse for | +| n | number \| bigint | The modulo | + + + +## modPow ⇒ bigint +Modular exponentiation a**b mod n + +**Kind**: global constant +**Returns**: bigint - a**b mod n + +| Param | Type | Description | +| --- | --- | --- | +| a | number \| bigint | base | +| b | number \| bigint | exponent | +| n | number \| bigint | modulo | + + + +## randBytes ⇒ Promise +Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process + +**Kind**: global constant +**Returns**: Promise - A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes + +| Param | Type | Description | +| --- | --- | --- | +| byteLength | number | The desired number of random bytes | +| forceLength | boolean | If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1 | + + + +## randBetween ⇒ Promise +Returns a cryptographically secure random integer between [min,max] + +**Kind**: global constant +**Returns**: Promise - A promise that resolves to a cryptographically secure random bigint between [min,max] + +| Param | Type | Description | +| --- | --- | --- | +| max | bigint | Returned value will be <= max | +| min | bigint | Returned value will be >= min | + + + +## isProbablyPrime ⇒ Promise +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) + +**Kind**: global constant +**Returns**: Promise - A promise that resolve to a boolean that is either true (a probably prime number) or false (definitely composite) + +| Param | Type | Description | +| --- | --- | --- | +| w | bigint | An integer to be tested for primality | +| iterations | number | The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3 | + + + +## prime ⇒ Promise +A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator + +**Kind**: global constant +**Returns**: Promise - A promise that resolves to a bigint probable prime of bitLength bits + +| Param | Type | Description | +| --- | --- | --- | +| bitLength | number | The required bit length for the generated prime | +| iterations | number | The number of iterations for the Miller-Rabin Probabilistic Primality Test | + + + +## egcdReturn : Object +A triple (g, x, y), such that ax + by = g = gcd(a, b). + +**Kind**: global typedef +**Properties** + +| Name | Type | +| --- | --- | +| g | bigint | +| x | bigint | +| y | bigint | + + +* * * diff --git a/build/build.browser.tests.js b/build/build.browser.tests.js new file mode 100644 index 0000000..4fac1e9 --- /dev/null +++ b/build/build.browser.tests.js @@ -0,0 +1,89 @@ +'use strict'; + +const rollup = require('rollup'); +const replace = require('rollup-plugin-replace'); +const resolve = require('rollup-plugin-node-resolve'); +const commonjs = require('rollup-plugin-commonjs'); +const multiEntry = require('rollup-plugin-multi-entry'); + +const fs = require('fs'); +const path = require('path'); +const pkgJson = require('../package.json'); + +const rootDir = path.join(__dirname, '..'); + + +// Let's first create the appropriate html file loading mocha, chai and a bundle of the tests +const templatePath = path.join(rootDir, 'src', 'browser-test-template.html'); +const dstDir = path.join(rootDir, 'test', 'browser'); +const dstFileName = path.join(dstDir, 'index.html'); + +const template = fs.readFileSync(templatePath, 'utf-8'); +const testsJs = ` + +`; +fs.writeFileSync(dstFileName, template.replace('{{TESTS}}', testsJs)); + +/* +Now we create a bundle of all the tests called test.js +require/import of the module and chai are removed since they will be loaded from the html file +*/ +const distFile = path.relative(path.join(rootDir, 'test'), pkgJson.main); +const requireModuleLine = `const ${camelise(pkgJson.name)} = require('${path.join(path.dirname(distFile), path.basename(distFile, '.js'))}');`; + +const buildOptions = [ + { // Browser + input: { + input: path.join(rootDir, 'test', '*.js'), + external: ['chai'], + plugins: [ + multiEntry({ exports: false }), + replace({ + 'const chai = require(\'chai\');': '', + [requireModuleLine]: '', + 'delimiters': ['', ''], + 'process.browser': true + }), + resolve({ + browser: true, + }), + commonjs() + ], + }, + output: { + file: path.join(rootDir, 'test', 'browser', 'tests.js'), + format: 'esm' + } + } +]; + +for (const options of buildOptions) { + build(options); +} + + + +/* --- HELPLER FUNCTIONS --- */ + +async function build(options) { + // create a bundle + const bundle = await rollup.rollup(options.input); + + // generate code + await bundle.generate(options.output); + + // or write the bundle to disk + await bundle.write(options.output); +} + +function camelise(str) { + return str.replace(/-([a-z])/g, + function (m, w) { + return w.toUpperCase(); + }); +} \ No newline at end of file diff --git a/build/build.rollup.js b/build/build.rollup.js new file mode 100644 index 0000000..ecb5921 --- /dev/null +++ b/build/build.rollup.js @@ -0,0 +1,135 @@ +'use strict'; + +const rollup = require('rollup'); +const replace = require('rollup-plugin-replace'); +const minify = require('rollup-plugin-babel-minify'); +const fs = require('fs'); +const path = require('path'); +const pkgJson = require('../package.json'); + +const rootDir = path.join(__dirname, '..'); +const srcDir = path.join(rootDir, 'src'); +const dstDir = path.join(rootDir, 'dist'); + +const buildOptions = [ + { // Browser + input: { + input: path.join(srcDir, 'main.js'), + plugins: [ + replace({ + 'process.browser': true + }) + ] + }, + output: { + file: path.join(dstDir, `${pkgJson.name}-${pkgJson.version}.browser.js`), + format: 'iife', + name: camelise(pkgJson.name) + } + }, + // { // Browser minified + // input: { + // input: path.join(srcDir, 'main.js'), + // plugins: [ + // replace({ + // 'process.browser': true + // }), + // minify({ + // 'comments': false + // }) + // ], + // }, + // output: { + // file: path.join(dstDir, `${pkgJson.name}-${pkgJson.version}.browser.min.js`), + // format: 'iife', + // name: camelise(pkgJson.name) + // } + // }, + { // Browser esm + input: { + input: path.join(srcDir, 'main.js'), + plugins: [ + replace({ + 'process.browser': true + }) + ] + }, + output: { + file: path.join(dstDir, `${pkgJson.name}-${pkgJson.version}.browser.mod.js`), + format: 'esm' + } + }, + // { // Browser esm minified + // input: { + // input: path.join(srcDir, 'main.js'), + // plugins: [ + // replace({ + // 'process.browser': true + // }), + // minify({ + // 'comments': false + // }) + // ], + // }, + // output: { + // file: path.join(dstDir, `${pkgJson.name}-${pkgJson.version}.browser.mod.min.js`), + // format: 'esm' + // } + // }, + { // Node + input: { + input: path.join(srcDir, 'main.js'), + plugins: [ + replace({ + 'process.browser': false + }) + ] + }, + output: { + file: path.join(dstDir, `${pkgJson.name}-${pkgJson.version}.node.js`), + format: 'cjs' + } + } +]; + +for (const options of buildOptions) { + build(options); +} + + + +// Let's manually build the worker file +const workerFilename = path.join(srcDir, 'workerPrimalityTest.js'); +const dstFileName = path.join(dstDir, 'workerPrimalityTest.js'); + +const workerFile = fs.readFileSync(workerFilename, 'utf-8'); + +fs.writeFileSync(dstFileName, workerFile.replace('{{IIFE}}', `./${pkgJson.name}-latest.browser.js`)); + + + +/* --- HELPLER FUNCTIONS --- */ + +async function build(options) { + // create a bundle + const bundle = await rollup.rollup(options.input); + + // generate code + await bundle.generate(options.output); + + // or write the bundle to disk + await bundle.write(options.output); + + // copy the latest build as pkg_name-latest + fs.copyFileSync( + options.output.file, + options.output.file.replace(`${pkgJson.name}-${pkgJson.version}.`, `${pkgJson.name}-latest.`) + ); +} + +function camelise(str) { + return str.replace(/-([a-z])/g, + function (m, w) { + return w.toUpperCase(); + }); +} \ No newline at end of file diff --git a/dist/bigint-utils-latest.browser.js b/dist/bigint-utils-latest.browser.js new file mode 100644 index 0000000..1413386 --- /dev/null +++ b/dist/bigint-utils-latest.browser.js @@ -0,0 +1,629 @@ +var bigintUtils = (function (exports) { + 'use strict'; + + /** + * Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0 + * + * @param {number|bigint} a + * + * @returns {bigint} the absolute value of a + */ + const abs = function (a) { + a = BigInt(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). + * @property {bigint} g + * @property {bigint} x + * @property {bigint} y + */ + /** + * 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 {number|bigint} a + * @param {number|bigint} b + * + * @returns {egcdReturn} + */ + const eGcd = function (a, b) { + a = BigInt(a); + b = BigInt(b); + let x = BigInt(0); + let y = BigInt(1); + let u = BigInt(1); + let v = BigInt(0); + + while (a !== BigInt(0)) { + let q = b / a; + let r = b % a; + let m = x - (u * q); + let n = y - (v * q); + b = a; + a = r; + x = u; + y = v; + u = m; + v = n; + } + return { + b: b, + x: x, + y: y + }; + }; + + /** + * Modular inverse. + * + * @param {number|bigint} a The number to find an inverse for + * @param {number|bigint} n The modulo + * + * @returns {bigint} the inverse modulo n + */ + const modInv = function (a, n) { + let egcd = eGcd(a, n); + if (egcd.b !== BigInt(1)) { + return null; // modular inverse does not exist + } else { + return toZn(egcd.x, n); + } + }; + + /** + * Modular exponentiation a**b mod n + * @param {number|bigint} a base + * @param {number|bigint} b exponent + * @param {number|bigint} n modulo + * + * @returns {bigint} a**b mod n + */ + const modPow = function (a, b, n) { + // See Knuth, volume 2, section 4.6.3. + n = BigInt(n); + a = toZn(a, n); + b = BigInt(b); + if (b < BigInt(0)) { + return modInv(modPow(a, abs(b), n), n); + } + let result = BigInt(1); + let x = a; + while (b > 0) { + var leastSignificantBit = b % BigInt(2); + b = b / BigInt(2); + if (leastSignificantBit == BigInt(1)) { + result = result * x; + result = result % n; + } + x = x * x; + x = x % n; + } + return result; + }; + + /** + * Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process + * + * @param {number} byteLength The desired number of random bytes + * @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 + * + * @returns {Promise} A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes + */ + const randBytes = async function (byteLength, forceLength = false) { + return new Promise((resolve) => { + let buf; + + { // 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] + * @param {bigint} max Returned value will be <= max + * @param {bigint} min Returned value will be >= min + * + * @returns {Promise} A promise that resolves to a cryptographically secure random bigint between [min,max] + */ + const randBetween = async function (max, min = 1) { + let bitLen = bitLength(max); + let byteLength = bitLen >> 3; + let remaining = bitLen - (byteLength * 8); + let extraBits; + if (remaining > 0) { + byteLength++; + extraBits = 2 ** remaining - 1; + } + + let rnd; + do { + let buf = await randBytes(byteLength); + // remove extra bits + if (remaining > 0) + buf[0] = buf[0] & extraBits; + rnd = fromBuffer(buf); + } while (rnd > max || rnd < min); + return rnd; + }; + + /** + * 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) { + /* + 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 === BigInt(2)) + return true; + else if ((w & BigInt(1)) === BigInt(0) || w === BigInt(1)) + 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 = [ + 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 i = 0; i < firstPrimes.length && (BigInt(firstPrimes[i]) <= w); i++) { + const p = BigInt(firstPrimes[i]); + if (w === p) + return true; + else if (w % p === BigInt(0)) + 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 = BigInt(0), d = w - BigInt(1); + while (d % BigInt(2) === BigInt(0)) { + d /= BigInt(2); + ++a; + } + + let m = (w - BigInt(1)) / (BigInt(2) ** a); + + loop: do { + let b = await randBetween(w - BigInt(1), 2); + let z = modPow(b, m, w); + if (z === BigInt(1) || z === w - BigInt(1)) + continue; + + for (let j = 1; j < a; j++) { + z = modPow(z, BigInt(2), w); + if (z === w - BigInt(1)) + continue loop; + if (z === BigInt(1)) + break; + } + return false; + } while (--iterations); + + 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++) { + const moduleDir = new URL('./', (document.currentScript && document.currentScript.src || new URL('bigint-utils-0.9.0.browser.js', document.baseURI).href)).pathname; + let newWorker = new Worker(`${moduleDir}/workerPrimalityTest.js`); + 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; + } + + exports.abs = abs; + exports.eGcd = eGcd; + exports.gcd = gcd; + exports.isProbablyPrime = isProbablyPrime; + exports.lcm = lcm; + exports.modInv = modInv; + exports.modPow = modPow; + exports.prime = prime; + exports.randBetween = randBetween; + exports.randBytes = randBytes; + exports.toZn = toZn; + + return exports; + +}({})); diff --git a/dist/bigint-utils-latest.browser.min.js b/dist/bigint-utils-latest.browser.min.js new file mode 100644 index 0000000..b581ef7 --- /dev/null +++ b/dist/bigint-utils-latest.browser.min.js @@ -0,0 +1 @@ +var bigintUtils=function(a){'use strict';function b(a){let b=BigInt(0);for(let c of a.values()){let a=BigInt(c);b=(b<>=BigInt(1))>BigInt(1));return c}const d=function(b){return b=BigInt(b),b>=BigInt(0)?b:-b},e=function(c,e){c=d(c),e=d(e);let f=BigInt(0);for(;!((c|e)&BigInt(1));)c>>=BigInt(1),e>>=BigInt(1),f++;for(;!(c&BigInt(1));)c>>=BigInt(1);do{for(;!(e&BigInt(1));)e>>=BigInt(1);if(c>e){let a=c;c=e,e=a}e-=c}while(e);return c<b?b+c: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(b,a){let c=g(b,a);return c.b===BigInt(1)?f(c.x,a):null},i=function(c,e,g){if(g=BigInt(g),c=f(c,g),e=BigInt(e),e{let d;const e=(a,d)=>{b&&(d[0]|=128),c(d)};d=new Uint8Array(a),l(d,e)})},k=async function(a,d=1){let e,f=c(a),g=f>>3,h=f-8*g;0a||i{onmessage=function(a){const b=self.crypto.getRandomValues(a.data.buf);self.postMessage({buf:b,id:a.data.id})}});return a}();return a.abs=d,a.eGcd=g,a.gcd=e,a.isProbablyPrime=async function(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{if(e.data.isPrime){for(let a=0;a=0. abs(a)==-a if a<0 + * + * @param {number|bigint} a + * + * @returns {bigint} the absolute value of a + */ +const abs = function (a) { + a = BigInt(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). + * @property {bigint} g + * @property {bigint} x + * @property {bigint} y + */ +/** + * 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 {number|bigint} a + * @param {number|bigint} b + * + * @returns {egcdReturn} + */ +const eGcd = function (a, b) { + a = BigInt(a); + b = BigInt(b); + let x = BigInt(0); + let y = BigInt(1); + let u = BigInt(1); + let v = BigInt(0); + + while (a !== BigInt(0)) { + let q = b / a; + let r = b % a; + let m = x - (u * q); + let n = y - (v * q); + b = a; + a = r; + x = u; + y = v; + u = m; + v = n; + } + return { + b: b, + x: x, + y: y + }; +}; + +/** + * Modular inverse. + * + * @param {number|bigint} a The number to find an inverse for + * @param {number|bigint} n The modulo + * + * @returns {bigint} the inverse modulo n + */ +const modInv = function (a, n) { + let egcd = eGcd(a, n); + if (egcd.b !== BigInt(1)) { + return null; // modular inverse does not exist + } else { + return toZn(egcd.x, n); + } +}; + +/** + * Modular exponentiation a**b mod n + * @param {number|bigint} a base + * @param {number|bigint} b exponent + * @param {number|bigint} n modulo + * + * @returns {bigint} a**b mod n + */ +const modPow = function (a, b, n) { + // See Knuth, volume 2, section 4.6.3. + n = BigInt(n); + a = toZn(a, n); + b = BigInt(b); + if (b < BigInt(0)) { + return modInv(modPow(a, abs(b), n), n); + } + let result = BigInt(1); + let x = a; + while (b > 0) { + var leastSignificantBit = b % BigInt(2); + b = b / BigInt(2); + if (leastSignificantBit == BigInt(1)) { + result = result * x; + result = result % n; + } + x = x * x; + x = x % n; + } + return result; +}; + +/** + * Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process + * + * @param {number} byteLength The desired number of random bytes + * @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 + * + * @returns {Promise} A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes + */ +const randBytes = async function (byteLength, forceLength = false) { + return new Promise((resolve) => { + let buf; + + { // 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] + * @param {bigint} max Returned value will be <= max + * @param {bigint} min Returned value will be >= min + * + * @returns {Promise} A promise that resolves to a cryptographically secure random bigint between [min,max] + */ +const randBetween = async function (max, min = 1) { + let bitLen = bitLength(max); + let byteLength = bitLen >> 3; + let remaining = bitLen - (byteLength * 8); + let extraBits; + if (remaining > 0) { + byteLength++; + extraBits = 2 ** remaining - 1; + } + + let rnd; + do { + let buf = await randBytes(byteLength); + // remove extra bits + if (remaining > 0) + buf[0] = buf[0] & extraBits; + rnd = fromBuffer(buf); + } while (rnd > max || rnd < min); + return rnd; +}; + +/** + * 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) { + /* + 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 === BigInt(2)) + return true; + else if ((w & BigInt(1)) === BigInt(0) || w === BigInt(1)) + 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 = [ + 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 i = 0; i < firstPrimes.length && (BigInt(firstPrimes[i]) <= w); i++) { + const p = BigInt(firstPrimes[i]); + if (w === p) + return true; + else if (w % p === BigInt(0)) + 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 = BigInt(0), d = w - BigInt(1); + while (d % BigInt(2) === BigInt(0)) { + d /= BigInt(2); + ++a; + } + + let m = (w - BigInt(1)) / (BigInt(2) ** a); + + loop: do { + let b = await randBetween(w - BigInt(1), 2); + let z = modPow(b, m, w); + if (z === BigInt(1) || z === w - BigInt(1)) + continue; + + for (let j = 1; j < a; j++) { + z = modPow(z, BigInt(2), w); + if (z === w - BigInt(1)) + continue loop; + if (z === BigInt(1)) + break; + } + return false; + } while (--iterations); + + 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++) { + const moduleDir = new URL('./', import.meta.url).pathname; + let newWorker = new Worker(`${moduleDir}/workerPrimalityTest.js`); + 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 }; diff --git a/dist/bigint-utils-latest.browser.mod.min.js b/dist/bigint-utils-latest.browser.mod.min.js new file mode 100644 index 0000000..a5b6532 --- /dev/null +++ b/dist/bigint-utils-latest.browser.mod.min.js @@ -0,0 +1 @@ +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<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{let d;const e=(a,d)=>{b&&(d[0]|=128),c(d)};d=new Uint8Array(a),getRandomValuesWorker(d,e)})},randBetween=async function(a,b=1){let c,d=bitLength(a),e=d>>3,f=d-8*e;0a||g{if(e.data.isPrime){for(let a=0;a{onmessage=function(a){const b=self.crypto.getRandomValues(a.data.buf);self.postMessage({buf:b,id:a.data.id})}});return a}();function fromBuffer(a){let b=BigInt(0);for(let c of a.values()){let a=BigInt(c);b=(b<>=BigInt(1))>BigInt(1));return c}export{abs,eGcd,gcd,isProbablyPrime,lcm,modInv,modPow,prime,randBetween,randBytes,toZn}; diff --git a/dist/bigint-utils-latest.node.js b/dist/bigint-utils-latest.node.js new file mode 100644 index 0000000..51363a5 --- /dev/null +++ b/dist/bigint-utils-latest.node.js @@ -0,0 +1,599 @@ +'use strict'; + +Object.defineProperty(exports, '__esModule', { value: true }); + +/** + * Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0 + * + * @param {number|bigint} a + * + * @returns {bigint} the absolute value of a + */ +const abs = function (a) { + a = BigInt(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). + * @property {bigint} g + * @property {bigint} x + * @property {bigint} y + */ +/** + * 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 {number|bigint} a + * @param {number|bigint} b + * + * @returns {egcdReturn} + */ +const eGcd = function (a, b) { + a = BigInt(a); + b = BigInt(b); + let x = BigInt(0); + let y = BigInt(1); + let u = BigInt(1); + let v = BigInt(0); + + while (a !== BigInt(0)) { + let q = b / a; + let r = b % a; + let m = x - (u * q); + let n = y - (v * q); + b = a; + a = r; + x = u; + y = v; + u = m; + v = n; + } + return { + b: b, + x: x, + y: y + }; +}; + +/** + * Modular inverse. + * + * @param {number|bigint} a The number to find an inverse for + * @param {number|bigint} n The modulo + * + * @returns {bigint} the inverse modulo n + */ +const modInv = function (a, n) { + let egcd = eGcd(a, n); + if (egcd.b !== BigInt(1)) { + return null; // modular inverse does not exist + } else { + return toZn(egcd.x, n); + } +}; + +/** + * Modular exponentiation a**b mod n + * @param {number|bigint} a base + * @param {number|bigint} b exponent + * @param {number|bigint} n modulo + * + * @returns {bigint} a**b mod n + */ +const modPow = function (a, b, n) { + // See Knuth, volume 2, section 4.6.3. + n = BigInt(n); + a = toZn(a, n); + b = BigInt(b); + if (b < BigInt(0)) { + return modInv(modPow(a, abs(b), n), n); + } + let result = BigInt(1); + let x = a; + while (b > 0) { + var leastSignificantBit = b % BigInt(2); + b = b / BigInt(2); + if (leastSignificantBit == BigInt(1)) { + result = result * x; + result = result % n; + } + x = x * x; + x = x % n; + } + return result; +}; + +/** + * Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process + * + * @param {number} byteLength The desired number of random bytes + * @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 + * + * @returns {Promise} A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes + */ +const randBytes = async function (byteLength, forceLength = false) { + return new Promise((resolve) => { + 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); + }); + } + }); +}; + + +/** + * Returns a cryptographically secure random integer between [min,max] + * @param {bigint} max Returned value will be <= max + * @param {bigint} min Returned value will be >= min + * + * @returns {Promise} A promise that resolves to a cryptographically secure random bigint between [min,max] + */ +const randBetween = async function (max, min = 1) { + let bitLen = bitLength(max); + let byteLength = bitLen >> 3; + let remaining = bitLen - (byteLength * 8); + let extraBits; + if (remaining > 0) { + byteLength++; + extraBits = 2 ** remaining - 1; + } + + let rnd; + do { + let buf = await randBytes(byteLength); + // remove extra bits + if (remaining > 0) + buf[0] = buf[0] & extraBits; + rnd = fromBuffer(buf); + } while (rnd > max || rnd < min); + return rnd; +}; + +/** + * 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) { + /* + 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 === BigInt(2)) + return true; + else if ((w & BigInt(1)) === BigInt(0) || w === BigInt(1)) + 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 = [ + 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 i = 0; i < firstPrimes.length && (BigInt(firstPrimes[i]) <= w); i++) { + const p = BigInt(firstPrimes[i]); + if (w === p) + return true; + else if (w % p === BigInt(0)) + 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 = BigInt(0), d = w - BigInt(1); + while (d % BigInt(2) === BigInt(0)) { + d /= BigInt(2); + ++a; + } + + let m = (w - BigInt(1)) / (BigInt(2) ** a); + + loop: do { + let b = await randBetween(w - BigInt(1), 2); + let z = modPow(b, m, w); + if (z === BigInt(1) || z === w - BigInt(1)) + continue; + + for (let j = 1; j < a; j++) { + z = modPow(z, BigInt(2), w); + if (z === w - BigInt(1)) + continue loop; + if (z === BigInt(1)) + break; + } + return false; + } while (--iterations); + + 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.eGcd = eGcd; +exports.gcd = gcd; +exports.isProbablyPrime = isProbablyPrime; +exports.lcm = lcm; +exports.modInv = modInv; +exports.modPow = modPow; +exports.prime = prime; +exports.randBetween = randBetween; +exports.randBytes = randBytes; +exports.toZn = toZn; diff --git a/dist/workerPrimalityTest.js b/dist/workerPrimalityTest.js new file mode 100644 index 0000000..31057f8 --- /dev/null +++ b/dist/workerPrimalityTest.js @@ -0,0 +1,14 @@ +'use strict'; + +//const window = self; + +importScripts('./bigint-utils-latest.browser.js'); // to be replaced during build with rollup replace + +onmessage = async function(event) { // Let's start once we are called + // event.data = {rnd: , iterations: } + const isPrime = await bigintUtils.isProbablyPrime(event.data.rnd, event.data.iterations); + postMessage({ + 'isPrime': isPrime, + 'value' : event.data.rnd + }); +}; \ No newline at end of file diff --git a/package-lock.json b/package-lock.json new file mode 100644 index 0000000..42626e3 --- /dev/null +++ b/package-lock.json @@ -0,0 +1,3515 @@ +{ + "name": "bigint-utils", + "version": "0.9.0", + "lockfileVersion": 1, + "requires": true, + "dependencies": { + "@babel/code-frame": { + "version": "7.0.0", + "resolved": "https://registry.npmjs.org/@babel/code-frame/-/code-frame-7.0.0.tgz", + "integrity": "sha512-OfC2uemaknXr87bdLUkWog7nYuliM9Ij5HUcajsVcMCpQrcLmtxRbVFTIqmcSkSeYRBFBRxs2FiUqFJDLdiebA==", + "dev": true, + "requires": { + 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"dev": true, + "requires": { + "camelcase": "^5.0.0", + "decamelize": "^1.2.0" + } + } + } + } + } +} diff --git a/package.json b/package.json new file mode 100644 index 0000000..e8bd3d1 --- /dev/null +++ b/package.json @@ -0,0 +1,46 @@ +{ + "name": "bigint-utils", + "version": "0.9.0", + "description": "Arbitrary precision modular arithmetics, cryptographically secure random numbers and prime generation/testing using native JS (stage 3) implementation of BigInt", + "keywords": [ + "modular arithmetics", + "prime", + "rng", + "prng", + "primality test", + "BigInt" + ], + "license": "MIT", + "author": { + "name": "Juan Hernández Serrano", + "email": "jserrano@entel.upc.edu", + "url": "https://github.com/juanelas" + }, + "repository": "github:juanelas/bigint-utils", + "main": "./dist/bigint-utils-latest.node.js", + "browser": "./dist/bigint-utils-latest.browser.mod.js", + "directories": { + "build": "./build", + "dist": "./dist", + "src": "./src", + "test": "./test" + }, + "scripts": { + "test": "mocha --timeout 600000", + "build": "node build/build.rollup.js", + "build:browserTests": "node build/build.browser.tests.js", + "build:docs": "jsdoc2md --template=README.hbs --files ./src/main.js > README.md", + "prepublishOnly": "npm run build && npm run build:docs" + }, + "devDependencies": { + "chai": "^4.2.0", + "jsdoc-to-markdown": "^4.0.1", + "mocha": "^6.1.3", + "rollup": "^1.10.0", + "rollup-plugin-babel-minify": "^8.0.0", + "rollup-plugin-commonjs": "^9.3.4", + "rollup-plugin-multi-entry": "^2.1.0", + "rollup-plugin-node-resolve": "^4.2.3", + "rollup-plugin-replace": "^2.2.0" + } +} diff --git a/src/browser-test-template.html b/src/browser-test-template.html new file mode 100644 index 0000000..04ec5a4 --- /dev/null +++ b/src/browser-test-template.html @@ -0,0 +1,15 @@ + + + + Mocha Tests + + + +
+ + + + + {{TESTS}} + + \ No newline at end of file diff --git a/src/main.js b/src/main.js new file mode 100644 index 0000000..7179c2a --- /dev/null +++ b/src/main.js @@ -0,0 +1,628 @@ +'use strict'; + +/** + * Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0 + * + * @param {number|bigint} a + * + * @returns {bigint} the absolute value of a + */ +export const abs = function (a) { + a = BigInt(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 + */ +export 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 + */ +export 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 + */ +export 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). + * @property {bigint} g + * @property {bigint} x + * @property {bigint} y + */ +/** + * 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 {number|bigint} a + * @param {number|bigint} b + * + * @returns {egcdReturn} + */ +export const eGcd = function (a, b) { + a = BigInt(a); + b = BigInt(b); + let x = BigInt(0); + let y = BigInt(1); + let u = BigInt(1); + let v = BigInt(0); + + while (a !== BigInt(0)) { + let q = b / a; + let r = b % a; + let m = x - (u * q); + let n = y - (v * q); + b = a; + a = r; + x = u; + y = v; + u = m; + v = n; + } + return { + b: b, + x: x, + y: y + }; +}; + +/** + * Modular inverse. + * + * @param {number|bigint} a The number to find an inverse for + * @param {number|bigint} n The modulo + * + * @returns {bigint} the inverse modulo n + */ +export const modInv = function (a, n) { + let egcd = eGcd(a, n); + if (egcd.b !== BigInt(1)) { + return null; // modular inverse does not exist + } else { + return toZn(egcd.x, n); + } +}; + +/** + * Modular exponentiation a**b mod n + * @param {number|bigint} a base + * @param {number|bigint} b exponent + * @param {number|bigint} n modulo + * + * @returns {bigint} a**b mod n + */ +export const modPow = function (a, b, n) { + // See Knuth, volume 2, section 4.6.3. + n = BigInt(n); + a = toZn(a, n); + b = BigInt(b); + if (b < BigInt(0)) { + return modInv(modPow(a, abs(b), n), n); + } + let result = BigInt(1); + let x = a; + while (b > 0) { + var leastSignificantBit = b % BigInt(2); + b = b / BigInt(2); + if (leastSignificantBit == BigInt(1)) { + result = result * x; + result = result % n; + } + x = x * x; + x = x % n; + } + return result; +}; + +/** + * Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process + * + * @param {number} byteLength The desired number of random bytes + * @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 + * + * @returns {Promise} A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes + */ +export const randBytes = async function (byteLength, forceLength = false) { + return new Promise((resolve) => { + let buf; + + if (!process.browser) { // 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); + }); + } else { // 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] + * @param {bigint} max Returned value will be <= max + * @param {bigint} min Returned value will be >= min + * + * @returns {Promise} A promise that resolves to a cryptographically secure random bigint between [min,max] + */ +export const randBetween = async function (max, min = 1) { + let bitLen = bitLength(max); + let byteLength = bitLen >> 3; + let remaining = bitLen - (byteLength * 8); + let extraBits; + if (remaining > 0) { + byteLength++; + extraBits = 2 ** remaining - 1; + } + + let rnd; + do { + let buf = await randBytes(byteLength); + // remove extra bits + if (remaining > 0) + buf[0] = buf[0] & extraBits; + rnd = fromBuffer(buf); + } while (rnd > max || rnd < min); + return rnd; +}; + +/** + * 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) + */ +export const isProbablyPrime = async function (w, iterations = 16) { + /* + 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 === BigInt(2)) + return true; + else if ((w & BigInt(1)) === BigInt(0) || w === BigInt(1)) + 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 = [ + 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 i = 0; i < firstPrimes.length && (BigInt(firstPrimes[i]) <= w); i++) { + const p = BigInt(firstPrimes[i]); + if (w === p) + return true; + else if (w % p === BigInt(0)) + 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 = BigInt(0), d = w - BigInt(1); + while (d % BigInt(2) === BigInt(0)) { + d /= BigInt(2); + ++a; + } + + let m = (w - BigInt(1)) / (BigInt(2) ** a); + + loop: do { + let b = await randBetween(w - BigInt(1), 2); + let z = modPow(b, m, w); + if (z === BigInt(1) || z === w - BigInt(1)) + continue; + + for (let j = 1; j < a; j++) { + z = modPow(z, BigInt(2), w); + if (z === w - BigInt(1)) + continue loop; + if (z === BigInt(1)) + break; + } + return false; + } while (--iterations); + + 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 + */ +export const prime = async function (bitLength, iterations = 16) { + return new Promise(async (resolve) => { + if (process.browser) { + let workerList = []; + for (let i = 0; i < self.navigator.hardwareConcurrency; i++) { + const moduleDir = new URL('./', import.meta.url).pathname; + let newWorker = new Worker(`${moduleDir}/workerPrimalityTest.js`); + 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 + }); + } + + } else { + 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; +} diff --git a/src/workerPrimalityTest.js b/src/workerPrimalityTest.js new file mode 100644 index 0000000..1d45592 --- /dev/null +++ b/src/workerPrimalityTest.js @@ -0,0 +1,14 @@ +'use strict'; + +//const window = self; + +importScripts('{{IIFE}}'); // to be replaced during build with rollup replace + +onmessage = async function(event) { // Let's start once we are called + // event.data = {rnd: , iterations: } + const isPrime = await bigintUtils.isProbablyPrime(event.data.rnd, event.data.iterations); + postMessage({ + 'isPrime': isPrime, + 'value' : event.data.rnd + }); +}; \ No newline at end of file diff --git a/test/01_PrimeValidation.js b/test/01_PrimeValidation.js new file mode 100644 index 0000000..0cdc0e7 --- /dev/null +++ b/test/01_PrimeValidation.js @@ -0,0 +1,60 @@ +'use strict'; + +// For the browser test builder to work you MUST import them module in a variable that +// is the camelised version of the package name. +const bigintUtils = require('../dist/bigint-utils-latest.node'); +const chai = require('chai'); + +const numbers = [ + { + value: BigInt(1), + prime: false + }, + { + value: BigInt(2), + prime: true + }, + { + value: BigInt(3), + prime: true + }, + { + value: BigInt(15), + prime: false + }, + { + value: BigInt(29), + prime: true + }, + { + value: BigInt('669483106578092405936560831017556154622901950048903016651289'), + prime: true + }, + { + value: BigInt('2074722246773485207821695222107608587480996474721117292752992589912196684750549658310084416732550077'), + prime: true + }, + { + value: BigInt('2074722246773485207821695222107608587480996474721117292752992589912196684750549658310084416732550079'), + prime: false + }, + { + value: BigInt('115922179551495973383410176342643722334557255682879605864838806293659619625004303206250384392546855063844106965156287951749387634112551089284595541103692716528774876311641700929986988023197242224581099872580798960693521778607396791006450968430359009613295725905514216842343121690916290236558767890728449777'), + prime: true + }, + { + value: BigInt('918145944120889203205646923554374144932845997937845799234617798611046542304088105084854788397071323714642587188481158334265864050544813693415594035822877094557870151480865568334936301231664228940480803192289508235412296324312748621874408067955753620604885023289655277704554716080844406284392300643321715285709865081125252390440327650852470312931679380011885102491340191287595160450544053114365852338670819405357496612993587404998677760882578064637552397840566752638770525765833183986360029736508910848408875329873614164495552615086579144675027852136994842529623698055210822311666048300438808691619782893307972452223713060928388502843564836966586109748062827799521852219158489504529458627699284110902303538160168376473182639384638674469114371472053977558648090155686345760457454061117853710619580819749222459422610617170567016772342291486643520567969321969827786373531753524990712622940069883277763528926899970596407140603912036918433859986491820017690762751824769335720368488097262208835708414085501930989486498185503469986946236128468697606998536541209764920494156326791142098506801288127033229779646920082892258428128572765585196779698362187479280520327053508580551167899837393726371144977951402741307021389967382422805567365901203'), + prime: true + } +]; + +describe('Testing validation of prime numbers', function () { + for (const num of numbers) { + describe(`isProbablyPrime(${num.value})`, function () { + it(`should return ${num.prime}`, async function () { + const ret = await bigintUtils.isProbablyPrime(num.value); + chai.expect(ret).to.equal(num.prime); + }); + }); + } +}); \ No newline at end of file diff --git a/test/02_PrimeGeneration.js b/test/02_PrimeGeneration.js new file mode 100644 index 0000000..e6c13ed --- /dev/null +++ b/test/02_PrimeGeneration.js @@ -0,0 +1,31 @@ +'use strict'; + +// For the browser test builder to work you MUST import them module in a variable that +// is the camelised version of the package name. +const bigintUtils = require('../dist/bigint-utils-latest.node'); +const chai = require('chai'); + +const bitLengths = [ + 256, + 512, + 1024, + 2048, + 3072 +]; + +describe('Testing generation of prime numbers', function () { + for (const bitLength of bitLengths) { + describe(`Executing prime(${bitLength})`, function () { + it(`should return a random ${bitLength}-bits probable prime`, async function () { + let prime = await bigintUtils.prime(bitLength); + const ret = await bigintUtils.isProbablyPrime(prime); + chai.expect(ret).to.equal(true); + let bits = 1; + do { + bits++; + } while ((prime >>= BigInt(1)) > BigInt(1)); + chai.expect(bits).to.equal(bitLength); + }); + }); + } +}); \ No newline at end of file diff --git a/test/browser/index.html b/test/browser/index.html new file mode 100644 index 0000000..3ed7ace --- /dev/null +++ b/test/browser/index.html @@ -0,0 +1,22 @@ + + + + Mocha Tests + + + +
+ + + + + + + + + \ No newline at end of file diff --git a/test/browser/tests.js b/test/browser/tests.js new file mode 100644 index 0000000..aa9cbd4 --- /dev/null +++ b/test/browser/tests.js @@ -0,0 +1,88 @@ +// For the browser test builder to work you MUST import them module in a variable that +// is the camelised version of the package name. + + + +const numbers = [ + { + value: BigInt(1), + prime: false + }, + { + value: BigInt(2), + prime: true + }, + { + value: BigInt(3), + prime: true + }, + { + value: BigInt(15), + prime: false + }, + { + value: BigInt(29), + prime: true + }, + { + value: BigInt('669483106578092405936560831017556154622901950048903016651289'), + prime: true + }, + { + value: BigInt('2074722246773485207821695222107608587480996474721117292752992589912196684750549658310084416732550077'), + prime: true + }, + { + value: BigInt('2074722246773485207821695222107608587480996474721117292752992589912196684750549658310084416732550079'), + prime: false + }, + { + value: BigInt('115922179551495973383410176342643722334557255682879605864838806293659619625004303206250384392546855063844106965156287951749387634112551089284595541103692716528774876311641700929986988023197242224581099872580798960693521778607396791006450968430359009613295725905514216842343121690916290236558767890728449777'), + prime: true + }, + { + value: BigInt('918145944120889203205646923554374144932845997937845799234617798611046542304088105084854788397071323714642587188481158334265864050544813693415594035822877094557870151480865568334936301231664228940480803192289508235412296324312748621874408067955753620604885023289655277704554716080844406284392300643321715285709865081125252390440327650852470312931679380011885102491340191287595160450544053114365852338670819405357496612993587404998677760882578064637552397840566752638770525765833183986360029736508910848408875329873614164495552615086579144675027852136994842529623698055210822311666048300438808691619782893307972452223713060928388502843564836966586109748062827799521852219158489504529458627699284110902303538160168376473182639384638674469114371472053977558648090155686345760457454061117853710619580819749222459422610617170567016772342291486643520567969321969827786373531753524990712622940069883277763528926899970596407140603912036918433859986491820017690762751824769335720368488097262208835708414085501930989486498185503469986946236128468697606998536541209764920494156326791142098506801288127033229779646920082892258428128572765585196779698362187479280520327053508580551167899837393726371144977951402741307021389967382422805567365901203'), + prime: true + } +]; + +describe('Testing validation of prime numbers', function () { + for (const num of numbers) { + describe(`isProbablyPrime(${num.value})`, function () { + it(`should return ${num.prime}`, async function () { + const ret = await bigintUtils.isProbablyPrime(num.value); + chai.expect(ret).to.equal(num.prime); + }); + }); + } +}); + +// For the browser test builder to work you MUST import them module in a variable that +// is the camelised version of the package name. + + + +const bitLengths = [ + 256, + 512, + 1024, + 2048, + 3072 +]; + +describe('Testing generation of prime numbers', function () { + for (const bitLength of bitLengths) { + describe(`Executing prime(${bitLength})`, function () { + it(`should return a random ${bitLength}-bits probable prime`, async function () { + let prime = await bigintUtils.prime(bitLength); + const ret = await bigintUtils.isProbablyPrime(prime); + chai.expect(ret).to.equal(true); + let bits = 1; + do { + bits++; + } while ((prime >>= BigInt(1)) > BigInt(1)); + chai.expect(bits).to.equal(bitLength); + }); + }); + } +});