working with worker file
This commit is contained in:
Juan Hernández Serrano
commit
faefecc21d
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{
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"env": {
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"node": true,
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"mocha": true,
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"worker": true
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},
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"parserOptions": {
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"ecmaVersion": 2017,
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"sourceType": "module"
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},
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"extends": "eslint:recommended",
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"rules": {
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"no-console": 0,
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"indent": [
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"error",
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4
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],
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"linebreak-style": [
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"error",
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"unix"
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],
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"quotes": [
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"error",
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"single"
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],
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"semi": [
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"error",
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"always"
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]
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},
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"globals": {
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"BigInt": "readonly",
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"window": "readonly",
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"Uint8Array": "readonly"
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}
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}
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MIT License
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Copyright (c) 2018 Juan Hernández Serrano
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Permission is hereby granted, free of charge, to any person obtaining a copy
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of this software and associated documentation files (the "Software"), to deal
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in the Software without restriction, including without limitation the rights
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to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies of the Software, and to permit persons to whom the Software is
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furnished to do so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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# bigint-utils
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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).
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_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)**_
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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).
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## Installation
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bigint-utils is distributed as both an ES6 and a CJS module.
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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.
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The CJS module is built as a standard node module.
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bigint-utils can be imported to your project with `npm`:
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```bash
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npm install bigint-utils
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```
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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).
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## Usage example
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With node js:
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```javascript
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const bigintUtils = require('bigint-utils');
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// Stage 3 BigInts with value 666 can be declared as BigInt('666')
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// or the shorter new no-so-linter-friendly syntax 666n
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let a = BigInt('5');
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let b = BigInt('2');
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let n = BigInt('19');
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console.log(bigintModArith.modPow(a, b, n)); // prints 6
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console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3
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console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2
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// Generation of a probable prime of 2048 bits
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const prime = await bigintUtils.prime(2048);
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// Testing if a prime is a probable prime (Miller-Rabin)
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if ( await bigintUtils.isProbablyPrime(prime) )
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// code if is prime
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// Get a cryptographically secure random number between 1 and 2**256 bits.
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const rnd = bigintUtils.randBetween(BigInt(2)**256);
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```
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From a browser, you can just load the module in a html page as:
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```html
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<script type="module">
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import * as bigintUtils from 'bigint-utils-latest.browser.mod.min.js';
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let a = BigInt('5');
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let b = BigInt('2');
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let n = BigInt('19');
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console.log(bigintModArith.modPow(a, b, n)); // prints 6
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console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3
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console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2
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(async function () {
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// Generation of a probable prime of 2018 bits
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const p = await bigintSecrets.prime(2048);
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// Testing if a prime is a probable prime (Miller-Rabin)
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const isPrime = await bigintSecrets.isProbablyPrime(p);
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alert(p.toString() + '\nIs prime?\n' + isPrime);
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// Get a cryptographically secure random number between 1 and 2**256 bits.
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const rnd = await bigintSecrets.randBetween(BigInt(2)**256);
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alert(rnd);
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})();
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</script>
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```
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|
||||||
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# bigint-utils JS Doc
|
||||||
|
|
||||||
|
{{>main}}
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|
||||||
|
* * *
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|
@ -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
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||||||
|
npm install bigint-utils
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||||||
|
```
|
||||||
|
|
||||||
|
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).
|
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|
|
||||||
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## Usage example
|
||||||
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|
||||||
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With node js:
|
||||||
|
```javascript
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||||||
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const bigintUtils = require('bigint-utils');
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||||||
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|
||||||
|
// 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');
|
||||||
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let b = BigInt('2');
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||||||
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let n = BigInt('19');
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console.log(bigintModArith.modPow(a, b, n)); // prints 6
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console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3
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console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2
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||||||
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||||||
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// Generation of a probable prime of 2048 bits
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||||||
|
const prime = await bigintUtils.prime(2048);
|
||||||
|
|
||||||
|
// Testing if a prime is a probable prime (Miller-Rabin)
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||||||
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if ( await bigintUtils.isProbablyPrime(prime) )
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// code if is prime
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|
||||||
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// Get a cryptographically secure random number between 1 and 2**256 bits.
|
||||||
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const rnd = bigintUtils.randBetween(BigInt(2)**256);
|
||||||
|
|
||||||
|
```
|
||||||
|
|
||||||
|
From a browser, you can just load the module in a html page as:
|
||||||
|
```html
|
||||||
|
<script type="module">
|
||||||
|
import * as bigintUtils from 'bigint-utils-latest.browser.mod.min.js';
|
||||||
|
|
||||||
|
let a = BigInt('5');
|
||||||
|
let b = BigInt('2');
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||||||
|
let n = BigInt('19');
|
||||||
|
|
||||||
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console.log(bigintModArith.modPow(a, b, n)); // prints 6
|
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console.log(bigintModArith.modInv(BigInt('2'), BigInt('5'))); // prints 3
|
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||||||
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console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))); // prints 2
|
||||||
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||||||
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(async function () {
|
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// Generation of a probable prime of 2018 bits
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||||||
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const p = await bigintSecrets.prime(2048);
|
||||||
|
|
||||||
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// Testing if a prime is a probable prime (Miller-Rabin)
|
||||||
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const isPrime = await bigintSecrets.isProbablyPrime(p);
|
||||||
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alert(p.toString() + '\nIs prime?\n' + isPrime);
|
||||||
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|
||||||
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// Get a cryptographically secure random number between 1 and 2**256 bits.
|
||||||
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const rnd = await bigintSecrets.randBetween(BigInt(2)**256);
|
||||||
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alert(rnd);
|
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|
})();
|
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</script>
|
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```
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# bigint-utils JS Doc
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## Constants
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<dl>
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<dt><a href="#abs">abs</a> ⇒ <code>bigint</code></dt>
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<dd><p>Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0</p>
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</dd>
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<dt><a href="#gcd">gcd</a> ⇒ <code>bigint</code></dt>
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<dd><p>Greatest-common divisor of two integers based on the iterative binary algorithm.</p>
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</dd>
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<dt><a href="#lcm">lcm</a> ⇒ <code>bigint</code></dt>
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<dd><p>The least common multiple computed as abs(a*b)/gcd(a,b)</p>
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</dd>
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<dt><a href="#toZn">toZn</a> ⇒ <code>bigint</code></dt>
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||||||
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<dd><p>Finds the smallest positive element that is congruent to a in modulo n</p>
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</dd>
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<dt><a href="#eGcd">eGcd</a> ⇒ <code><a href="#egcdReturn">egcdReturn</a></code></dt>
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||||||
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<dd><p>An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
|
||||||
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Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).</p>
|
||||||
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</dd>
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<dt><a href="#modInv">modInv</a> ⇒ <code>bigint</code></dt>
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||||||
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<dd><p>Modular inverse.</p>
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||||||
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</dd>
|
||||||
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<dt><a href="#modPow">modPow</a> ⇒ <code>bigint</code></dt>
|
||||||
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<dd><p>Modular exponentiation a**b mod n</p>
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||||||
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</dd>
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||||||
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<dt><a href="#randBytes">randBytes</a> ⇒ <code>Promise</code></dt>
|
||||||
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<dd><p>Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process</p>
|
||||||
|
</dd>
|
||||||
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<dt><a href="#randBetween">randBetween</a> ⇒ <code>Promise</code></dt>
|
||||||
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<dd><p>Returns a cryptographically secure random integer between [min,max]</p>
|
||||||
|
</dd>
|
||||||
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<dt><a href="#isProbablyPrime">isProbablyPrime</a> ⇒ <code>Promise</code></dt>
|
||||||
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<dd><p>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)</p>
|
||||||
|
</dd>
|
||||||
|
<dt><a href="#prime">prime</a> ⇒ <code>Promise</code></dt>
|
||||||
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<dd><p>A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator</p>
|
||||||
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</dd>
|
||||||
|
</dl>
|
||||||
|
|
||||||
|
## Typedefs
|
||||||
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|
||||||
|
<dl>
|
||||||
|
<dt><a href="#egcdReturn">egcdReturn</a> : <code>Object</code></dt>
|
||||||
|
<dd><p>A triple (g, x, y), such that ax + by = g = gcd(a, b).</p>
|
||||||
|
</dd>
|
||||||
|
</dl>
|
||||||
|
|
||||||
|
<a name="abs"></a>
|
||||||
|
|
||||||
|
## abs ⇒ <code>bigint</code>
|
||||||
|
Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
|
||||||
|
|
||||||
|
**Kind**: global constant
|
||||||
|
**Returns**: <code>bigint</code> - the absolute value of a
|
||||||
|
|
||||||
|
| Param | Type |
|
||||||
|
| --- | --- |
|
||||||
|
| a | <code>number</code> \| <code>bigint</code> |
|
||||||
|
|
||||||
|
<a name="gcd"></a>
|
||||||
|
|
||||||
|
## gcd ⇒ <code>bigint</code>
|
||||||
|
Greatest-common divisor of two integers based on the iterative binary algorithm.
|
||||||
|
|
||||||
|
**Kind**: global constant
|
||||||
|
**Returns**: <code>bigint</code> - The greatest common divisor of a and b
|
||||||
|
|
||||||
|
| Param | Type |
|
||||||
|
| --- | --- |
|
||||||
|
| a | <code>number</code> \| <code>bigint</code> |
|
||||||
|
| b | <code>number</code> \| <code>bigint</code> |
|
||||||
|
|
||||||
|
<a name="lcm"></a>
|
||||||
|
|
||||||
|
## lcm ⇒ <code>bigint</code>
|
||||||
|
The least common multiple computed as abs(a*b)/gcd(a,b)
|
||||||
|
|
||||||
|
**Kind**: global constant
|
||||||
|
**Returns**: <code>bigint</code> - The least common multiple of a and b
|
||||||
|
|
||||||
|
| Param | Type |
|
||||||
|
| --- | --- |
|
||||||
|
| a | <code>number</code> \| <code>bigint</code> |
|
||||||
|
| b | <code>number</code> \| <code>bigint</code> |
|
||||||
|
|
||||||
|
<a name="toZn"></a>
|
||||||
|
|
||||||
|
## toZn ⇒ <code>bigint</code>
|
||||||
|
Finds the smallest positive element that is congruent to a in modulo n
|
||||||
|
|
||||||
|
**Kind**: global constant
|
||||||
|
**Returns**: <code>bigint</code> - The smallest positive representation of a in modulo n
|
||||||
|
|
||||||
|
| Param | Type | Description |
|
||||||
|
| --- | --- | --- |
|
||||||
|
| a | <code>number</code> \| <code>bigint</code> | An integer |
|
||||||
|
| n | <code>number</code> \| <code>bigint</code> | The modulo |
|
||||||
|
|
||||||
|
<a name="eGcd"></a>
|
||||||
|
|
||||||
|
## eGcd ⇒ [<code>egcdReturn</code>](#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 | <code>number</code> \| <code>bigint</code> |
|
||||||
|
| b | <code>number</code> \| <code>bigint</code> |
|
||||||
|
|
||||||
|
<a name="modInv"></a>
|
||||||
|
|
||||||
|
## modInv ⇒ <code>bigint</code>
|
||||||
|
Modular inverse.
|
||||||
|
|
||||||
|
**Kind**: global constant
|
||||||
|
**Returns**: <code>bigint</code> - the inverse modulo n
|
||||||
|
|
||||||
|
| Param | Type | Description |
|
||||||
|
| --- | --- | --- |
|
||||||
|
| a | <code>number</code> \| <code>bigint</code> | The number to find an inverse for |
|
||||||
|
| n | <code>number</code> \| <code>bigint</code> | The modulo |
|
||||||
|
|
||||||
|
<a name="modPow"></a>
|
||||||
|
|
||||||
|
## modPow ⇒ <code>bigint</code>
|
||||||
|
Modular exponentiation a**b mod n
|
||||||
|
|
||||||
|
**Kind**: global constant
|
||||||
|
**Returns**: <code>bigint</code> - a**b mod n
|
||||||
|
|
||||||
|
| Param | Type | Description |
|
||||||
|
| --- | --- | --- |
|
||||||
|
| a | <code>number</code> \| <code>bigint</code> | base |
|
||||||
|
| b | <code>number</code> \| <code>bigint</code> | exponent |
|
||||||
|
| n | <code>number</code> \| <code>bigint</code> | modulo |
|
||||||
|
|
||||||
|
<a name="randBytes"></a>
|
||||||
|
|
||||||
|
## randBytes ⇒ <code>Promise</code>
|
||||||
|
Secure random bytes for both node and browsers. Browser implementation uses WebWorkers in order to not lock the main process
|
||||||
|
|
||||||
|
**Kind**: global constant
|
||||||
|
**Returns**: <code>Promise</code> - A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bytes
|
||||||
|
|
||||||
|
| Param | Type | Description |
|
||||||
|
| --- | --- | --- |
|
||||||
|
| byteLength | <code>number</code> | The desired number of random bytes |
|
||||||
|
| forceLength | <code>boolean</code> | If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1 |
|
||||||
|
|
||||||
|
<a name="randBetween"></a>
|
||||||
|
|
||||||
|
## randBetween ⇒ <code>Promise</code>
|
||||||
|
Returns a cryptographically secure random integer between [min,max]
|
||||||
|
|
||||||
|
**Kind**: global constant
|
||||||
|
**Returns**: <code>Promise</code> - A promise that resolves to a cryptographically secure random bigint between [min,max]
|
||||||
|
|
||||||
|
| Param | Type | Description |
|
||||||
|
| --- | --- | --- |
|
||||||
|
| max | <code>bigint</code> | Returned value will be <= max |
|
||||||
|
| min | <code>bigint</code> | Returned value will be >= min |
|
||||||
|
|
||||||
|
<a name="isProbablyPrime"></a>
|
||||||
|
|
||||||
|
## isProbablyPrime ⇒ <code>Promise</code>
|
||||||
|
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**: <code>Promise</code> - A promise that resolve to a boolean that is either true (a probably prime number) or false (definitely composite)
|
||||||
|
|
||||||
|
| Param | Type | Description |
|
||||||
|
| --- | --- | --- |
|
||||||
|
| w | <code>bigint</code> | An integer to be tested for primality |
|
||||||
|
| iterations | <code>number</code> | The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3 |
|
||||||
|
|
||||||
|
<a name="prime"></a>
|
||||||
|
|
||||||
|
## prime ⇒ <code>Promise</code>
|
||||||
|
A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator
|
||||||
|
|
||||||
|
**Kind**: global constant
|
||||||
|
**Returns**: <code>Promise</code> - A promise that resolves to a bigint probable prime of bitLength bits
|
||||||
|
|
||||||
|
| Param | Type | Description |
|
||||||
|
| --- | --- | --- |
|
||||||
|
| bitLength | <code>number</code> | The required bit length for the generated prime |
|
||||||
|
| iterations | <code>number</code> | The number of iterations for the Miller-Rabin Probabilistic Primality Test |
|
||||||
|
|
||||||
|
<a name="egcdReturn"></a>
|
||||||
|
|
||||||
|
## egcdReturn : <code>Object</code>
|
||||||
|
A triple (g, x, y), such that ax + by = g = gcd(a, b).
|
||||||
|
|
||||||
|
**Kind**: global typedef
|
||||||
|
**Properties**
|
||||||
|
|
||||||
|
| Name | Type |
|
||||||
|
| --- | --- |
|
||||||
|
| g | <code>bigint</code> |
|
||||||
|
| x | <code>bigint</code> |
|
||||||
|
| y | <code>bigint</code> |
|
||||||
|
|
||||||
|
|
||||||
|
* * *
|
||||||
|
|
@ -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 = `
|
||||||
|
<script type="module">
|
||||||
|
import * as ${camelise(pkgJson.name)} from '${path.relative(templatePath, pkgJson.browser)}'
|
||||||
|
window.${camelise(pkgJson.name)} = ${camelise(pkgJson.name)};
|
||||||
|
import './tests.js';
|
||||||
|
mocha.run();
|
||||||
|
</script>
|
||||||
|
`;
|
||||||
|
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();
|
||||||
|
});
|
||||||
|
}
|
||||||
|
|
@ -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();
|
||||||
|
});
|
||||||
|
}
|
||||||
|
|
@ -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;
|
||||||
|
|
||||||
|
}({}));
|
||||||
|
|
@ -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(8))+a}return b}function c(b){let c=1;do c++;while((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<<f},f=function(b,c){return c=BigInt(c),b=BigInt(b)%c,0>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<BigInt(0))return h(i(c,d(e),g),g);let j=BigInt(1),k=c;for(;0<e;){var l=e%BigInt(2);e/=BigInt(2),l==BigInt(1)&&(j*=k,j%=g),k*=k,k%=g}return j},j=async function(a,b=!1){return new Promise(c=>{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;0<h&&(g++,e=2**h-1);let i;do{let a=await j(g);0<h&&(a[0]&=e),i=b(a)}while(i>a||i<d);return i},l=function(){function a(a,e){c[b]=e,d.postMessage({buf:a,id:b}),b++}let b=0;const c={},d=function(a){const b=new window.Blob(["("+a.toString()+")()"],{type:"text/javascript"}),d=new Worker(window.URL.createObjectURL(b));return d.onmessage=function(a){const{id:b,buf:d}=a.data;c[b]&&(c[b](!1,d),delete c[b])},d}(()=>{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<e.length&&BigInt(e[a])<=c;a++){const b=BigInt(e[a]);if(c===b)return!0;if(c%b===BigInt(0))return!1}let f=BigInt(0),g=c-BigInt(1);for(;g%BigInt(2)===BigInt(0);)g/=BigInt(2),++f;let h=(c-BigInt(1))/BigInt(2)**f;loop:do{let a=await k(c-BigInt(1),2),b=i(a,h,c);if(b===BigInt(1)||b===c-BigInt(1))continue;for(let a=1;a<f;a++){if(b=i(b,BigInt(2),c),b===c-BigInt(1))continue loop;if(b===BigInt(1))break}return!1}while(--b);return!0},a.lcm=function(c,f){return c=BigInt(c),f=BigInt(f),d(c*f)/e(c,f)},a.modInv=h,a.modPow=i,a.prime=async function(a,c=16){{let d=[];for(let e=0;e<window.navigator.hardwareConcurrency;e++){const e=new URL("./",document.currentScript&&document.currentScript.src||new URL("bigint-utils-0.9.0.browser.min.js",document.baseURI).href).pathname;let f=new Worker(`${e}/workerPrimalityTest.js`);f.onmessage(async e=>{if(e.data.isPrime){for(let a=0;a<d.length;a++)d[a].terminate();for(;d.length;)d.pop();return e.data.value}else{let d=BigInt(0);d=b((await j(a/8,!0))),f.postMessage({rnd:d,iterations:c})}}),d.push(f)}for(const e of d){let d=BigInt(0);d=b((await j(a/8,!0))),e.postMessage({rnd:d,iterations:c})}}},a.randBetween=k,a.randBytes=j,a.toZn=f,a}({});
|
||||||
|
|
@ -0,0 +1,612 @@
|
||||||
|
/**
|
||||||
|
* 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('./', 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 };
|
||||||
|
|
@ -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<<e},lcm=function(c,d){return c=BigInt(c),d=BigInt(d),abs(c*d)/gcd(c,d)},toZn=function(b,c){return c=BigInt(c),b=BigInt(b)%c,0>b?b+c:b},eGcd=function(c,d){c=BigInt(c),d=BigInt(d);let e=BigInt(0),f=BigInt(1),g=BigInt(1),h=BigInt(0);for(;c!==BigInt(0);){let a=d/c,b=d%c,i=e-g*a,j=f-h*a;d=c,c=b,e=g,f=h,g=i,h=j}return{b:d,x:e,y:f}},modInv=function(b,a){let c=eGcd(b,a);return c.b===BigInt(1)?toZn(c.x,a):null},modPow=function(c,d,e){if(e=BigInt(e),c=toZn(c,e),d=BigInt(d),d<BigInt(0))return modInv(modPow(c,abs(d),e),e);let f=BigInt(1),g=c;for(;0<d;){var h=d%BigInt(2);d/=BigInt(2),h==BigInt(1)&&(f*=g,f%=e),g*=g,g%=e}return f},randBytes=async function(a,b=!1){return new Promise(c=>{let d;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;0<f&&(e++,c=2**f-1);let g;do{let a=await randBytes(e);0<f&&(a[0]&=c),g=fromBuffer(a)}while(g>a||g<b);return g},isProbablyPrime=async function(c,b=16){if(c===BigInt(2))return!0;if((c&BigInt(1))===BigInt(0)||c===BigInt(1))return!1;const e=[3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597];for(let a=0;a<e.length&&BigInt(e[a])<=c;a++){const b=BigInt(e[a]);if(c===b)return!0;if(c%b===BigInt(0))return!1}let f=BigInt(0),g=c-BigInt(1);for(;g%BigInt(2)===BigInt(0);)g/=BigInt(2),++f;let h=(c-BigInt(1))/BigInt(2)**f;loop:do{let a=await randBetween(c-BigInt(1),2),b=modPow(a,h,c);if(b===BigInt(1)||b===c-BigInt(1))continue;for(let a=1;a<f;a++){if(b=modPow(b,BigInt(2),c),b===c-BigInt(1))continue loop;if(b===BigInt(1))break}return!1}while(--b);return!0},prime=async function(a,b=16){{let c=[];for(let d,e=0;e<window.navigator.hardwareConcurrency;e++)d=new Worker("./workerPrimalityTest.js"),d.onmessage(async e=>{if(e.data.isPrime){for(let a=0;a<c.length;a++)c[a].terminate();for(;c.length;)c.pop();return e.data.value}else{let c=BigInt(0);c=fromBuffer((await randBytes(a/8,!0))),d.postMessage({rnd:c,iterations:b})}}),c.push(d);for(const d of c){let c=BigInt(0);c=fromBuffer((await randBytes(a/8,!0))),d.postMessage({rnd:c,iterations:b})}}},getRandomValuesWorker=function(){function a(a,e){c[b]=e,d.postMessage({buf:a,id:b}),b++}let b=0;const c={},d=function(a){const b=new window.Blob(["("+a.toString()+")()"],{type:"text/javascript"}),d=new Worker(window.URL.createObjectURL(b));return d.onmessage=function(a){const{id:b,buf:d}=a.data;c[b]&&(c[b](!1,d),delete c[b])},d}(()=>{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(8))+a}return b}function bitLength(b){let c=1;do c++;while((b>>=BigInt(1))>BigInt(1));return c}export{abs,eGcd,gcd,isProbablyPrime,lcm,modInv,modPow,prime,randBetween,randBytes,toZn};
|
||||||
|
|
@ -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;
|
||||||
|
|
@ -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: <bigint>, iterations: <number>}
|
||||||
|
const isPrime = await bigintUtils.isProbablyPrime(event.data.rnd, event.data.iterations);
|
||||||
|
postMessage({
|
||||||
|
'isPrime': isPrime,
|
||||||
|
'value' : event.data.rnd
|
||||||
|
});
|
||||||
|
};
|
||||||
File diff suppressed because it is too large
Load Diff
|
|
@ -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"
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
@ -0,0 +1,15 @@
|
||||||
|
<!DOCTYPE html>
|
||||||
|
<html>
|
||||||
|
<head>
|
||||||
|
<title>Mocha Tests</title>
|
||||||
|
<link rel="stylesheet" href="../../node_modules/mocha/mocha.css">
|
||||||
|
</head>
|
||||||
|
<body>
|
||||||
|
<div id="mocha"></div>
|
||||||
|
<script src="../../node_modules/mocha/mocha.js"></script>
|
||||||
|
<script src="../../node_modules/chai/chai.js"></script>
|
||||||
|
<script>mocha.setup('bdd'); mocha.setup({ timeout: 60000 });</script>
|
||||||
|
|
||||||
|
{{TESTS}}
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
|
|
@ -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;
|
||||||
|
}
|
||||||
|
|
@ -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: <bigint>, iterations: <number>}
|
||||||
|
const isPrime = await bigintUtils.isProbablyPrime(event.data.rnd, event.data.iterations);
|
||||||
|
postMessage({
|
||||||
|
'isPrime': isPrime,
|
||||||
|
'value' : event.data.rnd
|
||||||
|
});
|
||||||
|
};
|
||||||
|
|
@ -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 ${num.prime}`, async function () {
|
||||||
|
const ret = await bigintUtils.isProbablyPrime(num.value);
|
||||||
|
chai.expect(ret).to.equal(num.prime);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
}
|
||||||
|
});
|
||||||
|
|
@ -0,0 +1,31 @@
|
||||||
|
'use strict';
|
||||||
|
|
||||||
|
// For the browser test builder to work you MUST import them module in a variable that
|
||||||
|
// is the camelised version of the package name.
|
||||||
|
const bigintUtils = require('../dist/bigint-utils-latest.node');
|
||||||
|
const chai = require('chai');
|
||||||
|
|
||||||
|
const bitLengths = [
|
||||||
|
256,
|
||||||
|
512,
|
||||||
|
1024,
|
||||||
|
2048,
|
||||||
|
3072
|
||||||
|
];
|
||||||
|
|
||||||
|
describe('Testing generation of prime numbers', function () {
|
||||||
|
for (const bitLength of bitLengths) {
|
||||||
|
describe(`Executing prime(${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);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
}
|
||||||
|
});
|
||||||
|
|
@ -0,0 +1,22 @@
|
||||||
|
<!DOCTYPE html>
|
||||||
|
<html>
|
||||||
|
<head>
|
||||||
|
<title>Mocha Tests</title>
|
||||||
|
<link rel="stylesheet" href="../../node_modules/mocha/mocha.css">
|
||||||
|
</head>
|
||||||
|
<body>
|
||||||
|
<div id="mocha"></div>
|
||||||
|
<script src="../../node_modules/mocha/mocha.js"></script>
|
||||||
|
<script src="../../node_modules/chai/chai.js"></script>
|
||||||
|
<script>mocha.setup('bdd'); mocha.setup({ timeout: 60000 });</script>
|
||||||
|
|
||||||
|
|
||||||
|
<script type="module">
|
||||||
|
import * as bigintUtils from '../../dist/bigint-utils-latest.browser.mod.js'
|
||||||
|
window.bigintUtils = bigintUtils;
|
||||||
|
import './tests.js';
|
||||||
|
mocha.run();
|
||||||
|
</script>
|
||||||
|
|
||||||
|
</body>
|
||||||
|
</html>
|
||||||
|
|
@ -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);
|
||||||
|
});
|
||||||
|
});
|
||||||
|
}
|
||||||
|
});
|
||||||
Loading…
Reference in New Issue