436 lines
19 KiB
Markdown
436 lines
19 KiB
Markdown
[](https://standardjs.com)
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# bigint-crypto-utils
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Utils for working with cryptography using native JS ([ES-2020](https://tc39.es/ecma262/#sec-bigint-objects)) implementation of BigInt. It includes some extra functions to work with modular arithmetic along with secure random numbers and a fast strong probable prime generator/tester (parallelized multi-threaded Miller-Rabin primality tests if workers are supported). It can be used by any [Web Browser or webview supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility) and with Node.js (>=10.4.0).
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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).** Many platforms provide native support for cryptography, such as [Web Cryptography API](https://w3c.github.io/webcrypto/) or [Node.js Crypto](https://nodejs.org/dist/latest/docs/api/crypto.html).
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## Installation
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bigint-crypto-utils is distributed for [web browsers and/or webviews supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility) as an ES6 module or an IIFE file; and for Node.js (>=10.4.0), as a CJS module.
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bigint-crypto-utils can be imported to your project with `npm`:
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```bash
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npm install bigint-crypto-utils
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```
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NPM installation defaults to the ES6 module for browsers and the CJS one for Node.js.
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For web browsers, you can also directly download the [IIFE bundle](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/lib/index.browser.bundle.iife.js) or the [ES6 bundle module](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/lib/index.browser.bundle.mod.js) from GitHub.
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## Usage examples
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Import your module as :
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- Node.js
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```javascript
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const bigintCryptoUtils = require('bigint-crypto-utils')
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... // your code here
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```
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- JavaScript native or TypeScript project
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```javascript
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import * as bigintCryptoUtils from 'bigint-crypto-utils'
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... // your code here
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```
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> BigInt is [ES-2020](https://tc39.es/ecma262/#sec-bigint-objects). In order to use it with TypeScript you should set `lib` (and probably also `target` and `module`) to `esnext` in `tsconfig.json`.
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- JavaScript native browser ES6 mod
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```html
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<script type="module">
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import * as bigintCryptoUtils from 'lib/index.browser.bundle.mod.js' // Use you actual path to the broser mod bundle
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... // your code here
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</script>
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```
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- JavaScript native browser IIFE
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```html
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<head>
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...
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<script src="../../lib/index.browser.bundle.js"></script> <!-- Use you actual path to the browser bundle -->
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</head>
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<body>
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...
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<script>
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... // your code here
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</script>
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</body>
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```
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An example of usage could be:
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```javascript
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/* A BigInt with value 666 can be declared calling the bigint constructor as
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BigInt('666') or with the shorter 666n.
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Notice that you can also pass a number to the constructor, e.g. BigInt(666).
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However, it is not recommended since values over 2**53 - 1 won't be safe but
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no warning will be raised.
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*/
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const a = BigInt('5')
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const b = BigInt('2')
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const n = 19n
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console.log(bigintCryptoUtils.modPow(a, b, n)) // prints 6
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console.log(bigintCryptoUtils.modInv(2n, 5n)) // prints 3
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console.log(bigintCryptoUtils.modInv(BigInt('3'), BigInt('5'))) // prints 2
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console.log(bigintCryptoUtils.randBetween(2n ** 256n)) // Prints a cryptographically secure random number between 1 and 2**256 bits.
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async function primeTesting () {
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// Output of a probable prime of 2048 bits
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console.log(await bigintCryptoUtils.prime(2048))
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// Testing if a number is a probable prime (Miller-Rabin)
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const number = 27n
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const isPrime = await bigintCryptoUtils.isProbablyPrime(number)
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if (isPrime) {
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console.log(`${number} is prime`)
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} else {
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console.log(`${number} is composite`)
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}
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}
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primeTesting()
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```
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You can find examples in the [examples folder of the repository](https://github.com/juanelas/bigint-crypto-utils/tree/master/examples).
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## API reference documentation
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### Functions
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<dl>
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<dt><a href="#abs">abs(a)</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="#bitLength">bitLength(a)</a> ⇒ <code>number</code></dt>
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<dd><p>Returns the bitlength of a number</p>
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</dd>
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<dt><a href="#eGcd">eGcd(a, b)</a> ⇒ <code><a href="#egcdReturn">egcdReturn</a></code></dt>
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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="#gcd">gcd(a, b)</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, b)</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="#max">max(a, b)</a> ⇒ <code>bigint</code></dt>
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<dd><p>Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b</p>
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</dd>
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<dt><a href="#min">min(a, b)</a> ⇒ <code>bigint</code></dt>
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<dd><p>Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b</p>
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</dd>
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<dt><a href="#modInv">modInv(a, n)</a> ⇒ <code>bigint</code></dt>
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<dd><p>Modular inverse.</p>
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</dd>
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<dt><a href="#modPow">modPow(b, e, n)</a> ⇒ <code>bigint</code></dt>
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<dd><p>Modular exponentiation b**e mod n. Currently using the right-to-left binary method</p>
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</dd>
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<dt><a href="#toZn">toZn(a, n)</a> ⇒ <code>bigint</code></dt>
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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="#isProbablyPrime">isProbablyPrime(w, [iterations])</a> ⇒ <code>Promise.<boolean></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
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iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)</p>
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</dd>
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<dt><a href="#prime">prime(bitLength, [iterations])</a> ⇒ <code>Promise.<bigint></code></dt>
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<dd><p>A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
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The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI
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main process, and it can be much faster (if several cores or cpu are available).
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The node version can also use worker_threads if they are available (enabled by default with Node 11 and
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and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).</p>
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</dd>
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<dt><a href="#primeSync">primeSync(bitLength, [iterations])</a> ⇒ <code>bigint</code></dt>
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<dd><p>A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
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The sync version is NOT RECOMMENDED since it won't use workers and thus it'll be slower and may freeze thw window in browser's javascript. Please consider using prime() instead.</p>
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</dd>
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<dt><a href="#randBetween">randBetween(max, [min])</a> ⇒ <code>bigint</code></dt>
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<dd><p>Returns a cryptographically secure random integer between [min,max]</p>
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</dd>
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<dt><a href="#randBits">randBits(bitLength, [forceLength])</a> ⇒ <code>Promise.<(Buffer|Uint8Array)></code></dt>
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<dd><p>Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()</p>
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<p>Since version 3.0.0 this is an async function and a new randBitsSync function has been added. If you are migrating from version 2 call randBitsSync instead.</p>
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</dd>
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<dt><a href="#randBitsSync">randBitsSync(bitLength, [forceLength])</a> ⇒ <code>Buffer</code> | <code>Uint8Array</code></dt>
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<dd><p>Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()</p>
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</dd>
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<dt><a href="#randBytes">randBytes(byteLength, [forceLength])</a> ⇒ <code>Promise.<(Buffer|Uint8Array)></code></dt>
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<dd><p>Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()</p>
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</dd>
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<dt><a href="#randBytesSync">randBytesSync(byteLength, [forceLength])</a> ⇒ <code>Buffer</code> | <code>Uint8Array</code></dt>
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<dd><p>Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()</p>
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</dd>
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</dl>
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### Typedefs
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<dl>
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<dt><a href="#egcdReturn">egcdReturn</a> : <code>Object</code></dt>
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<dd><p>A triple (g, x, y), such that ax + by = g = gcd(a, b).</p>
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</dd>
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</dl>
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<a name="abs"></a>
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### abs(a) ⇒ <code>bigint</code>
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Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
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**Kind**: global function
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**Returns**: <code>bigint</code> - the absolute value of a
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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<a name="bitLength"></a>
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### bitLength(a) ⇒ <code>number</code>
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Returns the bitlength of a number
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**Kind**: global function
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**Returns**: <code>number</code> - - the bit length
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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<a name="eGcd"></a>
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### eGcd(a, b) ⇒ [<code>egcdReturn</code>](#egcdReturn)
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An iterative implementation of the extended euclidean algorithm or extended greatest common divisor algorithm.
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Take positive integers a, b as input, and return a triple (g, x, y), such that ax + by = g = gcd(a, b).
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**Kind**: global function
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**Returns**: [<code>egcdReturn</code>](#egcdReturn) - A triple (g, x, y), such that ax + by = g = gcd(a, b).
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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| b | <code>number</code> \| <code>bigint</code> |
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<a name="gcd"></a>
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### gcd(a, b) ⇒ <code>bigint</code>
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Greatest-common divisor of two integers based on the iterative binary algorithm.
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**Kind**: global function
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**Returns**: <code>bigint</code> - The greatest common divisor of a and b
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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| b | <code>number</code> \| <code>bigint</code> |
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<a name="lcm"></a>
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### lcm(a, b) ⇒ <code>bigint</code>
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The least common multiple computed as abs(a*b)/gcd(a,b)
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**Kind**: global function
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**Returns**: <code>bigint</code> - The least common multiple of a and b
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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| b | <code>number</code> \| <code>bigint</code> |
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<a name="max"></a>
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### max(a, b) ⇒ <code>bigint</code>
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Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
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**Kind**: global function
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**Returns**: <code>bigint</code> - maximum of numbers a and b
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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| b | <code>number</code> \| <code>bigint</code> |
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<a name="min"></a>
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### min(a, b) ⇒ <code>bigint</code>
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Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
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**Kind**: global function
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**Returns**: <code>bigint</code> - minimum of numbers a and b
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| Param | Type |
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| --- | --- |
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| a | <code>number</code> \| <code>bigint</code> |
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| b | <code>number</code> \| <code>bigint</code> |
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<a name="modInv"></a>
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### modInv(a, n) ⇒ <code>bigint</code>
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Modular inverse.
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**Kind**: global function
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**Returns**: <code>bigint</code> - the inverse modulo n or NaN if it does not exist
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| Param | Type | Description |
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| --- | --- | --- |
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| a | <code>number</code> \| <code>bigint</code> | The number to find an inverse for |
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| n | <code>number</code> \| <code>bigint</code> | The modulo |
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<a name="modPow"></a>
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### modPow(b, e, n) ⇒ <code>bigint</code>
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Modular exponentiation b**e mod n. Currently using the right-to-left binary method
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**Kind**: global function
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**Returns**: <code>bigint</code> - b**e mod n
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| Param | Type | Description |
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| --- | --- | --- |
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| b | <code>number</code> \| <code>bigint</code> | base |
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| e | <code>number</code> \| <code>bigint</code> | exponent |
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| n | <code>number</code> \| <code>bigint</code> | modulo |
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<a name="toZn"></a>
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### toZn(a, n) ⇒ <code>bigint</code>
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Finds the smallest positive element that is congruent to a in modulo n
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**Kind**: global function
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**Returns**: <code>bigint</code> - The smallest positive representation of a in modulo n
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| Param | Type | Description |
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| --- | --- | --- |
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| a | <code>number</code> \| <code>bigint</code> | An integer |
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| n | <code>number</code> \| <code>bigint</code> | The modulo |
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<a name="isProbablyPrime"></a>
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### isProbablyPrime(w, [iterations]) ⇒ <code>Promise.<boolean></code>
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The test first tries if any of the first 250 small primes are a factor of the input number and then passes several
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iterations of Miller-Rabin Probabilistic Primality Test (FIPS 186-4 C.3.1)
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**Kind**: global function
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**Returns**: <code>Promise.<boolean></code> - A promise that resolves to a boolean that is either true (a probably prime number) or false (definitely composite)
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| Param | Type | Default | Description |
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| --- | --- | --- | --- |
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| w | <code>number</code> \| <code>bigint</code> | | An integer to be tested for primality |
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| [iterations] | <code>number</code> | <code>16</code> | The number of iterations for the primality test. The value shall be consistent with Table C.1, C.2 or C.3 |
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<a name="prime"></a>
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### prime(bitLength, [iterations]) ⇒ <code>Promise.<bigint></code>
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A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
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The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI
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main process, and it can be much faster (if several cores or cpu are available).
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The node version can also use worker_threads if they are available (enabled by default with Node 11 and
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and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).
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**Kind**: global function
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**Returns**: <code>Promise.<bigint></code> - A promise that resolves to a bigint probable prime of bitLength bits.
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| Param | Type | Default | Description |
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| --- | --- | --- | --- |
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| bitLength | <code>number</code> | | The required bit length for the generated prime |
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| [iterations] | <code>number</code> | <code>16</code> | The number of iterations for the Miller-Rabin Probabilistic Primality Test |
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<a name="primeSync"></a>
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### primeSync(bitLength, [iterations]) ⇒ <code>bigint</code>
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A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator.
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The sync version is NOT RECOMMENDED since it won't use workers and thus it'll be slower and may freeze thw window in browser's javascript. Please consider using prime() instead.
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**Kind**: global function
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**Returns**: <code>bigint</code> - A bigint probable prime of bitLength bits.
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| Param | Type | Default | Description |
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| --- | --- | --- | --- |
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| bitLength | <code>number</code> | | The required bit length for the generated prime |
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| [iterations] | <code>number</code> | <code>16</code> | The number of iterations for the Miller-Rabin Probabilistic Primality Test |
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<a name="randBetween"></a>
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### randBetween(max, [min]) ⇒ <code>bigint</code>
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Returns a cryptographically secure random integer between [min,max]
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**Kind**: global function
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**Returns**: <code>bigint</code> - A cryptographically secure random bigint between [min,max]
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| Param | Type | Default | Description |
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| --- | --- | --- | --- |
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| max | <code>bigint</code> | | Returned value will be <= max |
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| [min] | <code>bigint</code> | <code>BigInt(1)</code> | Returned value will be >= min |
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<a name="randBits"></a>
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### randBits(bitLength, [forceLength]) ⇒ <code>Promise.<(Buffer\|Uint8Array)></code>
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Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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Since version 3.0.0 this is an async function and a new randBitsSync function has been added. If you are migrating from version 2 call randBitsSync instead.
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**Kind**: global function
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**Returns**: <code>Promise.<(Buffer\|Uint8Array)></code> - A Promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
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**Since**: 3.0.0
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| Param | Type | Default | Description |
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| --- | --- | --- | --- |
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| bitLength | <code>number</code> | | The desired number of random bits |
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| [forceLength] | <code>boolean</code> | <code>false</code> | If we want to force the output to have a specific bit length. It basically forces the msb to be 1 |
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<a name="randBitsSync"></a>
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### randBitsSync(bitLength, [forceLength]) ⇒ <code>Buffer</code> \| <code>Uint8Array</code>
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Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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**Kind**: global function
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**Returns**: <code>Buffer</code> \| <code>Uint8Array</code> - A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bits
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**Since**: 3.0.0
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| Param | Type | Default | Description |
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| --- | --- | --- | --- |
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| bitLength | <code>number</code> | | The desired number of random bits |
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| [forceLength] | <code>boolean</code> | <code>false</code> | If we want to force the output to have a specific bit length. It basically forces the msb to be 1 |
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<a name="randBytes"></a>
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### randBytes(byteLength, [forceLength]) ⇒ <code>Promise.<(Buffer\|Uint8Array)></code>
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Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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**Kind**: global function
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**Returns**: <code>Promise.<(Buffer\|Uint8Array)></code> - A promise that resolves to a Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
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| Param | Type | Default | Description |
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| --- | --- | --- | --- |
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| byteLength | <code>number</code> | | The desired number of random bytes |
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| [forceLength] | <code>boolean</code> | <code>false</code> | If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1 |
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<a name="randBytesSync"></a>
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### randBytesSync(byteLength, [forceLength]) ⇒ <code>Buffer</code> \| <code>Uint8Array</code>
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Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()
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**Kind**: global function
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**Returns**: <code>Buffer</code> \| <code>Uint8Array</code> - A Buffer/UInt8Array (Node.js/Browser) filled with cryptographically secure random bytes
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| Param | Type | Default | Description |
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| --- | --- | --- | --- |
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| byteLength | <code>number</code> | | The desired number of random bytes |
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| [forceLength] | <code>boolean</code> | <code>false</code> | If we want to force the output to have a bit length of 8*byteLength. It basically forces the msb to be 1 |
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<a name="egcdReturn"></a>
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### egcdReturn : <code>Object</code>
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A triple (g, x, y), such that ax + by = g = gcd(a, b).
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**Kind**: global typedef
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**Properties**
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| Name | Type |
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| --- | --- |
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| g | <code>bigint</code> |
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| x | <code>bigint</code> |
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| y | <code>bigint</code> |
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