bigint-crypto-utils/README.md

# bigint-crypto-utils 

Utils for working with cryptography using native JS (stage 3) implementation of BigInt. It includes some extra functions to work with modular arithmetics along with secure random numbers and a fast strong probable prime generation/testing (parallelised multi-threaded Miller-Rabin primality test). 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). In the former case, for multi-threaded primality tests, you should use Node.js 11 or enable at runtime with `node --experimental-worker` with Node.js >=10.5.0.

_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)._

## Installation
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.

bigint-crypto-utils can be imported to your project with `npm`:
```bash
npm install bigint-crypto-utils
```
NPM installation defaults to the ES6 module for browsers and the CJS one for Node.js.

For web browsers, you can also directly download the minimised version of the [IIFE file](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/dist/bigint-crypto-utils-latest.browser.min.js) or the [ES6 module](https://raw.githubusercontent.com/juanelas/bigint-crypto-utils/master/dist/bigint-crypto-utils-latest.browser.mod.min.js) from GitHub.

## Usage example

With node js:
```javascript
const bigintCryptoUtils = require('bigint-crypto-utils');

/* Stage 3 BigInts with value 666 can be declared as BigInt('666')
 or the shorter new no-so-linter-friendly syntax 666n.
 Notice that you can also pass a number, e.g. BigInt(666), but it is not
 recommended since values over 2**53 - 1 won't be safe but no warning will
 be raised.
*/
let a = BigInt('5');
let b = BigInt('2');
let n = BigInt('19');

console.log(bigintCryptoUtils.modPow(a, b, n)); // prints 6

console.log(bigintCryptoUtils.modInv(BigInt('2'), BigInt('5'))); // prints 3

console.log(bigintCryptoUtils.modInv(BigInt('3'), BigInt('5'))); // prints 2

// Generation of a probable prime of 2048 bits
const prime = await bigintCryptoUtils.prime(2048);

// Testing if a prime is a probable prime (Miller-Rabin)
if ( await bigintCryptoUtils.isProbablyPrime(prime) )
    // code if is prime

// Get a cryptographically secure random number between 1 and 2**256 bits.
const rnd = bigintCryptoUtils.randBetween(BigInt(2)**BigInt(256));

```

From a browser, you can just load the module in a html page as:
```html
  <script type="module">
    import * as bigintCryptoUtils from 'bigint-utils-latest.browser.mod.min.js';

    let a = BigInt('5');
    let b = BigInt('2');
    let n = BigInt('19');

    console.log(bigintCryptoUtils.modPow(a, b, n)); // prints 6

    console.log(bigintCryptoUtils.modInv(BigInt('2'), BigInt('5'))); // prints 3

    console.log(bigintCryptoUtils.modInv(BigInt('3'), BigInt('5'))); // prints 2

    (async function () {
      // Generation of a probable prime of 2018 bits
      const p = await bigintCryptoUtils.prime(2048);

      // Testing if a prime is a probable prime (Miller-Rabin)
      const isPrime = await bigintCryptoUtils.isProbablyPrime(p);
      alert(p.toString() + '\nIs prime?\n' + isPrime);

      // Get a cryptographically secure random number between 1 and 2**256 bits.
      const rnd = await bigintCryptoUtils.randBetween(BigInt(2)**BigInt(256));
      alert(rnd);
    })();
  </script>
```

# bigint-crypto-utils JS Doc

## Functions

<dl>
<dt><a href="#abs">abs(a)</a> ⇒ <code>bigint</code></dt>
<dd><p>Absolute value. abs(a)==a if a&gt;=0. abs(a)==-a if a&lt;0</p>
</dd>
<dt><a href="#eGcd">eGcd(a, b)</a> ⇒ <code><a href="#egcdReturn">egcdReturn</a></code></dt>
<dd><p>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).</p>
</dd>
<dt><a href="#gcd">gcd(a, b)</a> ⇒ <code>bigint</code></dt>
<dd><p>Greatest-common divisor of two integers based on the iterative binary algorithm.</p>
</dd>
<dt><a href="#isProbablyPrime">isProbablyPrime(w, iterations)</a> ⇒ <code>Promise</code></dt>
<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="#lcm">lcm(a, b)</a> ⇒ <code>bigint</code></dt>
<dd><p>The least common multiple computed as abs(a*b)/gcd(a,b)</p>
</dd>
<dt><a href="#modInv">modInv(a, n)</a> ⇒ <code>bigint</code></dt>
<dd><p>Modular inverse.</p>
</dd>
<dt><a href="#modPow">modPow(a, b, n)</a> ⇒ <code>bigint</code></dt>
<dd><p>Modular exponentiation a**b mod n</p>
</dd>
<dt><a href="#prime">prime(bitLength, iterations)</a> ⇒ <code>Promise</code></dt>
<dd><p>A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator. 
The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI 
main process, and it can be much faster (if several cores or cpu are available). 
The node version can also use worker_threads if they are available (enabled by default with Node 11 and 
and can be enabled at runtime executing node --experimental-worker with node &gt;=10.5.0).</p>
</dd>
<dt><a href="#randBetween">randBetween(max, min)</a> ⇒ <code>Promise</code></dt>
<dd><p>Returns a cryptographically secure random integer between [min,max]</p>
</dd>
<dt><a href="#randBits">randBits(bitLength, forceLength)</a> ⇒ <code>Promise</code></dt>
<dd><p>Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()</p>
</dd>
<dt><a href="#randBytes">randBytes(byteLength, forceLength)</a> ⇒ <code>Promise</code></dt>
<dd><p>Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()</p>
</dd>
<dt><a href="#toZn">toZn(a, n)</a> ⇒ <code>bigint</code></dt>
<dd><p>Finds the smallest positive element that is congruent to a in modulo n</p>
</dd>
</dl>

## Typedefs

<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(a) ⇒ <code>bigint</code>
Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0

**Kind**: global function  
**Returns**: <code>bigint</code> - the absolute value of a  

| Param | Type |
| --- | --- |
| a | <code>number</code> \| <code>bigint</code> | 

<a name="eGcd"></a>

## eGcd(a, b) ⇒ [<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 function  

| Param | Type |
| --- | --- |
| a | <code>number</code> \| <code>bigint</code> | 
| b | <code>number</code> \| <code>bigint</code> | 

<a name="gcd"></a>

## gcd(a, b) ⇒ <code>bigint</code>
Greatest-common divisor of two integers based on the iterative binary algorithm.

**Kind**: global function  
**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="isProbablyPrime"></a>

## isProbablyPrime(w, iterations) ⇒ <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 function  
**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="lcm"></a>

## lcm(a, b) ⇒ <code>bigint</code>
The least common multiple computed as abs(a*b)/gcd(a,b)

**Kind**: global function  
**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="modInv"></a>

## modInv(a, n) ⇒ <code>bigint</code>
Modular inverse.

**Kind**: global function  
**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(a, b, n) ⇒ <code>bigint</code>
Modular exponentiation a**b mod n

**Kind**: global function  
**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="prime"></a>

## prime(bitLength, iterations) ⇒ <code>Promise</code>
A probably-prime (Miller-Rabin), cryptographically-secure, random-number generator. 
The browser version uses web workers to parallelise prime look up. Therefore, it does not lock the UI 
main process, and it can be much faster (if several cores or cpu are available). 
The node version can also use worker_threads if they are available (enabled by default with Node 11 and 
and can be enabled at runtime executing node --experimental-worker with node >=10.5.0).

**Kind**: global function  
**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="randBetween"></a>

## randBetween(max, min) ⇒ <code>Promise</code>
Returns a cryptographically secure random integer between [min,max]

**Kind**: global function  
**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="randBits"></a>

## randBits(bitLength, forceLength) ⇒ <code>Promise</code>
Secure random bits for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()

**Kind**: global function  
**Returns**: <code>Promise</code> - A promise that resolves to a Buffer/UInt8Array filled with cryptographically secure random bits  

| Param | Type | Description |
| --- | --- | --- |
| bitLength | <code>number</code> | The desired number of random bits |
| forceLength | <code>boolean</code> | If we want to force the output to have a specific bit length. It basically forces the msb to be 1 |

<a name="randBytes"></a>

## randBytes(byteLength, forceLength) ⇒ <code>Promise</code>
Secure random bytes for both node and browsers. Node version uses crypto.randomFill() and browser one self.crypto.getRandomValues()

**Kind**: global function  
**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="toZn"></a>

## toZn(a, n) ⇒ <code>bigint</code>
Finds the smallest positive element that is congruent to a in modulo n

**Kind**: global function  
**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="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> | 


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