# 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 very fast strong probable prime generation/testing (parallelised multi-threaded Miller-Rabin primality test). 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-crypto-utils is distributed for [web browsers supporting BigInt](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/BigInt#Browser_compatibility) as an ES6 module or a 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 for Node.js.

For web browsers, you can also directly download 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
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)**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)**256);
      alert(rnd);
    })();
  </script>
```

# bigint-crypto-utils JS Doc

## Constants

<dl>
<dt><a href="#abs">abs</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> ⇒ <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> ⇒ <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</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> ⇒ <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> ⇒ <code>bigint</code></dt>
<dd><p>Modular inverse.</p>
</dd>
<dt><a href="#modPow">modPow</a> ⇒ <code>bigint</code></dt>
<dd><p>Modular exponentiation a**b mod n</p>
</dd>
<dt><a href="#prime">prime</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).</p>
</dd>
<dt><a href="#randBetween">randBetween</a> ⇒ <code>Promise</code></dt>
<dd><p>Returns a cryptographically secure random integer between [min,max]</p>
</dd>
<dt><a href="#randBytes">randBytes</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> ⇒ <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 ⇒ <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="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="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="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="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="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="prime"></a>

## prime ⇒ <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).

**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="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="randBytes"></a>

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

**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="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="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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