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# bigint-mod-arith
Some extra functions to work with modular arithmetic using native JS ([ES-2020](https://tc39.es/ecma262/#sec-bigint-objects)) implementation of BigInt. 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).
> 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-mod-arith 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-mod-arith can be imported to your project with `npm`:
```bash
npm install bigint-mod-arith
```
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 [IIFE bundle](https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/lib/index.browser.bundle.iife.js) or the [ESM bundle](https://raw.githubusercontent.com/juanelas/bigint-mod-arith/master/lib/index.browser.bundle.mod.js) from the repository.
## Usage example
Import your module as :
- Node.js
```javascript
const bigintModArith = require('bigint-mod-arith')
... // your code here
```
- JavaScript native or TypeScript project (including React and Angular)
```javascript
import * as bigintModArith from 'bigint-mod-arith'
... // your code here
```
- JavaScript native browser ES module
```html
```
- JavaScript native browser IIFE
```html
...
...
```
An example of usage could be:
```javascript
/* Stage 3 BigInts with value 666 can be declared as BigInt('666')
or the shorter 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.
*/
const a = BigInt('5')
const b = BigInt('2')
const n = 19n
console.log(bigintModArith.modPow(a, b, n)) // prints 6
console.log(bigintModArith.modInv(2n, 5n)) // prints 3
console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))) // prints 2
```
## API reference documentation
### bigint-mod-arith
Some common functions for modular arithmetic using native JS implementation of BigInt
* [bigint-mod-arith](#module_bigint-mod-arith)
* [~abs(a)](#module_bigint-mod-arith..abs) ⇒ bigint
* [~bitLength(a)](#module_bigint-mod-arith..bitLength) ⇒ number
* [~eGcd(a, b)](#module_bigint-mod-arith..eGcd) ⇒ egcdReturn
* [~gcd(a, b)](#module_bigint-mod-arith..gcd) ⇒ bigint
* [~lcm(a, b)](#module_bigint-mod-arith..lcm) ⇒ bigint
* [~max(a, b)](#module_bigint-mod-arith..max) ⇒ bigint
* [~min(a, b)](#module_bigint-mod-arith..min) ⇒ bigint
* [~modInv(a, n)](#module_bigint-mod-arith..modInv) ⇒ bigint \| NaN
* [~modPow(b, e, n)](#module_bigint-mod-arith..modPow) ⇒ bigint
* [~toZn(a, n)](#module_bigint-mod-arith..toZn) ⇒ bigint
* [~egcdReturn](#module_bigint-mod-arith..egcdReturn) : Object
#### bigint-mod-arith~abs(a) ⇒ bigint
Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0
**Kind**: inner method of [bigint-mod-arith](#module_bigint-mod-arith)
**Returns**: bigint - the absolute value of a
| Param | Type |
| --- | --- |
| a | number \| bigint |
#### bigint-mod-arith~bitLength(a) ⇒ number
Returns the bitlength of a number
**Kind**: inner method of [bigint-mod-arith](#module_bigint-mod-arith)
**Returns**: number - - the bit length
| Param | Type |
| --- | --- |
| a | number \| bigint |
#### bigint-mod-arith~eGcd(a, b) ⇒ 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**: inner method of [bigint-mod-arith](#module_bigint-mod-arith)
**Returns**: egcdReturn - A triple (g, x, y), such that ax + by = g = gcd(a, b).
| Param | Type |
| --- | --- |
| a | number \| bigint |
| b | number \| bigint |
#### bigint-mod-arith~gcd(a, b) ⇒ bigint
Greatest-common divisor of two integers based on the iterative binary algorithm.
**Kind**: inner method of [bigint-mod-arith](#module_bigint-mod-arith)
**Returns**: bigint - The greatest common divisor of a and b
| Param | Type |
| --- | --- |
| a | number \| bigint |
| b | number \| bigint |
#### bigint-mod-arith~lcm(a, b) ⇒ bigint
The least common multiple computed as abs(a*b)/gcd(a,b)
**Kind**: inner method of [bigint-mod-arith](#module_bigint-mod-arith)
**Returns**: bigint - The least common multiple of a and b
| Param | Type |
| --- | --- |
| a | number \| bigint |
| b | number \| bigint |
#### bigint-mod-arith~max(a, b) ⇒ bigint
Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b
**Kind**: inner method of [bigint-mod-arith](#module_bigint-mod-arith)
**Returns**: bigint - maximum of numbers a and b
| Param | Type |
| --- | --- |
| a | number \| bigint |
| b | number \| bigint |
#### bigint-mod-arith~min(a, b) ⇒ bigint
Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b
**Kind**: inner method of [bigint-mod-arith](#module_bigint-mod-arith)
**Returns**: bigint - minimum of numbers a and b
| Param | Type |
| --- | --- |
| a | number \| bigint |
| b | number \| bigint |
#### bigint-mod-arith~modInv(a, n) ⇒ bigint \| NaN
Modular inverse.
**Kind**: inner method of [bigint-mod-arith](#module_bigint-mod-arith)
**Returns**: bigint \| NaN - the inverse modulo n or NaN if it does not exist
| Param | Type | Description |
| --- | --- | --- |
| a | number \| bigint | The number to find an inverse for |
| n | number \| bigint | The modulo |
#### bigint-mod-arith~modPow(b, e, n) ⇒ bigint
Modular exponentiation b**e mod n. Currently using the right-to-left binary method
**Kind**: inner method of [bigint-mod-arith](#module_bigint-mod-arith)
**Returns**: bigint - b**e mod n
| Param | Type | Description |
| --- | --- | --- |
| b | number \| bigint | base |
| e | number \| bigint | exponent |
| n | number \| bigint | modulo |
#### bigint-mod-arith~toZn(a, n) ⇒ bigint
Finds the smallest positive element that is congruent to a in modulo n
**Kind**: inner method of [bigint-mod-arith](#module_bigint-mod-arith)
**Returns**: bigint - The smallest positive representation of a in modulo n
| Param | Type | Description |
| --- | --- | --- |
| a | number \| bigint | An integer |
| n | number \| bigint | The modulo |
#### bigint-mod-arith~egcdReturn : Object
A triple (g, x, y), such that ax + by = g = gcd(a, b).
**Kind**: inner typedef of [bigint-mod-arith](#module_bigint-mod-arith)
**Properties**
| Name | Type |
| --- | --- |
| g | bigint |
| x | bigint |
| y | bigint |