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[](https://opensource.org/licenses/MIT)
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[](https://standardjs.com)
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[](https://coveralls.io/github/juanelas/bigint-mod-arith?branch=master)
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# bigint-mod-arith
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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).
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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-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.
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bigint-mod-arith can be imported to your project with `npm` :
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```bash
npm install bigint-mod-arith
```
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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.
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## Usage example
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Import your module as :
- Node.js
```javascript
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const bigintModArith = require('bigint-mod-arith')
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... // your code here
```
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- JavaScript native or TypeScript project (including React and Angular)
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```javascript
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import * as bigintModArith from 'bigint-mod-arith'
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... // your code here
```
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- JavaScript native browser ES module
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```html
< script type = "module" >
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import * as bigintModArith from 'lib/index.browser.bundle.mod.js' // Use you actual path to the broser mod bundle
... // your code here
< / script >
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```
- JavaScript native browser IIFE
```html
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< head >
...
< script src = "../../lib/index.browser.bundle.iife.js" > < / script > <!-- Use you actual path to the browser bundle -->
< / head >
< body >
...
< script >
... // your code here
< / script >
< / body >
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```
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An example of usage could be:
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```javascript
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/* Stage 3 BigInts with value 666 can be declared as BigInt('666')
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or the shorter syntax 666n.
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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.
*/
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const a = BigInt('5')
const b = BigInt('2')
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const n = 19n
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console.log(bigintModArith.modPow(a, b, n)) // prints 6
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console.log(bigintModArith.modInv(2n, 5n)) // prints 3
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console.log(bigintModArith.modInv(BigInt('3'), BigInt('5'))) // prints 2
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```
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## API reference documentation
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< a name = "module_bigint-mod-arith" > < / a >
### 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 ) ⇒ < code > bigint</ code >
* [~bitLength(a) ](#module_bigint-mod-arith..bitLength ) ⇒ < code > number</ code >
* [~eGcd(a, b) ](#module_bigint-mod-arith..eGcd ) ⇒ < code > egcdReturn</ code >
* [~gcd(a, b) ](#module_bigint-mod-arith..gcd ) ⇒ < code > bigint</ code >
* [~lcm(a, b) ](#module_bigint-mod-arith..lcm ) ⇒ < code > bigint</ code >
* [~max(a, b) ](#module_bigint-mod-arith..max ) ⇒ < code > bigint</ code >
* [~min(a, b) ](#module_bigint-mod-arith..min ) ⇒ < code > bigint</ code >
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* [~modInv(a, n) ](#module_bigint-mod-arith..modInv ) ⇒ < code > bigint</ code > \| < code > NaN</ code >
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* [~modPow(b, e, n) ](#module_bigint-mod-arith..modPow ) ⇒ < code > bigint</ code >
* [~toZn(a, n) ](#module_bigint-mod-arith..toZn ) ⇒ < code > bigint</ code >
* [~egcdReturn ](#module_bigint-mod-arith..egcdReturn ) : < code > Object</ code >
< a name = "module_bigint-mod-arith..abs" > < / a >
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#### bigint-mod-arith~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**: inner method of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
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**Returns**: < code > bigint< / code > - the absolute value of a
| Param | Type |
| --- | --- |
| a | < code > number</ code > \| < code > bigint</ code > |
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< a name = "module_bigint-mod-arith..bitLength" > < / a >
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#### bigint-mod-arith~bitLength(a) ⇒ <code>number</code>
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Returns the bitlength of a number
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**Kind**: inner method of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
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**Returns**: < code > number< / code > - - the bit length
| Param | Type |
| --- | --- |
| a | < code > number</ code > \| < code > bigint</ code > |
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< a name = "module_bigint-mod-arith..eGcd" > < / a >
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#### bigint-mod-arith~eGcd(a, b) ⇒ <code>egcdReturn</code>
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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**: inner method of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
**Returns**: < code > egcdReturn< / code > - A triple (g, x, y), such that ax + by = g = gcd(a, b).
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| Param | Type |
| --- | --- |
| a | < code > number</ code > \| < code > bigint</ code > |
| b | < code > number</ code > \| < code > bigint</ code > |
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< a name = "module_bigint-mod-arith..gcd" > < / a >
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#### bigint-mod-arith~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**: inner method of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
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**Returns**: < code > bigint< / code > - The greatest common divisor of a and b
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| Param | Type |
| --- | --- |
| a | < code > number</ code > \| < code > bigint</ code > |
| b | < code > number</ code > \| < code > bigint</ code > |
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< a name = "module_bigint-mod-arith..lcm" > < / a >
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#### bigint-mod-arith~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**: inner method of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
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**Returns**: < code > bigint< / code > - The least common multiple of a and b
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| Param | Type |
| --- | --- |
| a | < code > number</ code > \| < code > bigint</ code > |
| b | < code > number</ code > \| < code > bigint</ code > |
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< a name = "module_bigint-mod-arith..max" > < / a >
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#### bigint-mod-arith~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**: inner method of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
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**Returns**: < code > bigint< / code > - maximum of numbers a and b
| Param | Type |
| --- | --- |
| a | < code > number</ code > \| < code > bigint</ code > |
| b | < code > number</ code > \| < code > bigint</ code > |
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< a name = "module_bigint-mod-arith..min" > < / a >
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#### bigint-mod-arith~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**: inner method of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
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**Returns**: < code > bigint< / code > - minimum of numbers a and b
| Param | Type |
| --- | --- |
| a | < code > number</ code > \| < code > bigint</ code > |
| b | < code > number</ code > \| < code > bigint</ code > |
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< a name = "module_bigint-mod-arith..modInv" > < / a >
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#### bigint-mod-arith~modInv(a, n) ⇒ <code>bigint</code> \| <code>NaN</code>
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Modular inverse.
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**Kind**: inner method of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
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**Returns**: < code > bigint</ code > \| < code > NaN</ code > - the inverse modulo n or NaN if it does not exist
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| 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 |
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< a name = "module_bigint-mod-arith..modPow" > < / a >
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#### bigint-mod-arith~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**: inner method of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
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**Returns**: < code > bigint< / code > - b**e mod n
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| Param | Type | Description |
| --- | --- | --- |
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| b | < code > number</ code > \| < code > bigint</ code > | base |
| 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 = "module_bigint-mod-arith..toZn" > < / a >
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#### bigint-mod-arith~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**: inner method of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
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**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 |
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< a name = "module_bigint-mod-arith..egcdReturn" > < / a >
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#### bigint-mod-arith~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**: inner typedef of [<code>bigint-mod-arith</code> ](#module_bigint-mod-arith )
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**Properties**
| Name | Type |
| --- | --- |
| g | < code > bigint< / code > |
| x | < code > bigint< / code > |
| y | < code > bigint< / code > |
