246 lines
9.6 KiB
Markdown
246 lines
9.6 KiB
Markdown
[](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
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npm install bigint-mod-arith
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```
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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 :
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- Node.js
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```javascript
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const bigintModArith = require('bigint-mod-arith')
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... // your code here
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```
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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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```
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- JavaScript native browser ES module
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```html
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<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
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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.iife.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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/* 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
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recommended since values over 2**53 - 1 won't be safe but no warning will
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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(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>
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### bigint-mod-arith
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Some common functions for modular arithmetic using native JS implementation of BigInt
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* [bigint-mod-arith](#module_bigint-mod-arith)
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* [~abs(a)](#module_bigint-mod-arith..abs) ⇒ <code>bigint</code>
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* [~bitLength(a)](#module_bigint-mod-arith..bitLength) ⇒ <code>number</code>
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* [~eGcd(a, b)](#module_bigint-mod-arith..eGcd) ⇒ <code>egcdReturn</code>
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* [~gcd(a, b)](#module_bigint-mod-arith..gcd) ⇒ <code>bigint</code>
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* [~lcm(a, b)](#module_bigint-mod-arith..lcm) ⇒ <code>bigint</code>
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* [~max(a, b)](#module_bigint-mod-arith..max) ⇒ <code>bigint</code>
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* [~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>
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* [~toZn(a, n)](#module_bigint-mod-arith..toZn) ⇒ <code>bigint</code>
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* [~egcdReturn](#module_bigint-mod-arith..egcdReturn) : <code>Object</code>
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<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
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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="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
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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="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)
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**Returns**: <code>egcdReturn</code> - 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="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 |
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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="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 |
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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="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
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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="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
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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="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 |
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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="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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| --- | --- | --- |
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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="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
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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="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**
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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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