bigint-mod-arith/README.md

bigint-mod-arith

Some extra functions to work with modular arithmetic using native JS (ES-2020) implementation of BigInt. It can be used by any Web Browser or webview supporting BigInt 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. Many platforms provide native support for cryptography, such as Web Cryptography API or Node.js Crypto.

Installation

bigint-mod-arith is distributed for web browsers and/or webviews supporting BigInt 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:

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 or the ES6 bundle module from GitHub.

Usage example

Import your module as :

• Node.js

  const bigintCryptoUtils = require('bigint-mod-arith')
  ... // your code here
  

• JavaScript native project

  import * as bigintCryptoUtils from 'bigint-mod-arith'
  ... // your code here
  

• Javascript native browser ES6 mod

  <script type="module">
     import * as bigintCryptoUtils from 'lib/index.browser.bundle.mod.js'  // Use you actual path to the broser mod bundle
     ... // your code here
   </script>
  import as bcu from 'bigint-mod-arith'
  ... // your code here
  

• JavaScript native browser IIFE

  <script src="../../lib/index.browser.bundle.js"></script>
  <script>
    ... // your code here
  </script>
  

• TypeScript

  import * as bigintCryptoUtils from 'bigint-mod-arith'
  ... // your code here
  

  BigInt is ES-2020. In order to use it with TypeScript you should set lib (and probably also target and module) to esnext in tsconfig.json.

/* 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.
*/
const a = BigInt('5')
const b = BigInt('2')
const 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

JS Doc

abs(a) ⇒ bigint

Absolute value. abs(a)==a if a>=0. abs(a)==-a if a<0

Kind: global function
Returns: bigint - the absolute value of a

Param	Type
a	number | bigint

bitLength(a) ⇒ number

Returns the bitlength of a number

Kind: global function
Returns: number - - the bit length

Param	Type
a	number | bigint

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: global function
Returns: egcdReturn - A triple (g, x, y), such that ax + by = g = gcd(a, b).

Param	Type
a	number | bigint
b	number | bigint

gcd(a, b) ⇒ bigint

Greatest-common divisor of two integers based on the iterative binary algorithm.

Kind: global function
Returns: bigint - The greatest common divisor of a and b

Param	Type
a	number | bigint
b	number | bigint

lcm(a, b) ⇒ bigint

The least common multiple computed as abs(a*b)/gcd(a,b)

Kind: global function
Returns: bigint - The least common multiple of a and b

Param	Type
a	number | bigint
b	number | bigint

max(a, b) ⇒ bigint

Maximum. max(a,b)==a if a>=b. max(a,b)==b if a<=b

Kind: global function
Returns: bigint - maximum of numbers a and b

Param	Type
a	number | bigint
b	number | bigint

min(a, b) ⇒ bigint

Minimum. min(a,b)==b if a>=b. min(a,b)==a if a<=b

Kind: global function
Returns: bigint - minimum of numbers a and b

Param	Type
a	number | bigint
b	number | bigint

modInv(a, n) ⇒ bigint

Modular inverse.

Kind: global function
Returns: bigint - 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

modPow(b, e, n) ⇒ bigint

Modular exponentiation b**e mod n. Currently using the right-to-left binary method

Kind: global function
Returns: bigint - b**e mod n

Param	Type	Description
b	number | bigint	base
e	number | bigint	exponent
n	number | bigint	modulo

toZn(a, n) ⇒ bigint

Finds the smallest positive element that is congruent to a in modulo n

Kind: global function
Returns: bigint - The smallest positive representation of a in modulo n

Param	Type	Description
a	number | bigint	An integer
n	number | bigint	The modulo

egcdReturn : Object

A triple (g, x, y), such that ax + by = g = gcd(a, b).

Kind: global typedef
Properties

Name	Type
g	bigint
x	bigint
y	bigint