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

• JavaScript native or TypeScript project

  import * as bigintModArith 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.

• JavaScript native browser ES6 mod

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

• JavaScript native browser IIFE

  <script src="../../lib/index.browser.bundle.js"></script> <!-- Use you actual path to the browser bundle -->
  <script>
    ... // your code here
  </script>
  

And you could use it like in the following:

/* 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
  • ~abs(a) ⇒ bigint
  • ~bitLength(a) ⇒ number
  • ~eGcd(a, b) ⇒ egcdReturn
  • ~gcd(a, b) ⇒ bigint
  • ~lcm(a, b) ⇒ bigint
  • ~max(a, b) ⇒ bigint
  • ~min(a, b) ⇒ bigint
  • ~modInv(a, n) ⇒ bigint
  • ~modPow(b, e, n) ⇒ bigint
  • ~toZn(a, n) ⇒ bigint
  • ~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
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
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
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
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
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
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
Returns: bigint - minimum of numbers a and b

Param	Type
a	number | bigint
b	number | bigint

bigint-mod-arith~modInv(a, n) ⇒ bigint

Modular inverse.

Kind: inner method of bigint-mod-arith
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

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
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
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
Properties

Name	Type
g	bigint
x	bigint
y	bigint