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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 ESM bundle from the repository.
Usage example
Import your module as :
- Node.js
const bigintModArith = require('bigint-mod-arith') ... // your code here - JavaScript native or TypeScript project (including React and Angular)
import * as bigintModArith from 'bigint-mod-arith' ... // your code here - JavaScript native browser ES module
<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
<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>
An example of usage could be:
/* 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|NaN - ~modPow(b, e, n) ⇒
bigint - ~toZn(a, n) ⇒
bigint - ~egcdReturn :
Object
- ~abs(a) ⇒
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 | NaN
Modular inverse.
Kind: inner method of 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
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 |