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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 ES6 bundle module from GitHub.
Usage example
Import your module as :
- Node.js
const bigintModArith = require('bigint-mod-arith') ... // your code here
- JavaScript native project
import * as bigintModArith from 'bigint-mod-arith' ... // your code here
- JavaScript native browser ES6 mod
<script type="module"> import * as bigintModArith from 'lib/index.browser.bundle.mod.js' // Use you actual path to the browser 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>
- TypeScript
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 alsotarget
andmodule
) toesnext
intsconfig.json
.
/* 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
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 |