Deno Random Prime Numbers 🦕

A random prime number generator for Deno.

This module can generate a pseudorandom prime number with a bigint type from a:

• desired bit-length (e.g. 1024-bit); and
• an optional number of primality tests

NOTE: This module is currently exposed to a variable time attack and therefore shouldn't be used for cryptography until further notice.

Created by Jacob Ian Matthews - Website | GitHub

Usage

Generate a Random Prime Number

randomPrime(bitlength, tests)

Where:

• randomPrime() returns a bigint.
• bitlength is a number that is >= 8.
• tests is an optional number with a default value of 5.

Example:

import { randomPrime } from "https://deno.land/x/random_prime/mod.ts";

// Generate a random 1024-bit prime number with 5 primality tests
var prime: bigint = randomPrime(1024)

// Generate a random 2048-bit prime number with 10 primality tests
var prime: bigint = randomPrime(2048, 10)

Test if a BigInt is a Prime Number with Miller-Rabin

isProbablePrime(candidate, tests)

Where:

• isProbablePrime() returns a boolean.
• candidate is a bigint.
• tests is an optional number with a default value of 10.

Example:

import { isProbablePrime } from "https://deno.land/x/random_prime/mod.ts";

// Have a number to test for primality
const candidate: bigint = 167n;

// Check if candidate is a probable prime with 10 primality tests
isProbablePrime(candidate) ? console.log("probable prime") : console.log("composite");

Performance Information

Increasing the number of primality tests and increasing the bit-length will decrease the speed of prime number generation.

The probability that a composite number is incorrectly classified as a prime number decreases with an increased number of primality tests such that:

P(misclassified)=(1/4)^t

Where:

• t is the number of tests.

License

MIT License.

References

The Miller-Rabin Primality Test algorithm was sourced from:
Menezes, A., P. van Oorschot and S. Vanstone. 1996. Handbook of Applied Cryptography. Boca Raton, Florida: Taylor & Francis Group, LLC.