https://github.com/yaffle/quadraticsievefactorization

Quadratic Sieve integer factorization method for JavaScript bigints
https://github.com/yaffle/quadraticsievefactorization

javascript quadratic-sieve

Last synced: about 1 month ago
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Quadratic Sieve integer factorization method for JavaScript bigints

• Host: GitHub
• URL: https://github.com/yaffle/quadraticsievefactorization
• Owner: Yaffle
• Created: 2021-12-24T21:46:16.000Z (almost 3 years ago)
• Default Branch: main
• Last Pushed: 2024-06-26T07:29:14.000Z (5 months ago)
• Last Synced: 2024-09-27T13:34:26.940Z (about 2 months ago)
• Topics: javascript, quadratic-sieve
• Language: JavaScript
• Homepage:
• Size: 342 KB
• Stars: 4
• Watchers: 2
• Forks: 0
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# QuadraticSieveFactorization

Integer factorization using [Quadratic Sieve](https://en.wikipedia.org/wiki/Quadratic_sieve) algorithm in JavaScript.

The variant is multipolynomial self-initializing with two large-primes.

There is series of videos explaining the algorithm at https://www.youtube.com/playlist?list=PL0OUqr2O9PxLd35SgBiWIxuLgm7mYksfp .

Useful info can also be found at https://www.rieselprime.de/ziki/Self-initializing_quadratic_sieve and at https://www.enseignement.polytechnique.fr/informatique/INF558/TD/td_5/S0025-5718-1987-0866119-8.pdf .

See other links in the code.

# Example

```javascript

import factorize from './QuadraticSieveFactorization.js';

console.time();

const f = factorize(2n**128n + 1n);

console.timeEnd();

// ~50ms

console.assert(f === 5704689200685129054721n || f === 59649589127497217n, f);

```

# Usage notes:

* Do not call for the **prime numbers**. It may hang for them. Check if the number is prime instead.

* Do not call for the **[perfect powers](https://en.wikipedia.org/wiki/Perfect_power)**. it may hang for them. Check if the number is a perfect power instead. 

* Do not call for the **numbers with a small factor**, it is as slow as for semiprimes with similar factor size for them. Try other algorithms to check for small factors instead.

* The returned value is a some factor, not necessary prime.

See https://www.rieselprime.de/ziki/Factorization for the more detailed usage notes.

# Demo

See [demo](https://yaffle.github.io/QuadraticSieveFactorization/demo.html).

# Performance

The code uses only single thread.

It takes approximately 1.5 hours to factor [RSA-100](https://en.wikipedia.org/wiki/RSA_numbers#RSA-100) 

and 13.5 hours to factor [RSA-110](https://en.wikipedia.org/wiki/RSA_numbers#RSA-110) on Core i7-1165G7

Probably larger numbers will cause lack of memory.