Integer Factorisation, Fermat & Machine Learning on a Classical Computer

TL;DR

This paper presents a deep learning-based probabilistic approach to integer factorisation, transforming the problem into a binary classification task using Fermat's method and synthetic training data, aiming for a scalable solution.

Contribution

It introduces a novel combination of Fermat's factorisation and deep learning to approach integer factorisation on classical computers.

Findings

Initial experiments show promise but need further development.

Synthetic data generation is effective for training classifiers.

The approach opens new avenues for classical integer factorisation methods.

Abstract

In this paper we describe a deep learning--based probabilistic algorithm for integer factorisation. We use Lawrence's extension of Fermat's factorisation algorithm to reduce the integer factorisation problem to a binary classification problem. To address the classification problem, based on the ease of generating large pseudo--random primes, a corpus of training data, as large as needed, is synthetically generated. We will introduce the algorithm, summarise some experiments, analyse where these experiments fall short, and finally put out a call to others to reproduce, verify and see if this approach can be improved to a point where it becomes a practical, scalable factorisation algorithm.