Integer Factorisation, Fermat & Machine Learning on a Classical Computer
This addresses the problem of integer factorization for cryptography and number theory, but it is incremental as it builds on existing methods without demonstrated practical improvements.
The paper tackles integer factorization by reducing it to a binary classification problem using Lawrence's extension of Fermat's algorithm and a deep learning approach, with experiments conducted but no concrete numerical results reported on performance or scalability.
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.