Scaling up prime factorization with self-organizing gates: A memcomputing approach

TL;DR

This paper demonstrates that the MEMCPU platform can efficiently scale prime factorization of large biprimes, especially using the congruence model, with potential for real-time applications through ASIC implementation.

Contribution

It introduces a novel memcomputing approach with structure-dependent tuning for prime factorization, achieving scalable performance on large biprimes unlike traditional methods.

Findings

MEMCPU's congruence model scaled up to 300-bit biprimes

Factorization times follow a quadratic polynomial in the number of bits

Potential for real-time factorization with ASIC implementation

Abstract

We report preliminary results on using the MEMCPU\texttrademark{} Platform to compute the prime factorization of large biprimes. The first approach, the direct model, directly returns the factors of a given biprime. The second approach, the congruence model, returns smooth congruences to address the bottleneck of standard sieve methods. The models have size-dependent structure, and the MEMCPU Platform requires structure-dependent tuning for optimal performance. Therefore, for both models, we tuned the platform on sample problems up to a given size according to available resources. Then we generated RSA-like benchmark biprimes to perform rigorous scaling analysis. The MEMCPU timings over the tuned range followed low degree polynomials in the number of bits, markedly different than other tested methods including general number field sieve. MEMCPU's congruence model was the most promising, which was scaled up to 300-bit factorization problems while following a $2^{nd}$ degree polynomial fit. We also discuss the approach to tuning the MEMCPU Platform for problems beyond the reach of today's most advanced methods. Finally, basic analysis of the acceleration expected from an ASIC implementation is provided and suggests the possibility of real time factorization of large biprimes.