Integer Factorization with a Neuromorphic Sieve

TL;DR

This paper introduces a neuromorphic sieve that drastically accelerates integer factorization by enabling constant-time smoothness checks, leveraging neuromorphic hardware's parallelism and synaptic integration.

Contribution

It presents a novel neuromorphic approach to integer sieving, significantly improving the efficiency of the factorization process over traditional methods.

Findings

Achieved constant-time smoothness checks using neuromorphic hardware

Modified existing factorization software to utilize neuromorphic coprocessors

Demonstrated potential for faster large integer factorization processes

Abstract

The bound to factor large integers is dominated by the computational effort to discover numbers that are smooth, typically performed by sieving a polynomial sequence. On a von Neumann architecture, sieving has log-log amortized time complexity to check each value for smoothness. This work presents a neuromorphic sieve that achieves a constant time check for smoothness by exploiting two characteristic properties of neuromorphic architectures: constant time synaptic integration and massively parallel computation. The approach is validated by modifying msieve, one of the fastest publicly available integer factorization implementations, to use the IBM Neurosynaptic System (NS1e) as a coprocessor for the sieving stage.