A Probabilistic Computing Approach to the Closest Vector Problem for Lattice-Based Factoring

TL;DR

This paper explores using probabilistic computing to efficiently approximate the closest vector problem in lattice cryptography, significantly reducing computational resources needed for lattice-based factoring of semiprimes.

Contribution

It introduces a probabilistic computing algorithm for CVP approximation refinement and demonstrates its effectiveness in lattice-based factoring, outperforming quantum and classical methods.

Findings

Capable of finding maximal CVP approximation in linear time

Reduces lattice instances by up to 100x compared to other methods

Effective in factoring semiprimes with fewer resources

Abstract

The closest vector problem (CVP) is a fundamental optimization problem in lattice-based cryptography and its conjectured hardness underpins the security of lattice-based cryptosystems. Furthermore, Schnorr's lattice-based factoring algorithm reduces integer factoring (the foundation of current cryptosystems, including RSA) to the CVP. Recent work has investigated the inclusion of a heuristic CVP approximation `refinement' step in the lattice-based factoring algorithm, using quantum variational algorithms to perform the heuristic optimization. This coincides with the emergence of probabilistic computing as a hardware accelerator for randomized algorithms including tasks in combinatorial optimization. In this work we investigate the application of probabilistic computing to the heuristic optimization task of CVP approximation refinement in lattice-based factoring. We present the design of a probabilistic computing algorithm for this task, a discussion of `prime lattice' parameters, and experimental results showing the efficacy of probabilistic computing for solving the CVP as well as its efficacy as a subroutine for lattice-based factoring. The main results found that (a) this approach is capable of finding the maximal available CVP approximation refinement in time linear in problem size and (b) probabilistic computing used in conjunction with the lattice parameters presented can find the composite prime factors of a semiprime number using up to 100x fewer lattice instances than similar quantum and classical methods.