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.

翻译：最接近向量问题（CVP）是格基密码学中的基础优化问题，其公认的困难性构成了格基密码系统安全性的基石。此外，Schnorr的格基分解算法将整数分解（当前包括RSA在内的密码系统的基础）归约为CVP。近期研究探讨了在格基分解算法中引入启发式CVP近似“精化”步骤，利用量子变分算法执行启发式优化。这与概率计算作为随机算法硬件加速器的兴起相契合，此类算法涵盖组合优化任务。本研究探讨了概率计算在格基分解中CVP近似精化的启发式优化任务中的应用。我们提出了针对该任务的概率计算算法设计，讨论了“素数格”参数，并通过实验结果表明概率计算在求解CVP及其作为格基分解子程序方面的有效性。主要研究发现：（a）该方法能够以问题规模线性时间找到可用的最大CVP近似精化解；（b）结合所提出的格参数，概率计算在分解半素数时所需的格实例数量可比同类量子与经典方法减少高达100倍。