Parallel Improved Schnorr-Euchner Enumeration SE++ for the CVP and SVP

Abstract

The Closest Vector Problem (CVP) and the Shortest Vector Problem (SVP) are prime problems in lattice-based cryptanalysis, since they underpin the security of many lattice-based cryptosystems. Despite the importance of these problems, there are only a few CVP-solvers publicly available, and their scalability was never studied. This paper presents a scalable implementation of an enumeration-based CVP-solver for multi-cores, which can be easily adapted to solve the SVP. In particular, it achieves super-linear speedups in some instances on up to 8 cores and almost linear speedups on 16 cores when solving the CVP on a 50-dimensional lattice. Our results show that enumeration-based CVP-solvers can be parallelized as effectively as enumeration-based solvers for the SVP, based on a comparison with a state of the art SVP-solver. In addition, we show that we can optimize the SVP variant of our solver in such a way that it becomes 35%-60% faster than the fastest enumeration-based SVP-solver to date.