Heterogeneous Implementation of a Voronoi Cell-Based SVP Solver

Abstract

This paper presents a new, heterogeneous CPU+GPU attacks against lattice-based (postquantum) cryptosystems based on the Shortest Vector Problem (SVP), a central problem in lattice-based cryptanalysis. To the best of our knowledge, this is the first SVP-attack against lattice-based cryptosystems using CPUs and GPUs simultaneously. We show that Voronoi-cell based CPU+GPU attacks, algorithmically improved in previous work, are suitable for the proposed massively parallel platforms. Results show that 1) heterogeneous platforms are useful in this scenario, as they increment the overall memory available in the system (as GPU's memory can be used effectively), a typical bottleneck for Voronoi-cell algorithms, and we have also been able to increase the performance of the algorithm on such a platform, by successfully using the GPU as a co-processor, 2) this attack can be successfully accelerated using conventional GPUs and 3) we can take advantage of multiple GPUs to attack lattice-based cryptosystems. Experimental results show a speedup up to 7.6× for 2 GPUs hosted by an Intel Xeon E5-2695 v2 CPU (12 cores ×2 sockets) using only 1 core and gains in the order of 20% for 2 GPUs hosted by the same machine using all 22 CPU threads (2 are reserved for orchestrating the GPUs), compared to single-CPU execution using the entire 24 threads available.

Keywords

• Lattices
• lattice-based cryptanalysis
• Voronoi-cell
• algorithms
• high performance computing
• parallelism