Gauss sieve algorithm on GPUs

Abstract

Lattice-based cryptanalysis is an important field in cryptography since lattice problems are among the most robust assumptions, and have been used to construct most cryptographic primitives. In this research, we focus on the Gauss Sieve algorithm, a heuristic lattice sieving algorithm proposed by Micciancio and Voulgaris. We propose the technique of lifting computations in prime-cyclotomic ideals into that in cyclic ideals. Lifting makes rotations easier to compute and reduces the complexity of inner products from O(n3) to O(n2). We implemented our Gauss Sieve on GPUs by adapting the framework of Ishiguro et al. in a single GPU, and the one of Bos et al. among multiple GPUs. We found a short vector at dimension 130 in the Darmstadt Ideal SVP Challenge (currently in first place in the Hall of Fame) using 8 GPUs in 824 h using our implementation.