Paper 2015/211

Faster sieving for shortest lattice vectors using spherical locality-sensitive hashing

Thijs Laarhoven and Benne de Weger

Abstract

Recently, it was shown that angular locality-sensitive hashing (LSH) can be used to significantly speed up lattice sieving, leading to a heuristic time complexity for solving the shortest vector problem (SVP) of $2^{0.337n + o(n)}$ (and space complexity $2^{0.208n + o(n)}$. We study the possibility of applying other LSH methods to sieving, and show that with the spherical LSH method of Andoni et al.\ we can heuristically solve SVP in time $2^{0.298n + o(n)}$ and space $2^{0.208n + o(n)}$. We further show that a practical variant of the resulting SphereSieve is very similar to Wang et al.'s two-level sieve, with the key difference that we impose an order on the outer list of centers.