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

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 20.337n+o(n) (and space complexity 20.208n+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 20.298n+o(n) and space 20.208n+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.