Faster Sieving for Shortest Lattice Vectors Using Spherical Locality-Sensitive Hashing

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 (and space complexity 2. 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 and space 2. 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.