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 $$2^{0.337n + on}$$20.337n+on and space complexity $$2^{0.208n + on}$$20.208n+on. 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 $$2^{0.298n + on}$$20.298n+on and space $$2^{0.208n + on}$$20.208n+on. 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.