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

Conference paper

DOI: 10.1007/978-3-319-22174-8_6

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9230)
Cite this paper as:
Laarhoven T., de Weger B. (2015) Faster Sieving for Shortest Lattice Vectors Using Spherical Locality-Sensitive Hashing. In: Lauter K., Rodríguez-Henríquez F. (eds) Progress in Cryptology -- LATINCRYPT 2015. LATINCRYPT 2015. Lecture Notes in Computer Science, vol 9230. Springer, Cham

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.

Keywords

Shortest vector problem (svp) Sieving algorithms Nearest neighbor problem Locality-sensitive hashing (lsh) Lattice cryptography 

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceEindhoven University of TechnologyEindhovenThe Netherlands

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