Cryptology ePrint Archive: Report 2014/019

Lazy Modulus Switching for the BKW Algorithm on LWE

Martin R. Albrecht and Jean-Charles Faugère and Robert Fitzpatrick and Ludovic Perret

Abstract: Some recent constructions based on LWE do not sample the secret uniformly at random but rather from some distribution which produces small entries. The most prominent of these is the binary-LWE problem where the secret vector is sampled from {0, 1}∗ or {−1, 0, 1}∗. We present a variant of the BKW algorithm for binary-LWE and other small secret variants and show that this variant reduces the complexity for solving binary-LWE. We also give estimates for the cost of solving binary-LWE instances in this setting and demonstrate the advantage of this BKW variant over standard BKW and lattice reduction techniques applied to the SIS problem. Our variant can be seen as a combination of the BKW algorithm with a lazy variant of modulus switching which might be of independent interest.

Category / Keywords: foundations / Learning with Errors

Original Publication (with major differences): IACR-PKC-2014

Date: received 7 Jan 2014

Contact author: martinralbrecht+eprint at googlemail com

Available format(s): PDF | BibTeX Citation

Version: 20140108:174824 (All versions of this report)

Short URL: ia.cr/2014/019