### Coded-BKW: Solving LWE Using Lattice Codes

Qian Guo, Thomas Johansson, and Paul Stankovski

##### Abstract

In this paper we propose a new algorithm for solving the Learning With Errors (LWE) problem based on the steps of the famous Blum-Kalai-Wasserman (BKW) algorithm. The new idea is to introduce an additional procedure of mapping subvectors into codewords of a lattice code, thereby increasing the amount of positions that can be cancelled in each BKW step. The procedure introduces an additional noise term, but it is shown that by using a sequence of lattice codes with different rates the noise can be kept small. Developed theory shows that the new approach compares favorably to previous methods. It performs particularly well for the binary-LWE case, i.e., when the secret vector is sampled from $(0,1)^*$.

Available format(s)
Category
Foundations
Publication info
Keywords
LWEbinary-LWEBKWCoded-BKWLattice codes.
Contact author(s)
fywzguoqian @ gmail com
History
Short URL
https://ia.cr/2016/310

CC BY

BibTeX

@misc{cryptoeprint:2016/310,
author = {Qian Guo and Thomas Johansson and Paul Stankovski},
title = {Coded-BKW: Solving LWE Using Lattice Codes},
howpublished = {Cryptology ePrint Archive, Paper 2016/310},
year = {2016},
note = {\url{https://eprint.iacr.org/2016/310}},
url = {https://eprint.iacr.org/2016/310}
}

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