### LP Solutions of Vectorial Integer Subset Sums - Cryptanalysis of Galbraith's Binary Matrix LWE

Alexander May and Gottfried Herold

##### Abstract

We consider Galbraith's space efficient LWE variant, where the $(m \times n)$-matrix $A$ is binary. In this binary case, solving a vectorial subset sum problem over the integers allows for decryption. We show how to solve this problem using (Integer) Linear Programming. Our attack requires only a fraction of a second for all instances in a regime for $m$ that cannot be attacked by current lattice algorithms. E.g.\ we are able to solve 100 instances of Galbraith's small LWE challenge $(n,m) = (256, 400)$ all in a fraction of a second. We also show under a mild assumption that instances with $m \leq 2n$ can be broken in polynomial time via LP relaxation. Moreover, we develop a method that identifies weak instances for Galbraith's large LWE challenge $(n,m)=(256, 640)$.

Available format(s)
Category
Public-key cryptography
Publication info
Published by the IACR in PKC 2017
DOI
10.1007/978-3-662-54365-8_1
Keywords
Binary matrix LWELinear ProgrammingCryptanalysis
Contact author(s)
gottfried herold @ rub de
History
Short URL
https://ia.cr/2018/741

CC BY

BibTeX

@misc{cryptoeprint:2018/741,
author = {Alexander May and Gottfried Herold},
title = {LP Solutions of Vectorial Integer Subset Sums - Cryptanalysis of Galbraith's Binary Matrix LWE},
howpublished = {Cryptology ePrint Archive, Paper 2018/741},
year = {2018},
doi = {10.1007/978-3-662-54365-8_1},
note = {\url{https://eprint.iacr.org/2018/741}},
url = {https://eprint.iacr.org/2018/741}
}

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