Paper 2018/741
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 $(n,m)=(256, 640)$.
Metadata
- Available format(s)
-
PDF
- 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
- 2018-08-15: received
- Short URL
- https://ia.cr/2018/741
- License
-
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},
url = {https://eprint.iacr.org/2018/741}
}