## Cryptology ePrint Archive: Report 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 $(n,m)=(256, 640)$.

Category / Keywords: public-key cryptography / Binary matrix LWE, Linear Programming, Cryptanalysis

Original Publication (in the same form): IACR-PKC-2017
DOI:
10.1007/978-3-662-54365-8_1