[Resource Topic] 2018/741: LP Solutions of Vectorial Integer Subset Sums - Cryptanalysis of Galbraith's Binary Matrix LWE

Welcome to the resource topic for 2018/741

Title:
LP Solutions of Vectorial Integer Subset Sums - Cryptanalysis of Galbraith’s Binary Matrix LWE

Authors: Alexander May, 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).

ePrint: https://eprint.iacr.org/2018/741

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