Lattice decoding attacks on binary LWE

Abstract

We consider the binary-LWE problem, which is the learning with errors problem when the entries of the secret vector are chosen from {0, 1} or {-1, 0, 1}. Our main result is an improved lattice decoding algorithm for binary-LWE, by translating to the inhomogeneous short integer solution (ISIS) problem, and then re-scaling the lattice. We also discuss modulus switching as an approach to the problem. Our conclusion is that binary-LWE is easier than general LWE. We give experimental results, and theoretical estimates for parameters that achieve certain security levels. © 2014 Springer International Publishing Switzerland.