Cryptology ePrint Archive: Report 2013/839

Lattice Decoding Attacks on Binary LWE

Shi Bai and Steven D. Galbraith

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 $\{ -1, 0, 1 \}$ (and the error vector is sampled from a discrete Gaussian distribution). Our main result is an improved lattice decoding algorithm for binary-LWE which first translates the problem to the inhomogeneous short integer solution (ISIS) problem, and then solves the closest vector problem using a re-scaling of 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 that can be used to choose parameters for binary-LWE to achieve certain security levels.

Category / Keywords: lattice decoding attacks, learning with errors, closest vector problem.

Original Publication (with minor differences): ACISP 2014

Date: received 11 Dec 2013, last revised 24 Apr 2014

Contact author: S Bai at auckland ac nz

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Version: 20140424:083229 (All versions of this report)

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