Cryptology ePrint Archive: Report 2014/1026

Lattices with Symmetry

H. W. Lenstra, Jr. and A. Silverberg

Abstract: For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a provably deterministic polynomial-time algorithm to accomplish this, based on the work of Gentry and Szydlo. The techniques involve algorithmic algebraic number theory, analytic number theory, commutative algebra, and lattice basis reduction.

Category / Keywords: foundations / lattices, Gentry-Szydlo algorithm, ideal lattices, lattice-based cryptography

Date: received 31 Dec 2014, last revised 10 Sep 2015

Contact author: asilverb at math uci edu

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Version: 20150910:154914 (All versions of this report)

Short URL: ia.cr/2014/1026

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