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: lattices, Gentry-Szydlo algorithm, ideal lattices, lattice-based cryptography

Original Publication (with minor differences): IACR-JOC-2016

Date: received 31 Dec 2014, last revised 3 Oct 2016

Contact author: asilverb at math uci edu

Available format(s): PDF | BibTeX Citation

Note: Published in Journal of Cryptology. Minor typos corrected.

Version: 20161004:021520 (All versions of this report)

Short URL:

Discussion forum: Show discussion | Start new discussion

[ Cryptology ePrint archive ]