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: ia.cr/2014/1026
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