Paper 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.

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

Metadata
Available format(s)
PDF
Publication info
A minor revision of an IACR publication in JOC 2016
Keywords
latticesGentry-Szydlo algorithmideal latticeslattice-based cryptography
Contact author(s)
asilverb @ math uci edu
History
2016-10-04: last of 2 revisions
2015-01-02: received
See all versions
Short URL
https://ia.cr/2014/1026
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2014/1026,
      author = {H.  W.  Lenstra Jr. and A.  Silverberg},
      title = {Lattices with Symmetry},
      howpublished = {Cryptology ePrint Archive, Paper 2014/1026},
      year = {2014},
      note = {\url{https://eprint.iacr.org/2014/1026}},
      url = {https://eprint.iacr.org/2014/1026}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.