Lattices with Symmetry
Number Theory
2016-10-05 v3 Cryptography and Security
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.
Cite
@article{arxiv.1501.00178,
title = {Lattices with Symmetry},
author = {H. W. Lenstra and A. Silverberg},
journal= {arXiv preprint arXiv:1501.00178},
year = {2016}
}
Comments
Published in Journal of Cryptology. Minor typos corrected