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.