Lattices with Symmetry

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.

Published in Journal of Cryptology. Minor typos corrected

References in corpus (1)

• Roots of unity in orders

Cited by in corpus (1)

• Algorithms for commutative algebras over the rational numbers