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Title:
Lattices with Symmetry
Authors: H. W. Lenstra Jr., 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.
ePrint: https://eprint.iacr.org/2014/1026
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