We construct noninteractive statistical zero-knowledge (NISZK) proof systems for a variety of standard approximation problems on lattices, such as the shortest independent vectors...
We prove the equivalence, up to a small polynomial approximation factor n/ log n, of the lattice problems uSVP (unique Shortest Vector Problem), BDD (Bounded Distance Decoding) and...
We show that approximating the shortest vector problem (in any p norm) to within any constant factor less than p 2 is hard for NP under reverse unfaithful random reductions with i...
The contact polytope of a lattice is the convex hull of its shortest vectors. In this paper we reveal the face structure of the contact polytope of the Leech lattice. We classify i...
We introduce the use of Fourier analysis on lattices as an integral part of a lattice based construction. The tools we develop provide an elegant description of certain Gaussian d...