Improving BDD Cryptosystems in General Lattices

A prime goal of Lattice-based cryptosystems is to provide an enhanced security assurance by remaining secure with respect to quantum computational complexity, while remaining practical on conventional computer systems. In this paper, we define and analyze a superclass of GGH-style nearly-orthogonal bases for use in private keys, together with a subclass of Hermite Normal Forms for use in Miccianciostyle public keys and discuss their benefits when used in Bounded Distance Decoding cryptosystems in general lattices. We propose efficient methods for the creation of such nearly-orthogonal private bases and “Optimal” Hermite Normal Forms and discuss timing results for these methods. Finally, we propose a class of cryptosystems based on the use of these constructions and provide a fair comparison between this class of cryptosystems and related cryptosystems.