Lattice Based Cryptography: A Global Improvement.

Abstract

We describe a general technique to simplify as well as to improve several lattice based cryptographic protocols. The technique is rather straightforward and is easily applied to the protocols, and gives both a simpler analysis and better performance than the original protocols. The improvement is global: the modified protocols are simpler, faster, require less storage, use less bandwidth and need less random bits than the originals. Moreover, the improvement is achieved without any loss in security: we formally prove that the modified protocols are at least as secure as the original ones. In fact, the modified protocols might even be more secure as the adversary gets less information. We exemplify our technique on the Goldreich-Goldwasser zero-knowledge proof systems for lattice problems and the GGH public key cryptosystem. Partially supported by DARPA grant DABT63-96-C-0018 and NTT grant 67627-00. 1 1 Introduction Various cryptographic protocols based on the hardness of la...