Lattice Based Cryptography: A Global Improvement

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 modiied 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 modiied protocols are at least as secure as the original ones. In fact, the modiied 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.