Improving GGH cryptosystem using generalized low density lattices

摘要

A new Goldreich-Goldwasser-Halevi (GGH) cryptosystem is proposed using Generalized Low Density (GLD) lattices. These low density lattices can alleviate a major drawback of the GGH scheme, namely the huge size of its public key. Indeed, we show that the new GGH that we propose in this paper reduces the key size by one order of magnitude. In addition, we show that the key generation complexity as well as those of the encryption and decryption phases are significantly decreased. The security of this new GGH is highlighted through a security analysis that reviews all known attacks on GGH systems. This allows us to conclude that our scheme does not add any new vulnerability as compared with the existing GGH schemes.