Abstract. In this paper, we first critically analyze two existing latticebased cryptosystems, namely GGH and Micciancio, and identify their drawbacks. Then, we introduce a method for improving the implementation of GGH using the Chinese Remainder Theorem (CRT). Furthermore, we also propose another cryptosystem optimized for CRT, drawing on the strengths of both cryptosystems. We provide a fair comparison between our scheme and the existing ones.