In the public-key cryptosystems which are based on lattice, AD’s public-key cryptosystem, NTRU and Regev’s public-key cryptosystem are the most famous public-key cryptosystems. Through hard problems, security and computational complexity, we analyze and research these three public-key cryptosystems. The connection and difference among these three public-key cryptosystems are given in this paper. We also compare the cryptosystems based on lattice with the cryptosystems based on other hard problems, giving the advantages of the cryptosystems based on lattice.