Study And Application Of NTRU Public-Key Cryptosystem

Fast public-key cryptosystems find more applications than the traditional public key cryptosystems and the design of fast public-key cryptosystem has been an interesting topic in the literature of public-key cryptographic community. This paper studies a typical fast public-key cryptosystem----NTRU, provides the detail description and the mathematical foundation of the NTRU algorithm, discusses the security of NTRU, and applies it to the design of systems in real life practice. The first chapter introduces the algorithm of NTRU and the state of art of the public-key cryptography, and points out the weakness of NTRU; The second chapter elaborates on the mathematical foundation of NTRU, discusses the hard problems SVP and CVP in lattice theory. Our contributions are given in the last three chapters.1.Discuss the NTRU and its improved algorithms in detail and analyze the hard problem underlying the NTRU encryption algorithm. It is also pointed out that NTRU suffers from the drawback of decryption failure.2.The security analysis of NTRU is given and the main attacks on NTRU are summarized. The advantages and the disadvantages of NAEP are discussed.3.Apply NTRU to the design of systems in real life practiceFirstly, a secure model of remote examination system is presented. The new model gains higher speed of encryption than that of existing models due to the adoption of NTRU. It also satisfies the security requirements in the case of many users.At last, security model e-government system is presented. The new model uses NTRU as the encryption algorithm, so it can obtain higher speed of key generation. The new model also improves the running efficiency of the Server.