Study On The Signature Based On NTRU

Along with the appearance of the paper, "New directions in cryptography", the curtain of the public key cryptosystem (PKC) was unclosed. In the network, the PKC is especially important. NTRU is a new PKC, and this paper mainly discussed the signature based on NTRU. In chapter one, the history, classifies of cryptosystem, PKC and digital signature are introduced. NTRU is a PKC based on the problem of Lattice, so in chapter two, the concept and property of lattice and some hard problems of lattice (SVP (the shortest vector problem), CVP (the closest vector problem) and SBP (the smallest basis problem)) are researched. And two methods of reducing the lattice base—Gauss arithmetic and LLL arithmetic are also introduced. In the end of this chapter, we presents the NTRU arithmetic in detail, and the methods of attack NTRU. And we especially introduced the lattice based attacks in this chapter. At the beginning of the chapter three, the old signatures schemes based on NTRU-NSS, R-NSS and NTRUSign are discussed. Because the NSS and R-NSS have been broken, we also present the methods to break NSS and R-NSS. In chapter four, we use the CVP problem to construct two new signature schemes based NTRU, and analyze them to explain their advantages. Charper five shows the proxy signature, an offshoot of digital signature. Application and the security levels of proxy signature are intuduced at first. Then some important proxy signature scheme- MUO, LKK and KPW are discussed. At second part of this chapter, a new proxy signature scheme based on NTRUSign is presented, and the detail security analyses are adopted. To show its advantage, we compare it with other proxy signatures.