Digital Signatures Based On The Elliptic Curve

Information security is one of the most important problems in modem information society and becomes a new important subject in the information science. Digital signature, which can prove authentication, integrity and non-repudiation, is one of the key techniques of information security and plays a very important role in E-commerce and E-governance. In the other hand, elliptic curve cryptosystem (ECC) provides the highest strength-per-key-bit of any known cryptosystem. ECC not only has the higher security but also has less computation overheads,shorter key size and narrower bandwidth.Therefore, as the deepening of digital signature research and the rapid development of E-commerce and E-governance, research on digital signature based on the Elliptic curves has been an important field of digital signuture research. This thesis maily discusses the digital siganature scheme based on the elliptic curve over a finite field and the elliptic cure over ring Zn. The main contributions are as follows.1.Propose a mathematical problem.To solve such problem need to solve the discrete logarithm problem over a finite field and the prime factoring problem at the same time.2.Design an improved E1Gamal digital signature sheme, which is based both on the ECC discrete logarithm problem over a finite field and the prime factoring problem.3.Improve the Shao digital signature scheme. The improved digtal signature scheme is based on the ECC discrete logarithm problem and the prime factoring problem at the same time, which can resist the forgery attack.4.Propose a blind signature based on the elliptic curve over the ring Zn. The security of this scheme is also based on the the prime factoring problem and the ECC discrete logarithm problem, in which the the prime factoring problem can resist the attack of the short exponent attacks.5.Propose a multi-signature based on the elliptic curve over the ring Zn.The security of this scheme is based on the ECC discrete logarithm problem.Furthermore,it is easy to choose elliptic curves over ring Zn applicable to digital signature scheme by means of the selection of primitive element.