Analysis And Design Of Elliptic Curve Digital Signature Scheme

In recent years,with the popularization of computer network and the rapid development of communication technology,the network has more and more impact on our daily life.Network office,e-government,e-commerce,digital city and other words,in our lives have been everywhere.It can be said that information is permeating all aspects of our lives.The network brings many conveniences to our life,but at the same time,it also brings many hidden dangers.For example,computer viruses,Internet hackers,electronic eavesdropping,electronic fraud and other phenomena followed,resulting in a lot of social problems.Therefore,when people use the network,how to conveniently and effectively access to the information they want,how to shield some of their unwanted information,how to protect their own information security,these issues have become the focus of people have to pay attention to.In 1987,Miller and Koblitz proposed the elliptic curve cryptosystem independently,and applied the research results of elliptic curve to cryptography.Elliptic curve cryptography is a public key cryptosystem involving finite field multiplication groups,which uses a group of elliptic curves over finite fields to approximate the multiplication group of finite fields,thus obtaining a similar public key cryptosystem.This kind of safety system is the difficulty of solving the discrete logarithm problem based on elliptic curve,has yet to find a sub exponential time algorithm to solve this problem,so it has some advantages compared to other public key cryptosystems,such as in the security strength under the same system parameters and shorter key size,larger choice etc..It is these characteristics that have attracted the attention of cryptography researchers for many years.Digital signature is one of the key technologies to solve the problem of modern information security,and it is also one of the important applications of public key cryptography.In recent years,the basic theory and Application Research of digital signature are very active.All kinds of new concepts,new theories and new signature schemes emerge in endlessly,and continue to develop.I studied and analyzed the elliptic curve digital signature scheme,the main work of this paper is as follows:(1)In this paper,an elliptic curve digital signature scheme has been analyzed,and the flaws and shortcomings are found.This paper presents a forgery attack method,and proves that this attack method can effectively attack the scheme.Then,the shortcomings of this scheme are analyzed,and the signature scheme is improved.Moreover,it is proved that the improved scheme improves the security compared with the original scheme.(2)In this paper,the improved scheme in(1)is further improved.New elliptic curve digital signature scheme is proposed by combining its advantages with the advantages of other signature schemes.The correctness and security of the proposed scheme are also analyzed and proved.