Based On Elliptic Curve Cryptosystem And A Number Of Algorithms And Protocols

Implementing various cryptosystems,based on the Abel group composed of the points on elliptic curves,has already developed into an extremely important subject in cryptology research. While elliptic curve cryptography has just emerged as an interesting branch of cryptology since 1985,which use relatively shorter key in procuring security to the same extent.In this paper,we explain the theory of elliptic curves and discuss some work of design cryptographic algorithms and protocols. A considerable large part of the principle of elliptic curve is described,and a comparison of elliptic curve discrete logarithm problem (ECDLP) and conventional discrete logarithm problem is also given. Then the author focus on schemes including identification,digital signature and deniable authentication,and several classical algorithms are addressed as well.In addition,we analyze the differences between standard security paradigm and random oracle paradigm. Based on all above,by using elliptic curve,we establish a new identification scheme and its corresponding digital signature scheme under random paradigm . At the end of the paper,two efficient deniable authentication protocols are presented on the basis of Aumann and Rabin's scheme.