Research Of Group Signature Based On Conic Curve Over Z_n

In1998, conic curve cryptography was firstly brought forward by Professor Zhenfu Cao, and the famous cryptography scholar C.Schnorr thinks that it is the most interesting cryptographic algorithm currently other than elliptic curve cryptography. Various calculations on conic curve group are simpler than those on elliptic curve group, including an exciting feature is that the encoding and decoding on it are easier to implement. Meanwhile, conic curve group of residue class ring based on mold n can also be established, so it make the password system which is equivalent to the large integer factorization can easily be constructed. The express embedded, computing of order and operations of points on Conic curve group are relatively easy, especially its inverse calculation is simple, so the design of cryptographic algorithms on it is very attractive. Conic curve cryptography has become an important research content in cryptography field.Conic curve based on ring Zn can expediently combine the problem of large integer factoring and discrete logarithm, and thus the signature scheme of double problems can easily be constructed, therefore, the group signature schemes constructed on this curve possess better security. At the same time, the express embedded, computing of order and operations of points on Conic curve group based on Zn are convenient, and the algorithm of computing group elements’multiple with the introduction of normal binary can improve operational efficiency, so the programs constructed on the curve have faster operational speed and are easier to realize.This paper mainly studies public key algorithm and group signature scheme on conic curve, the main work is as follows:Firstly,this paper carry out a systematic study on public key cryptography algorithm of conic curve, and summarize some of classic public key cryptography system which are built on conic curve. Then on this basis, a cryptographic scheme combined double problems is constructed on conic curve based on residue class ring.Then on the basis of deeper study on conic curve, combining some advantages of existing group signature schemes, a dynamic group signature scheme with forward security is designed on conic curve based on Zn. Finally, this paper briefly discuss the correlative concepts of e-commerce, and then make our group signature scheme apply in the electronic currency system practically.