The Elliptical Curve Group Signature Scheme And Its Application In Electronic Cash System

With the rapid development of electronic commerce, as its core technology,electronic payment has evolved greatly in recent years. The modern payment tool--electronic cash emerges and develops quickly. Therefore, it brings higher requirements on the modern payment systems. But there are many open problems in the current electronic cash system, such as membership revocation, transferability, divisibility, multiple banks and so on. The group signature, as an especial digital signature, offers the ability to hide interior structure of the organizations, so it can be widely used for electronic voting, electronic bidding, electronic cash system, identity escrow in electronic government affair and electronic commerce.The subject investigated in this paper is an electronic cash system scheme with multiple banks based on the elliptical curve group signature. Aiming at the existing problems of the group signature and electronic cash, we have designed a new group signature with secure and efficient member revocation, and reduced loss for the leakage of key firstly. And then a new electronic cash system scheme of multiple banks with more functions has been established.Firstly, to solve the problems of the existed group signature based on the Elliptical Curve PKC, this paper has designed an efficient and secure group signature scheme with the method of dividing system time into sections and the idea of dynamic accumulators. When group members have to be increased or withdrawn, the group manager only needs to evolve the key and update the evidence, the calculated amount is just the dot product on the elliptical curve; the length of the signature and the key is shorter,the process of signature and verify is comparatively simple. Moreover, the new group signature scheme has been proved security in the BSZ model.Secondly, this paper has designed a fair off-line electronic cash system scheme with multiple banks based on the new group signature scheme introduced above. This system provides the functions of preventing customers from juggling the sum of electronic cash, member revocation, finding double-spending, preventing criminal activities such as blackmailing, money laundering and illegal purchases, and revocable anonymity for customers. Moreover, this system scheme has been showed more efficient because it is based on the new secure and efficient group signature.