Electronic Cash System with Multiple Banks

Secure and efficient electronic payment systems are significant for electronic commerce. Electronic cash (e cash, or digital cash) is a very important electronic payment system. The first electronic cash scheme was suggested by Chaum in 1982. In the scheme the technique of blind signatures was used to guarantee the privacy of users. But this complete anonymity of electronic cash can be used for criminal activities, such as money laundering, blackmailing [7] . To overcome this drawback, J. Camenisch et al. [6] and Y. Frankel et al . [4] proposed the concept of ‘Fair Off line Electronic Cash’ independently in 1996. They also presented two schemes of fair off line electronic cash. The untraceability of fair off line electronic cash is not completely. It can be revoked by a trusted third party so that the criminal activities making use of the complete anonymity of electronic cash can be prevented. By now the electronic coins in fair electronic cash schemes available are issued by only one bank. However, in practice a shop and its users may use different banks so it is more convenient to use electronic coins issued by multiple banks. The purpose of this paper is to present a fair electronic cash system that is applicable to the situation where the shop and its users may use different banks. Since in a country or district there may be more than one banks who are able to issue electronic cash. We assume these banks form a group under control of an authorized party such as the Central Bank of the country, we propose a model for fair electronic cash issued by multiple banks for the first time. A scheme of fair electronic cash with multiple banks in which a user can be traced is presented by using the improved group signature scheme of Cam97 [5] and group blind signature scheme of Lys98 [6] . Our system of fair electronic cash with multiple banks has the following properties: (1) The user can spend his electronic coin anonymously. No bank can trace any electronic coin. (2) To check the validity of a received coin the shop just needs to perform a simple verification procedure using a single public key of the bank group. This is very convenient for the shop, since he just needs to know the public key of the bank group.(3) The group of all banks just has one public key,and this public key is independent of the number of banks. Furthermore the length of the group public key does not change with the increase of the number of banks.(4) Given an electronic coin, nobody but the Central Bank can know by which bank it is issued. This can provide anonymity for the banks.(5) No banks including the Central bank can issue electronic coin on behalf of another bank. (6) The Central Bank can determine which bank issued it when an electronic coin is found something wrong (for example, double spend),and then this bank can find who is the owner of this coin with the help of the trusted third parity(i.e. trace back).(7) Each bank can trace an electronic coin with the help of the trusted third party according to the information supplied by its user(i.e. trace forward). Finally, a disadvantage in the design of withdrawal and payment protocols of electronic cash using the existing group signature schemes is pointed out with its reasons analyzed. Moreover, a way of removing this disadvantage is given.