Dynamic fair electronic cash model without trustees

A new fair electronic cash system is proposed based on group blind signature and secret sharing scheme. Our proposed system is dynamic: we propose a method to delete the dishonest banks that maybe attack the system, which was not mentioned in the previous literatures. Our proposed scheme does not need a trusted third party to trace users: a shop owning suspicious e-coin and the bank having issued the coin can collaborate to find the user using secret sharing scheme, however, any one of them can't trace the user alone. Furthermore, a novel e-coin tracing method is used to prevent criminal activities: under normal situation, the bank issues ordinary e-coin, while under abnormal situation such as blackmailing, kidnapping etc., the bank issues marked e-coin, and at the step of deposit, any bank in the group can recognize the marked e-coin. Also, our scheme is constructed for multiple banks as in the real life, thus it is more practical.