Fair E-Cash System without Trustees for Multiple Banks

A new fair electronic cash system is proposed based on ACJT group blind signature and secret sharing scheme. We use a novel method to trace the e-coin: 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. Furthermore, our proposed scheme does not need a special trusted third party besides the Central Bank 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. Also, our scheme is constructed for multiple banks as in the real life, thus it is more practical.