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.