A Provably Secure E-Cash Scheme with Loss-Tracing

E-cash should be spent anonymously in normal circumstances, while in many schemes, the trusted authority is the only one who acts as customer-tracer and e-coin-tracer for preventing illegal transactions, but it is not the case in the reality. In our practical scheme, the bank traces double-spenders without the help of others, and the trusted third party traces e-coins and the owner only when the customer is involved in crimes. When customers lose their e-coins for some reasons, the loss-tracing can be triggered in our scheme which is neglected by almost all existing schemes, so if the lost coins haven't been spent by anyone, the customers can get the refund from the bank. And then the security proofs for our E-cash scheme are provided in the random oracle model.