How to make e-cash with non-repudiation and anonymity

Current e-cash systems enable anonymity services to protect users´ privacy, but most of them do not provide the nonrepudiation service such that many problems exist in the systems like denying, losing, misusing, stealing, and double-spending, etc. We propose an e-cash system in which a one-time public key is embedded in the partial blind signature to provide the nonrepudiation service against the above attacks. We also demonstrates that the combination of the partial blind digital signature and anonymous digital signature makes the e-cash systems more robust and fair than before.