Compact E-Cash with Practical and Complete Tracing

E-cash has its merits comparing with other payment modes. However, there are two problems, which are how to achieve practical/complete tracing and how to achieve it in compact E-cash. First, the bank and the TTP (i.e., trusted third party) have different duties and powers in the reality. Therefore, double-spending tracing is bank's task, while unconditional tracing is TTP's task. In addition, it is desirable to provide lost-coin tracing before they are spent by anyone else. Second, compact E-cash is an efficient scheme, but tracing the coins from double-spender without TTP results in poor efficiency. To solve the problems, we present a compact E-cash scheme. For this purpose, we design an embedded structure of knowledge proof based on a new pseudorandom function and improve the computation complexity from O(k) to O(1). Double-spending tracing needs leaking dishonest users' secret knowledge, but preserving the anonymity of honest users needs zero-knowledge property, and our special knowledge proof achieves it with complete proofs. Moreover, the design is also useful for other applications, where both keeping zero-knowledge and leaking information are necessary.