Many researches on the electronic cash (e-cash) system have been carried out with proliferation of electronic commerce. But there is no one outstanding system satisfying all requirements of e-cash efficiently, and researchers try to cover the requirements partially or totally. One of the requirements is $\emph{fair tracing}$ problem.
In e-cash system, a customer withdraws electronic$ \emph{coins}$ from bank and pays the coins to a merchant in the off-line manner. Finally, the merchant deposits the paid coins to the bank. To protect the privacy of customer, each payment should be anonymous and it can be achieved by blind signature. However $\emph{unconditional anonymity}$ may be misused for untraceable blackmailing of customer, which is also called $\emph{perfect crime}$. Furthermore, unconditional anonymity makes ease money laundering, illegal purchase, and bank robbery.
We propose an e-cash tracing scheme which has not only fair tracing ability but also lower computational complexity for comparisons. Many other protocols allow $\emph{optimistic}$ fair tracing which means that illegal tracing can be found after deposits in a bank. But in this scheme, illegal tracing done by bank is impossible. We propose a marking mechanism based on an Okamoto-Schnorr blind signature and Verifiable Secret Sharing scheme.
Besides, for double spending prevention of e-cash, we adopted Schnorr``s one-time signature scheme. If we only consider the anonymity problem, the system will be exposed by double spending threat. So, we are trying to solve this two problem simultaneously.
Finally, we will consider a variant of this scheme and compare it with other protocol.