An Improved Off-Line Electronic Cash Scheme

With the development of the electronic commerce (e-commerce), the untraceable electronic cash is an attractive payment tool for e-commerce, because its anonymity property can ensure the privacy of spenders. Recently, Ziba et al. proposed a new untraceable offline electronic cash system. The authors claimed that their scheme can detect a malicious consumer who spends a coin more than once. In this paper, we show that Ziba et al.'s scheme cannot reveal the identity of the double-spender. Besides, it is vulnerable to several possible frauds like stealing e-cash, illegal spending and deposit, as they have claimed. To make up for these defects, we propose a rescue scheme and show that our improvement is secure against double-spending detection and possible frauds. Furthermore, our scheme upholds all desirable properties of electronic cash, and it is based on cryptographic techniques (Schnorr and blind signatures) and the discrete logarithm problem.