An Efficient Fair Off-Line Electronic Cash System with Extensions to Checks and Wallets with Observers

In this paper, we present a privacy-protecting off-line electronic cash system which is fair, that is, the transactions are (potentially) traceable by a trusted authority but anonymous otherwise. Our scheme, based on a modification of Brands’restrictive blind signature scheme [2], is significantly more efficient than that of [11], while offering the same functionalities (off-line trusted authority, direct identification of the owner1 of a coin when the tracing of a user from his coin is performed by the trusted authority). Furthermore, we show how to extend our system to wallets with observers [9] and to electronic checks [1, 2, 15]. These two extensions are more efficient than previous ones [2, 6]. The first extension is featured by a high computational efficiency and low storage requirements for observers. The second extension provides checks which are more efficiently computed than checks in [2] (twice as fast) and which also require less memory for their storage (half as much).