Off-line digital cash schemes providing untraceability, anonymity and change

Several ecash systems have been proposed in the last twenty years or so, each offering features similar to real cash. One feature which to date has not been provided is that of a payee giving change to a payer for an e-coin in an off-line setting. In this paper, we indicate how an off-line ecash system can solve the change-giving problem. In addition, our protocol offers the usual expected features of anonymity and unlinkability of the payer, but can reveal the identity of an individual who illegally tries to spend ecash twice.