Electronic payment systems come in many forms including digital checks, debit cards, credit cards, and stored value cards. The usual security features for such systems are privacy (protection from eavesdropping), authenticity (provides user identification and message integrity), and no repudiation (prevention of later denying having performed a transaction) . The type of electronic payment system focused on in this paper is electronic cash. As the name implies, electronic cash is an attempt to construct an electronic payment system modelled after our paper cash system. Paper cash has such features as being: portable (easily carried), recognizable (as legal tender) hence readily acceptable, transferable (without involvement of the financial network), untraceable (no record of where money is spent), anonymous (no record of who spent the money) and has the ability to make "change." The designers of electronic cash focused on preserving the features of untraceability and anonymity. Thus, electronic cash is defined to be an electronic payment system that provides, in addition to the above security features, the properties of user anonymity and payment untraceability..