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Under the extraordinary growth of international interconnected computer networks, the paperless society is coming true soon. Both cash and checks will be processed in electronic form. Money will be only a lot of electronic data that have been manipulated by the bank. Unfortunately, electronic cash and electronic check systems are under the threats derived from financial crime. In this thesis, some effective methods are proposed for secure electronic payment systems that include (1) electronic cash system without overspending, (2) secure electronic check system, and (3) network fund transfer. In electronic cash, we present how a smart card can be incorporated in the protocols to provide prior restraint against overspending by the customer, instead of just detection after the fact. A withdrawal counter and a payment counter are inside the smart card. Before payment, the smart card first checks whether the accumulated amounts of the payment counter are less than the withdrawal amounts. If yes, then the customer can pay electronic cash for this consume. In addition, we arrange the digital signature scheme in smart card. By this two concepts, we accomplish the goal that the customer can not spend more electronic cash than withdrawn by the customer. To secure electronic check, we use the method that system operations of which based on paper check. A current payee can verify the previous digital signatures. Owing to different computable complexity, we present how every previous signature and composite previous signatures can be verified. The payee also sends received electronic check to the bank for verifying. By this method, we can establish a traceable, unforged and unduplicated electronic check system. Furthermore, the secure electronic cashier*s check is also discussed. Finally, the method of network fund transfer is proposed. In this method, we adopt digital signature and challenge/response protocols to prevent replay attack and cheating. It makes people who are legal and authorized can take advantage of world wide web to conduct funds transfer safely.
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