近年來，由於網際網路的快速發展，使得電子商務 (Electronic-Commerce) 的發展亦隨之快速成長，目前架構於網際網路之電子化服務包括了：電子付款 (Electronic Payment)、電子拍賣 ( Electronic Auction) 、電子投票 (Electronic Voting) 、...等等；其中以電子付款的應用最為廣。在電子付款方面，常見的機制包括了：電子現金 ( Electronic Cash) 、電子支票 ( Electronic Check) 及電子錢包 ( Electronic Wallet) 。目前大部份的電子付款系統是以複雜的離散對數機制來建立其安全性，但對於效率性而言，所需花費的時間運算成本卻是相當龐大的負擔。本文使用單向雜湊函數的特性改善了2001年Hsien等人提出之電子旅行支票系統中解離散對數機制的效率性問題，提出一個兼具安全性與效率性之新的電子旅行支票系統，並符合時下大額付款及小額付款的需要，設計出線上付款與離線付款二種模式，因此，本系統適於實際的施行使用上。

Nowadays, Electronic-Commerce has been booming as the Internet gets more and more popular. At present, many kinds of Electronic Services including Electronic Payment, Electronic Auction and Electronic Voting have been developed on the Internet. The most successful one among these services is the Electronic Payment System such as Electronic Cash, Electronic Check and Electronic Wallet. Until now most Electronic Payment Systems are based on an elaborate Discrete Logarithm for its security purpose. This raises a big issue regarding efficiency. Therefore, on the basis of the “Electronic Traveler’ s Check System” pro­posed by Hsien in 2001 using Discrete Logarithm. In this thesis, we introduce a new “Electronic Traveler’s Check System”based on the “Hash Function”to improve the efficiency. Our mechanism provides both on-line and off-line payment modes. Therefore, our system is practical for the real life implementation.