網際網路的盛行帶動電子商務的發展，許多電子交易的付款技術也因應而出，例如電子貨幣、信用卡與電子錢包等。其中電子貨幣就如同紙鈔一樣，具有匿名與不可追蹤的特性，適合使用在網際網路上作各種電子交易。一般來說，電子貨幣可分為線上（on-line）電子貨幣和非線上（off-line）電子貨幣兩種型態，這兩種電子貨幣各有不同的應用及所適用的環境。
過去所提出的電子貨幣架構都只支援其中一種電子付款型態，因此使用者必須要在提領之前就決定他們要使用的電子貨幣型態。在本篇論文中，我們將提出一個整合線上和非線上電子貨幣的新架構，使用者只需提領單一型態的電子貨幣，即可使用於線上電子貨幣或非線上電子貨幣的交易中。我們的架構提供使用者更便利的環境，且對銀行和商店來說，更具適應性（flexibility）。在我們所提出的新架構中，除了滿足電子貨幣機制所必須具備的特性外，更提供了適應性的特色。

Due to ubiquity of internet, the development of electronic commerce is growing up rapidly. Many payment mechanisms of electronic transactions are proposed, such as electronic cash, credit cards, and electronic wallets. Electronic cash (e-cash) is like the digital version of paper cash, which possesses some key features such as anonymity and untraceability, and it can be used on the Internet for various electronic transactions. In general, electronic cash is classified into two types which are on-line electronic cash and off-line electronic cash. Each of them is suitable for different applications and environments.
All of the proposed electronic cash schemes only focus on one of two types. In these schemes, users must decide which type of electronic cash they will use later before withdrawing. However, in this thesis we propose a novel electronic cash scheme which supports a user to withdraw a generic e-cash and then decide to spend it as an on-line e-cash or an off-line e-cash. Our proposed scheme is more convenient for users and more flexible for the bank and shops. It not only satisfies the necessary properties of electronic cash but also provides flexibility.

1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Overview of the Thesis . . . . . . . . . . . . . . . . . . . . . . 2
2 Related Works 4
2.1 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1.1 David Chaum’s Blind Signature . . . . . . . . . . . . . 4
2.1.2 El-Gamal’s Signatures . . . . . . . . . . . . . . . . . . 5
2.2 Literature Review . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2.1 David Chaum’s E-cash Scheme . . . . . . . . . . . . . 5
2.2.2 Brand’s Scheme . . . . . . . . . . . . . . . . . . . . . . 6
2.2.3 Qiu et al.’s Scheme . . . . . . . . . . . . . . . . . . . . 9
2.2.4 Hou and Tan’s Scheme . . . . . . . . . . . . . . . . . . 12
2.2.5 Wang and Xuan’s Scheme . . . . . . . . . . . . . . . . 14
3 The Proposed Architecture and Requirements 17
3.1 Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4 The Integrated On/Off-line Electronic Cash Scheme 20
4.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
4.2 The Withdrawing Protocol . . . . . . . . . . . . . . . . . . . . 21
4.3 The On-Line E-Cash Payment Protocol . . . . . . . . . . . . . 23
4.4 The Off-Line E-Cash Payment Protocol . . . . . . . . . . . . . 25
5 Characteristic Analysis and Comparisons 28
5.1 Anonymity/Untraceability . . . . . . . . . . . . . . . . . . . . 28
5.2 Revokability . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
5.3 Double-Spending Checking . . . . . . . . . . . . . . . . . . . . 29
5.4 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
6 Conclusions 32
References 33
Appendix 36
A The implementation of the Scheme 36
B The Key Part of the Source Codes 54

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