隨著行動網路通訊環境日趨成熟， 我們只需一個擁有連接網路功能的行動裝置，就能隨時隨地使用網路及各種服務，如網路付款、網上購物、網上拍賣等。現今享用這些網上服務的人數日益增長，由此可見電子商務廣受大眾歡迎，與此同時，電子商務的安全問題和使用者權益亦相對地不可忽視，因此需要有更完善的架構以達到這些需求。電子貨幣無疑是電子商務範疇中相當受到矚目的研究主題，其所具備的特性可用以保障使用者的隱私與權利。一般來說，電子貨幣分為線上電子貨幣和離線電子貨幣，此兩種機制各有其優缺點並可運用於不同的應用之上。在本論文中，我們提出一套基於盲簽章技術之可證明安全且可附加日期的離線電子貨幣協定，保持一般電子貨幣應有的安全特性，如：匿名控制、雙重支付檢測及不可偽造之外，貨幣到期日與存款日可同時被附加於該電子貨幣之上；貨幣到期日可用於協助銀行處理龐大的資料庫，避免無窮盡增長的問題，而存款日則能讓存款者自行加附在電子錢上且不被任何人所更改，以確保存款人日後能正確計算出應得的利息。最後，我們亦提出安全分析及證明以說明本協定之安全性。

With the convenience of mobile network, people can do different kinds of activities, such as payments, shopping, auctions, and so on, whenever and wherever. Electronic commerce (e-commerce) has become so popular that the number of people using these online services has been increasing enormously in recent years. Hence, the security issues of e-commerce and the rights of users in transaction have raised our concerns. Electronic cash (e-cash) is definitely one of the most popular research topics among e-commerce area. It is very important that e-cash has to be able to hold the anonymity and accuracy in order to preserve the privacy and rights of customers. There are two types of e-cash in general, which are online e-cash and offline e-cash. Both systems have their own pros and cons, and they can be used to construct various applications. In this thesis, we propose a provably secure and efficient offline e-cash scheme with date attachability based on blind signature technique, where expiration date and deposit date can be embedded in an e-cash, simultaneously. With the help of expiration date, the bank can manage the huge database much more easily against unlimited growth, and the deposit date cannot be forged so that users are able to calculate the amount of interests they can receive in the future correctly. Furthermore, our scheme maintains the properties of e-cash, which are anonymity control, double-spending checking and unforgeability. We also provide security analysis and formal proofs in this thesis.

論文審定書 i
誌謝 iii
中文摘要 iv
英文摘要 v
1 Introduction 1
1.1 Types of E-Cash and Security Requirements . . . . . . . . . . . . . . 1
1.1.1 Types of E-Cash . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Security Requirements . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Our Contribution and Paper Organization . . . . . . . . . . . . . . . 4
2 Related Works 6
2.1 Review of Chang and Lai’s Scheme . . . . . . . . . . . . . . . . . . . 6
2.1.1 Initialization Phase . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 Withdrawal Phase . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.3 Unblinding Phase . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.4 Date-Attaching Phase . . . . . . . . . . . . . . . . . . . . . . 8
2.1.5 Depositing Phase . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2 Review of Eslami and Talebi’s Scheme . . . . . . . . . . . . . . . . . 9
2.2.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Withdrawal Protocol . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.3 Payment Protocol . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.4 Deposit Protocol . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.2.5 Exchange Protocol . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Preliminaries 14
3.1 Chaum’s Blind Signature Scheme . . . . . . . . . . . . . . . . . . . . 14
3.2 Chameleon Hashing Based on Discrete Logarithm . . . . . . . . . . . 15
4 The Proposed Date Attachable Offline Electronic Cash Scheme 17
4.1 Outline of the Proposed Scheme . . . . . . . . . . . . . . . . . . . . . 17
4.2 The Proposed Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2.1 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2.2 Withdrawal Protocol . . . . . . . . . . . . . . . . . . . . . . . 20
4.2.3 Payment Protocol . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.2.4 Deposit Protocol . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2.5 E-Cash Renewal Protocol . . . . . . . . . . . . . . . . . . . . 27
4.2.6 Double-spending Checking and Anonymity Control . . . . . . 29
5 Security Proofs 31
5.1 E-Cash Unlinkability . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
5.2 E-Cash Unforgeability . . . . . . . . . . . . . . . . . . . . . . . . . . 35
5.3 E-Cash Conditional Traceability . . . . . . . . . . . . . . . . . . . . . 47
5.4 E-Cash No Swindling . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6 E-cash Advanced Features and Performance Comparisons 64
6.1 Features Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.2 Performance Comparisons . . . . . . . . . . . . . . . . . . . . . . . . 65
7 Conclusion 68

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