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研究生:游曜駿
研究生(外文):Yao-chun Yu
論文名稱:具快速撤銷匿名性於雙重花費使用者之電子貨幣協定
論文名稱(外文):An E-Cash Protocol with Efficient Double-Spending Revocability
指導教授:范俊逸范俊逸引用關係
指導教授(外文):Chun-I Fan
學位類別:碩士
校院名稱:國立中山大學
系所名稱:資訊工程學系研究所
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2009
畢業學年度:97
語文別:英文
論文頁數:46
中文關鍵詞:電子錢重複花費不可追蹤性匿名性變色龍雜湊函數
外文關鍵詞:Double-SpendingChameleon Hash FunctionsE-CashAnonymityUntraceability
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網路的快速發展帶動著各種電子商務服務與應用的出現,隨著信用卡、電子折價
卷、電子錢等技術的提出,在網路上進行交易已經不是遙不可及的夢想,在這篇碩士
論文裡,我們深入探討電子錢技術,了解電子錢所需具備的特性,並提出一個具匿名
性與不可追蹤性的電子錢協定。在我們的電子錢協定中,當使用者重覆使用電子錢
時,銀行在不需要第三方公正單位的介入之下,可以直接撤銷該使用者的匿名性,可
以提高撤銷匿名性時的效率,維持電子錢交易的公平,並且當電子錢被使用於非法的
交易上時,第三方公正單位可出面將匿名性撤消,以維持社會安全。當某些情況發生
時,警察必須要追蹤某些特定使用者時,我們也可以達到追蹤使用者的效果。我們使
用到變色龍雜湊函數以及RSA簽章系統來達到我們所需要的特性。
Due to the fast progress of the internet technologies, electronic commerce becomes
more and more popular. Many people and businesses deal with their transactions via the
internet. The technologies of credit cards, electronic tickets, e-cash, and other advanced services
have realized the vision of electronic commerce. In this thesis, we propose an off-line
e-cash scheme with anonymity, untraceability, double-spending checking, and traceability.
Anonymity and untraceability must be possessed in any e-cash scheme. In an off-line e-cash
scheme, the bank or the third party (TTP) must be able to revoke the anonymity of a user who
doubly spent her/his e-cash(s). In our proposed e-cash scheme, the bank can fast derive the
identity of the user who doubly spent her/his e-cash(s) without the participation of TTP. If
some illegal transactions are reported, TTP can also directly revoke the anonymity of the user
who spent her/his e-cash(s) in the illegal transactions. In addition, the police needs to trace
a specific user in some situation, and we propose a process to satisfy this requirement,called
traceability.
Chapter 1 Introduction 1
1.1 Organization of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Chapter 2 Related Works 3
2.1 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.1.1 David Chaum’s Blind Signature . . . . . . . . . . . . . . . . . . . . 3
2.1.2 Krawczyk and Rabin’s Scheme: Chameleon Signatures . . . . . . . . 4
2.1.3 Shamir and Tauman’s Scheme: Improved Online/Offline Signature
Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 Related Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 David Chaum’s E-Cash Scheme . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Brands’ E-Cash Scheme . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.3 Joseph et al.’s E-Cash Scheme . . . . . . . . . . . . . . . . . . . . . 12
Chapter 3 The Architecture and Requirements in Our Proposed E-Cash Scheme 15
3.1 The architecture of our e-cash scheme . . . . . . . . . . . . . . . . . . . . . 15
3.2 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Chapter 4 Our Proposed Scheme 18
4.1 Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2 Initialization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3 The Withdrawal Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.3.1 The Normal Withdrawal Protocol . . . . . . . . . . . . . . . . . . . 20
4.3.2 The Exception of the Withdrawal Protocol . . . . . . . . . . . . . . . 22
4.4 The Payment Protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Chapter 5 Characteristic Analysis and Comparisons 25
5.1 Anonymity Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.1.1 Revokability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.1.2 Traceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.2 Untraceability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
5.3 Comparisons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Chapter 6 Security 29
6.1 Security Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.2 Unlinkability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
6.3 Unforgeability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Chapter 7 Conclusions 34
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