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研究生:邱國哲
研究生(外文):Kuo-Zhe Chiou
論文名稱:離線電子現金系統之研究
論文名稱(外文):The Research of Off-line Electronic Cash Systems
指導教授:顏嵩銘顏嵩銘引用關係
指導教授(外文):Sung-Ming Yen
學位類別:碩士
校院名稱:國立中央大學
系所名稱:資訊工程研究所
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:2004
畢業學年度:92
語文別:英文
論文頁數:75
中文關鍵詞:追蹤公平交易匿名撤銷匿名性電子現金系統
外文關鍵詞:TracingFair paymentAnonymityAnonymity revocationElectronic cash
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隨著電子商務在網際網路上的蓬勃發展,電子付費系統在今日已成為重要的議題,如何確保線上交易之安全性和便利性更是消費者關注的問題。其中,在如何以電子化形式付費的研究上,電子現金系統(Electronic Cash System)更成為其重要的研究之一。
由David Chaum所提出的電子現金系統,讓消費者可以在匿名的情況下,和店家進行離線方式的交易,並且保證電子金錢之不可偽造性。但是,犯罪者卻可以利用匿名之性質來透過電子現金系統進行洗錢或勒索之犯罪之行為。因此,現今的電子現金系統都具備匿名撤銷機制來防範犯罪。
在本論文的第三章會介紹幾個電子現金系統,包含具有匿名撤銷的系統以及非常有效率的系統。前者,這類系統採用兩個密碼技術:雙重付費偵測(Double-spending Detection)以及追蹤(Tracing),來有效地進行匿名撤銷之功能。同時也指出匿名撤銷機制卻造成這類系統在計算成本上以及通訊成本上沈重的負擔。後者,根據“一次提款多個單位電子金錢”之觀念,採用了批次簽章(Batch Signature)之密碼技術,大大地提升了電子現金系統之效率。然而,此系統在防範犯罪的能力上比較薄弱。
針對電子現金系統效率之議題,本論文根據“一次提款多個單位電子金錢”之概念,提出了兩個有效率的電子現金系統。
本論文第四章介紹第一個所提出的系統,此系統改良於PayWord。除了改變單向雜湊函數鏈的產生方式之外,並採用部份盲簽章(Partially Blind Signature)之技術,使得所提出的系統比一般電子現金系統都來得有效率且比較安全。
第二個提出的系統詳述於本論文之第五章。在考量安全與效率之議題下,提出一個新的盲簽章來建構出此系統。在安全考量下,此系統具備了雙重付費偵測和追蹤之功能;在效率考量下,採用批次簽章之技術提升本系統之效率。
最後在本論文之第六章,提出了幾項對電子現金系統之討論,做為未來研究的方向。
On-line business has gradually become an important issue nowadays
due to the tremendous growth of electronic commerce on Internet.
Especially, electronic cash system is one of most popular research
topics for paying electronically.

Electronic cash system proposed by David Chaum makes electronic payment
on Internet possible with anonymity, off-line, and unforgeability.
However, malicious user can freely commit crimes by means of the
property of anonymity. In consideration of preventing
criminal activities, the anonymity revocation has become a
desired requirement.

Unfortunately, although anonymity revocation can protect electronic cash
system from being misused, it makes the category of systems inefficient at
the same time.

In this thesis, some electronic cash systems with revocable anonymity are
introduced. These systems prevent criminal activities by means of the two
most common cryptographic techniques double-spending detection and tracing.
However, these systems are inefficient and impractical. Then one very
efficient electronic cash system is presented that it is possible to resolve the
problem of efficiency of those revocable anonymity systems.

We propose two electronic cash systems concerning about efficient issue.
The first one takes advantage of hash function operation in PayWord to reduce
the use of public key operations while maintaining the anonymity property.
This system is very efficient because hash function operation is
faster than public key operation.

We propose a new blind signature which combines with batch cryptography to
construct another electronic cash system. The main idea is that amortizing
the expensive computation cost accross many coins. Moreover, in terms of
ensuring the system from being misused, it provides double-spending
detection and tracing capability. Finally, we suggest that the proposed
system works with elliptic curve in terms of security,
computational speed, and space requirement. Finally, the complete view of
the system converted to elliptic curve cryptography are also provided.
1 Introduction 1
1.1 Introduction to E-cash System.......................................1
1.2 Overview of the Thesis..............................................3
2 Preliminary 5
2.1 The Basic Model of Modern E-cash System.............................5
2.2 The Requirements of Modern E-cash System............................6
2.3 Introduction to Blind Signature.....................................7
2.3.1 RSA Blind Signature...............................................7
2.3.2 Schnorr Blind Signature...........................................8
2.3.3 Partially Blind Signature.........................................9
2.3.4 Nyberg-Rueppel Blind Signature...................................10
2.4 Summary............................................................12
3 Review of Off-line E-cash Systems 14
3.1 The First E-cash System............................................15
3.1.1 The first e-cash system..........................................15
3.1.2 Security analysis................................................16
3.2 An Off-line E-cash System with Revocable Anonymity.................16
3.2.1 Brands e-cash system.............................................17
3.2.2 Proving equality of logarithms...................................19
3.2.3 An Off-line E-cash System with Revocable Anonymity...............20
3.3 An Efficient E-cash System Using Nyberg-Rueppel Blind Signature....24
3.3.1 Proving equality of logarithms...................................24
3.3.2 The proposed e-cash system.......................................25
3.4 A Very Efficient E-cash System Using Batch Signature...............28
3.4.1 Batch Schnorr signature..........................................29
3.4.2 The proposed e-cash system.......................................30
3.4.3 Remarks and Discussions..........................................33
3.5 Summary............................................................33
4 An Efficient E-cash System Using Hash Chain 36
4.1 Review of PayWord..................................................36
4.1.1 Payword certificate..............................................37
4.1.2 Commitment to a payword chain....................................37
4.1.3 Spending paywords................................................38
4.1.4 Depositing spent paywords........................................38
4.2 A New Efficient E-cash System......................................38
4.2.1 System setup.....................................................39
4.2.2 Withdrawal protocol..............................................39
4.2.3 Payment protocol.................................................40
4.2.4 Deposit protocol.................................................40
4.3 Remarks and Discussions............................................40
4.3.1 Security Analysis................................................40
4.3.2 Efficiency Analysis..............................................41
5 An Efficient E-cash System with Revocable Anonymity 43
5.1 Previous Work......................................................43
5.2 New Blind Signature................................................44
5.3 A New E-cash System................................................46
5.3.1 Registration protocol............................................46
5.3.2 Withdrawal protocol..............................................47
5.3.3 Payment protocol.................................................48
5.3.4 Deposit protocol.................................................49
5.3.5 Tracing protocol.................................................49
5.3.6 Security analysis................................................50
5.3.7 Efficiency analysis..............................................50
5.4 A Variant of The Proposed System...................................52
5.4.1 Elliptic curve cryptography (ECC)................................52
5.4.2 Proof of equality of logarithms using ECC........................53
5.4.3 The improved system using ECC....................................54
5.5 Remarks and Discussions............................................58
6 Conclusions 60
6.1 Brief Review of Main Contributions.................................60
6.2 Further Research Topics and Directions.............................60
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