網路技術的進步對整個社會產生極大的影響力，因為網路交易已應用在日常生活中，使人們能夠在網路上進行交易。公平交易要求雙方在對等的情況下，都能獲得所需之物。例如，一位顧客在付款之後，他將得到所需要的商品。同樣情況，一位商家在寄給顧客所訂之商品後，他也將得到支付。藉由訊息的傳送，交易雙方能驗證被加密後的商品、商品的解密鑰匙和支付款項，並達到公平交易的原則。雖然網路交易已日漸普及，當任何心存不良的局外人擁有一些特別的設備或軟體時，他們便能攔截在網路裡的訊息，或者假冒他人傳送錯誤的訊息。因此匿名機制保證交易雙方的身分在交易的過程中不會被洩露。
在本論文中，我們提出一套新的匿名公平交易協定。在協定機制中，公證單位將擔任中間人的角色。此交易協定特色如下：(1) 確保公平交易、(2) 確保買賣雙方在交易過程中的匿名性、(3) 確保買賣雙方都能收到預期的項目、 (4) 較具效率的訊息交換。

The improvement of network technology has a great impact on whole society. As a result of the network, exchange has already been applied to our daily life and then people can transact business on the network. Fair exchange requires that both parties can all ob-tain expected item in reciprocity case. For instance, after a customer (C) made the pay-ment then he will receive the merchandise. In the same way, a merchant (M) sent the merchandise to the customer should get the payment. With the transmission of messages, both parties can verify the encrypted product, product decryption key, and payment, and reach the principle of fair exchange. Though the network exchange has already been popularized day by day, while any malicious outsider that has some special equipment or software can intercept the information in the network, or imitate others to convey wrong information. Hence anonymity ensures that the identity of two parties is not revealed during the exchange process.
In this thesis, we propose a new anonymous fair exchange protocol. A trusted third party (TTP) will act as the intermediary between the two parties. This protocol has fol-lowing features: (1) guaranteeing the fair exchange in transaction, (2) assuring anonymity for both parties during the transaction, (3) ensuring that both parties all can prove the correctness of the receiving message, (4) message exchange is efficient.

ACKNOWLEDGMENT (in Chinese) I
ABSTRACT (in Chinese) II
ABSTRACT (in English) III
CONTENTS IV
LIST OF FIGURES V
LIST OF TABLES VI
CHAPTER 1 INTRODUCTION 1
1.1 Overview 1
1.2 Organization of the thesis 3
CHAPTER 2 PRELIMINARIES 4
2.1. Introduction to Number Theory [13] 4
2.1.1. Fermat’s Theorem 4
2.1.2. Euler’s Totient Function 4
2.1.3. Euler’s Theorem 5
2.2. The RSA Algorithm [13] 5
2.3. The Hash Function [13] 8
2.4. Notations 8
2.5. Assumptions 10
CHAPTER 3 THE PROPOSED PROTOCOL 13
3.1. Description of our Protocol 13
3.2. Sketch of this fair exchange protocol 13
3.3. The Basic Protocol 15
3.4. Key Recovery Protocol 21
CHAPTER 4 PROTOCOL ANALYSIS 24
4.1. Analysis of True Fair Exchange 24
4.1.1. While C has improper behaviors 24
4.1.2. While M has improper behaviors 25
4.2. Analysis of Anonymity 25
4.3. Analysis of Collusion 27
4.3.1. Two parties’ collusion 27
4.3.2. Three parties’ collusion 28
4.4. Analysis of Computation of Encryption and Decryption 28
CHAPTER 5 CONCLUSION 30
REFERENCES 31

[1] N. Asokan, M. Schunter and M. Waidner, “Optimistic protocols for fair exchange,” ACM Conference on Computer and Communications Security, Switzerland, pp. 6-17, April 1997.
[2] N. Asokan, V. Shoup and M. Waidner, “Asynchronous protocols for optimistic fair exchange,” IEEE Symposium on Security and Privacy, Oakland, CA, pp.86-100, May 1998.
[3] N. Asokan, V. Shoup and M. Waidner, “Optimistic fair exchange of digital signa-tures,” IEEE Journal on Selected Areas in Communications, vol. 18, pp.593-610, 2000.
[4] F. Bao and R. Deng, “An efficient fair exchange protocol with an off-line semi-trusted third party,” International Workshop on Cryptographic Techniques and E-Commerce, pp.37-47, 1999.
[5] I. Ray and I. Ray, “An optimistic fair exchange e-commerce protocol with automated dispute resolution,” First International Conference on Electronic Commerce and Web Technologies, EC-Web 2000, Lecture Notes in Computer Science, vol. 1875, Springer, Berlin, pp.84-93, 2000.
[6] I. Ray and I. Ray, “An anonymous fair exchange e-commerce protocol,” 15th Interna-tional Parallel and Distributed Processing Symposium, pp.1790-1797, April 2001.
[7] Q. Shi, N. Zhang and M. Merabti, “Signature-based approach to fair document ex-change,” IEE Proceedings-Communications, vol. 150, No. 1, pp.21-27, Feb. 2003.
[8] Q. Shi, N. Zhang and M. Merabti, “An efficient protocol for anonymous and fair document exchange,” International Journal of Computer and Telecommunications Net-working, vol. 41, No. 1, pp.19-28, January 2003.
[9] M. Franklin and M. Reiter, “Fair exchange with a semi-trusted third party,” ACM Conference on Computer and Communication Security, Zurich, Switzerland, pp.1-5, April 1997.
[10] B. Schneier, Applied cryptography. John Wiley, 1996.
[11] R. L. Rivest, A. Shamir and L.M. Adleman, “A method for obtaining digital signa-tures and public-key cryptosystems,” Communications of the ACM, pp. 120-126, 1978.
[12] S. Low, N. Maxemchuk, and S. Paul, “Anonymous credit cards,” In J. Stern, editor, Proceedings of the 2nd ACM Conference on Computer and Communications Security, pp.108-117, Fairfax, Virginia, Nov. 1994.
[13] W. Stallings, Cryptography and Network Security: Principles and Practice. New Jer-sey: Prentice Hill, 1998.