在本篇論文中，我們提出了一個應用於群組通訊方面的金鑰管理機制，並配合行動用戶的異質性，使得群組通訊系統在做金鑰更新時，可以更有效率、花費更少並節省時間。
在群組通訊網路中，使用者總是進進出出。當有新的行動用戶成員欲加入或是離開此群組時，群組中相關的網路安全群組金鑰就必須有所更新，以確保目前在群組中的使用者可以繼續在此群組中使用群組通訊網路，也確定離開的使用者將不再獲得此群組中的任何服務，保障群組中各用戶的權利。
我們利用中央集權式的金鑰管理方法，且固定了其邏輯樹狀結構的骨幹之分支度與深度，並考慮各種使用者的屬性。當行動用戶加入此群組服務時，我們可以適當的將之分配到某些特定的樹葉節點，再經由程式的模擬，計算群組中的行動用戶成員有所異動時，其每單位時間內所花費的平均花費，我們可以得知我們所提出的方法在某些情況下，有較佳的效能。

The key update cost is an important parameter of the performance evaluation of the secure group communications in the wireless networks. It is a very public issue to reduce the key update cost. In the tree-based multicast key management scheme, a user is randomly assigned to one of the all leaf nodes. In this thesis, we divide the users into two groups which are new call users and handoff call users. Then, we propose that new call users are assigned to some of the special leaf nodes in the key tree and the handoff call users are assigned to others. This scheme is called class-based multicast key management scheme. We analyze this two multicast key management schemes for secure group communications. This thesis shows that class-based scheme could reduce the key update cost in some special case.

致 謝 I
中文摘要 III
Abstract IV
目 錄 V
圖目錄 VII
第一章 緒論 1
1-1 研究背景 1
1-2 研究動機 2
1-3 論文架構 3
第二章 中央集權式的金鑰管理機制系統架構 4
2-1 存取控制(Access Control) 4
2-2 中央集權式群組金鑰管理 5
2-2-1新成員加入 6
2-2-2舊成員離開 7
第三章 行動用戶的金鑰管理 10
3-1 行動用戶的機率模型 10
3-2 系統的邏輯樹狀架構之操作方式 11
3-2-1 系統初始狀態 11
3-2-2 新成員加入且系統無服務的行動用戶成員 12
3-2-3 新成員加入且系統有正在服務的行動用戶成員 13
3-2-4 舊成員離開且系統有正在服務的行動用戶成員 15
3-2-5 舊成員離開且系統已無服務的行動用戶成員 17
3-3 使用者分配方法 (User Assignment Scheme) 18
3-3-1 使用者種類 18
3-3-2 Balance-based assignment scheme 20
3-3-3 Class-based assignment scheme 23
第四章 模擬結果與討論 26
第五章 結論 52
參考文獻 53

[1] Sheldon M. Ross, Introduction to Probability Models, 7th Edition 2000, Academic Press, San Diego, CA, USA.

[2] Rung-Hung Gau, “Performance Analysis of Multicast Key Backbone for Secure Group Communications,” IEEE Communications Letters, Vol. 10, No. 7, July 2006, p.555-557.

[3] Rung-Hung Gau, and Chung-Wei Lin, “Location management of correlated mobile users in the UMTS,” IEEE Transactions on Mobile Computing, Vol. 4, No. 6, Nov.-Dec. 2005, p.641-651.

[4] Xiaozhou Steve Li, Yang Richard Yang, Mohamed G. Gouda, and S.Lam, “Batch Rekey-ing for Secure Group Communications,” ACM SIGCOMM 1997, p.277-288

[5] M. J. Moyer, J. R. Rao, and P. Rohatgi, “Maintaining Balanced Key Trees for Secure Multicast,” INTERNET-DRAFT, June 1999.

[6] Chung Key Wong, Mohamed Gouda and Simon S.Lam, “Secure Group Communications Using Key Groups,” IEEE/ACM Transaction on Networking, Vol.8, No. 1, Feb. 2000,
p.16-30.

[7] Radha Poovendran, and John S. Baras, “An Information-Theoretic Approach for Design and Analysis of Rooted-Tree-Based Multicast Key Management Schemes,” IEEE Transcations on Information Theory, Vol. 47, No. 7, November 2001, p.2824-2834.
[8] X. Brian Zhang, Simon S. Lam, Dong-Young Lee, and Y. Richard Yang, “Protocol Design for Scalable and Reliable Group Rekeying,” IEEE/ACM Transactions on Networking, Vol. 11, No. 6, Dec. 2003, p.908-922.

[9] Yinian Mao, Yan Sun, Min Wu and K. J. Ray Liu, “Dynamic join-exit amortization and scheduling for time-efficient group key agreement,” INFORCOM 2004. Twenty-third Annual Joint Conference of the IEEE Computer and Communications Societies, Vol. 4, March 2004, p.2617-2627.

[10] Yu-Lun Huang, Shiuhpyng Shieh, Fu-Shen Ho, and Jian-Chyuan Wang, “Efficient Key distribution schemes for secure media delivery in pay-TV systems,” IEEE Transactions on Multimedia, Vol.6, No. 5, Oct. 2004, p.760-769.

[11]Wee Hock Desmond Ng, Michael Howarth , Zhili Sun, and Haitham Cruickshank, ”Dy-namic Balanced Key Tree Management for Secure Multicast Communications,” IEEE Transactions on Computers, Vol. 56, NO.5, May 2007, p.590-605.

[12] Y. Fang, I. Chlamtac, and Y.B.Lin, “Channel Occupancy Times and Handoff Rate for Mobile Computing and PCS Networks,” IEEE Transactions on Computers, Vol. 147, No. 6, Jun. 1998, p.679-692.

[13] Yan Sun, Wide Trappe, and K.J.Ray Liu, “A scalable Multicast Key Management Scheme for Heterogeneous Wireless Networks,” IEEE/ACM Transactions on Network-ing, Vol. 12, No. 4, Aug. 2004, p.444-458.

[14] D. Gross and C. M. Harris, “Fundamentals of Queueing Theory,” 3rd Edition, John Wi-ley and Sons, Inc, 1998.

[15] Yuguang Fang, Imrich Chlamtac, “Modeling and Performance Analysis for Wireless Mobile Networks: A New Analytical Approach,” IEEE/ACM Transactions on Net-working, Vol. 13, No. 5, Oct. 2004, p.989-1002.

[16] Yuguang Fang, Imrich Chlamtac, “Teletraffic Analysis and Mobility Modeling of PCS Networks,” IEEE/ACM Transactions on Networking, Vol. 13, No.5, Oct. 2004, p.989-1002.