在這篇論文中，我們提出了一個應用於群組通訊方面的金鑰管理機制有效方法，並配合上行動用戶成員彼此間的相關性，使得群組通訊系統在做金鑰更新時可以更有效率、更少花費並節省時間。

在群組通訊網路中，每當有行動用戶成員新加入或離開此群組，群組中有關網路安全方面的金鑰管理機制就必須做更新的動作，以確保只有目前有符合資格的行動用戶成員得以在此群組通訊中來接受網路應用服務、資料傳輸、訊息交換……等的無線通訊行為。大部分的用邏輯樹狀結構的金鑰管理機制，其邏輯樹狀結構中的骨幹部分都是可變動的，以適應於在做金鑰更新時可以有效率且方面於管理。相反地，本論文中所提出的方法，反而是著重在行動用戶成員的群組關係，我們利用中央集權式的金鑰管理機制方法，並固定了其邏輯樹狀結構的骨幹之分支度與深度，再加上考慮了行動用戶成員之間的相關性，當行動用戶成員加入此群組通訊服務時，是以群組為單位而非單一行動用戶成員的加入，利用此特性我們可以有效地管理此群組通訊中的行動用戶成員，再經由程式模擬時，計算每當有行動用戶成員的更動，必須做金鑰更新時其每單位時間內所花的平均花費可發現，可以有效地節省花費並改善系統效能。

In this thesis, we propose and analyze a multicast key backbone for secure group communications. We also utilize the correlated relationships between the mobile users in the wireless communications networks. When a batch member joins or leaves the group communications, the system has to update and distribute encryption keys to assure that only active members could receive the latest information. In previous tree-based multicast key management schemes, the depth of the key tree is unbounded and analytically deriving the exact value of the corresponding average update cost remains an open problem. And in previous schemes, the different mobile user arrives in and leaves from the system at different time. In contrast, the depth of the proposed multicast key backbone is fixed and the arriving or leaving users are more than one. We utilize these two characteristics and simulate the system to get the average update cost per time unit. We can find that this scheme can improve the efficiency of the system in some special cases when updating the new key.

第一章序論........................................1
1.1 研究背景與動機................................1
1.1.1 網路安全....................................1
1.1.2 行動用戶的相關性............................3
1.1.3 綜合討論....................................3
1.2 論文架構......................................4
第二章中央集權式的金鑰管理機制系統架構............5
2.1 存取控制......................................5
2.2 中央集權式群組金鑰管理........................6
2.2.1 新成員加入..................................7
2.2.2 舊成員離開..................................8
2.3 平衡樹........................................9
2.4 行動用戶的相關性..............................9
2.5 邏輯樹狀架構骨幹之固定........................10
第三章行動相關用戶的金鑰管理......................11
3.1 行動用戶的機率模型............................11
3.1.1 行動用戶的行為模式..........................11
3.1.2 行動用戶的相關性............................13
3.1.3 行動用戶行為的模擬機率模型..................15
3.2 系統的邏輯樹狀架構............................17
3.2.1 系統初始狀態................................17
3.2.2 新成員加入且系統無服務的行動用戶成員........18
3.2.3 新成員加入且系統有正在服務的行動用戶成員....19
3.2.4 舊成員離開且系統尚有正在服務的行動用戶成員..22
3.2.5 舊成員離開且系統已無服務的行動用戶成員......25
第四章模擬結果與討論..............................26
第五章結論........................................36
參考文獻..........................................38

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