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研究生： 陳建甫
Chen, Chien-Fu
論文名稱： 建構網際網路安全之群體導向金鑰樹管理
Group-oriented Management of Key Trees for Secure Internet
指導教授： 郭耀煌
Kuo, Yau-Hwang
學位類別： 碩士
Master
系所名稱： 電機資訊學院 - 資訊工程學系
Department of Computer Science and Information Engineering
論文出版年： 2003
畢業學年度： 91
語文別： 英文
論文頁數： 69
中文關鍵詞： 群體金鑰 、群體導向管理 、金鑰管理
外文關鍵詞： Group Key, Group-oriented Management, Key Management
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    • 　　近年來隨著科技的進步與普及，人們的生活方式和網路習習相關；日常的食、衣、住、行、育、樂等活動莫不和網際網路緊緊相連。由於許多的事物都在網路的環境中發生，因此網路安全的課題逐漸受到大家的重視；現在已經有許多人致力於這方面的研究和努力，而他們也有很好的成果與貢獻。在眾多的安全議題中，我們所關心的是群體金鑰的問題，也就是如何讓群體中的每個成員使用共同的金鑰來交換訊息；此外，在成員有所變動時，例如新成員的加入或舊成員的離開，群體金鑰勢必需要重新計算以確保其安全性，如何快速、安全、有效率的求出新的金鑰，也是我們所關心的事情。

    　　在本篇論文中，我們提出以群體導向的方式來管理金鑰樹。在許多的應用，例如視訊會議或網路連線遊戲中，整個大群體中通常會有小群體的存在，小群體中也需要以安全的方式來傳遞資料。以傳統金鑰樹管理的方法，例如TGDH，是無法達成小群內的安全性。此外由於計算群體金鑰所使用的演算法，所有成員必需花費大量的指數運算，這卻是影響TGDH性能的一個重要因素，經由此種群體導向的管理方式，我們減低為了求得群體金鑰所需的指數運算次數。而在整個群體金鑰更新的過程中，發起者會送出一個含有隱蔽金鑰的訊息，我們也減低了這個訊息的大小，這更是影響所有金鑰樹性能的一個指標。因此，我們提出的方法應用於管理群體金鑰上，不僅能夠顯現出更好的性能，更能提供更多的資訊給成員們利用。

    　　The ways of life are bound up with network as the progress and popularization of science and technology. Our routine is related to Internet and since many things occur in network environment, people pay much attention to the subject of network security gradually. Now a lot of people work for relevant research and made great contributions. We are interested in group key management among these topics. Members of a group use the same key to exchange information and in order to ensure security, the group key must be updated when membership changes such as affiliation of a new member or deletion of old members. It is essential to compute the new group key rapidly, securely and efficiently.

    　　In this thesis, we propose group-oriented management of key trees. The whole group usually has subgroups and data must be delivered securely inside any subgroup such as Video Conference and on-line games. Traditional manners of key tress like TGDH cannot achieve the goal and it costs a great quantity of exponentiation computation to calculate the group key due to its algorithm. By means of group-oriented management of key trees, we reduce the cost. Next the sponsor transmits a message containing blinded keys during the process of re-keying and we also reduce this message size that is consultation to evaluate performance of key trees. Therefore, our approach applied to group key management not only performs well but also supplies members with more information.

    Contents I List of Figures III List of Tables V Chapter 1 Introduction 1 　　1.1 Background 1 　　1.2 Motivation 2 　　1.3 Organization 3 Chapter 2 Group Key Management 4 　　2.1 Diffie-Hellman Key Exchange 4 　　2.2 Group Communication 5 　　　　2.2.1 GKM Requirements 6 　　　　2.2.2 Group Membership Events 7 　　2.3 Previous Approaches of Group Key Management 8 　　　　2.3.1 Simple Key Distribution Center (SKDC) 8 　　　　2.3.2 Group Diffie-Hellman (GDH) 9 　　　　2.3.3 Logical Key Hierarchy (LKH) 9 　　　　2.3.4 One-way Function Tree (OFT) 10 　　　　2.3.5 Efficient Large-group Key Distribution (ELK) 11 　　　　2.3.6 Tree-based Group Diffie-Hellman (TGDH) 11 Chapter 3 Approach for Group-oriented Management of Key Trees 12 　　3.1 Notations and Definitions 12 　　3.2 Join Operation 16 　　3.3 Leave Operation 20 　　3.4 Merge Operation 22 　　3.5 Partition Operation 25 Chapter 4 Performance Analysis and Discussion 29 　　4.1 Cost Analysis of TGDH 29 　　4.2 Cost Analysis of GOT 31 　　　　4.2.1 Cost Analysis of GOT in Join Operation 31 　　　　4.2.2 Cost Analysis of GOT in Leave Operation 35 　　　　4.2.3 Cost Analysis of GOT in Merge Operation 37 　　　　4.2.4 Cost Analysis of GOT in Partition Operation 38 　　4.3 Message Size Analysis 41 　　　　4.3.1 Message Size in Join Operation 41 　　　　4.3.2 Message Size in Leave Operation 43 Chapter 5 Simulation and Result 45 　　5.1 Comparison of Key Tree Height 45 　　5.2 Join Cost 46 　　　　5.2.1 Comparison of Join Cost between TGDH and GOT 46 　　　　5.2.2 Join Cost of Different Subgroups 49 　　5.3 Leave Cost 52 　　　　5.3.1 Comparison of Leave Cost between TGDH and GOT 52 　　　　5.3.2 Leave Cost of Different Subgroups 55 　　5.4 Merger Cost 58 　　5.5 Partition Cost 58 　　5.6 Message Size 61 　　　　5.6.1 Join Comparison 61 　　　　5.6.2 Leave Comparison 62 Chapter 6 Conclusion 65 　　6.1 Conclusion 65 　　6.2 Future Works 65 References 67 List of Figures Fig. 2.1 Diffie-Hellman key exchange 5 Fig. 3.1 A key tree 14 Fig. 3.2 Combination of several sub-trees 14 Fig. 3.3 Join operation (no new subgroup is added.) 18 Fig. 3.4 View the key tree as subgroup relation 19 Fig. 3.5 Join operation (a new subgroup is added to the group.) 20 Fig. 3.6 Leave operation (one subgroup is deleted from the group.) 21 Fig. 3.7 Leave operation (no subgroup is deleted from the group.) 22 Fig. 3.8 Two key tress T1 and T2 24 Fig. 3.9 Merge operation (T1 and T2 merge together.) 24 Fig. 3.10 Partition operation: h(Sl) is equal to 1. 26 Fig. 3.11 Partition operation (one subgroup raises one level.) 27 Fig. 3.12 Partition operation (two subgroups raise one level.) 28 Fig. 4.1 A new member joins the group (m=4). 29 Fig. 4.2 The key tree has three subgroups. 32 Fig. 4.3 A member of a new subgroup is added to the key tree. 33 Fig. 4.4 The structure of key trees 39 Fig. 5.1 Height of key trees with different group size 46 Fig. 5.2 Comparison of join cost (average) 47 Fig. 5.3 Join cost range of GOT 48 Fig. 5.4 Comparison of join cost 49 Fig. 5.5 Join cost of different subgroups 50 Fig. 5.6 Join cost range of GOT with different subgroups (m=20) 51 Fig. 5.7 Join cost range of GOT with different subgroups (m=10) 52 Fig. 5.8 Comparison of leave cost (average) 53 Fig. 5.9 Leave cost range of GOT 54 Fig. 5.10 Comparison of leave cost 55 Fig. 5.11 Leave cost of different subgroups 56 Fig. 5.12 Leave cost range of GOT with different subgroups (m=20) 57 Fig. 5.13 Leave cost range of GOT with different subgroups (m=10) 57 Fig. 5.14 Comparison of merge cost 58 Fig. 5.15 Comparison of partition cost (m=20) 59 Fig. 5.16 Comparison of partition cost (m=10) 59 Fig. 5.17 Partition cost range of GOT with different subgroups (m=20) 60 Fig. 5.18 Partition cost range of GOT with different subgroups (m=10) 61 Fig. 5.19 Comparison of message size (Join) 62 Fig. 5.20 The ratio of message size in join operation 62 Fig. 5.21 Comparison of message size (Leave) 63 Fig. 5.22 The ratio of message size in leave operation 63 List of Tables Table 3.1 Basic notations 13 Table 4.1 All combination of ni when m=5 34 Table 4.2 Conditions that two subgroups raise one level. 40 Table 5.1 Max join cost (GOT) vs. join cost (TGDH) 50 Table 5.2 Max leave cost (GOT) vs. leave cost (TGDH) 56

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