臺灣博碩士論文加值系統

本論文藉著橢圓曲線密碼學與Diffie-Hellman的金鑰交換方法，並參照Lee等人與Biswas所提出的金鑰產生協定，提出了兩種植基於橢圓曲線密碼學的多重群組金鑰分配協定，讓群組的參與者們可以透過本協定產生多把通訊金鑰。
本論文所提出的方法相較於以往的方法，可以在運算量及通訊量更少的情況下產生更多把金鑰，並且能有效地在成員變動時，更新所有的群組金鑰，以維持使用者在傳遞訊息時的安全性，並同時證明本論文所提出的兩種方法，皆能保有參與者們的私密值，以及能抵擋竊聽攻擊和已知金鑰攻擊法。

The purpose of this study is to develop two multiple group key distribution protocols based on elliptic curve cryptography. They will allow all members in a group to share multiple group keys after executing the proposed protocol.
Comparing with the existed schemes, our protocols are more efficient and more suitable for many applications. Besides, the security of the proposed protocols is the same with breaking elliptic curve cryptosystem. When the members join or leave, our protocols can renew group keys efficiently. And we prove that our protocols can protect the secret values of the members, and they can prevent the eavesdropping attack and the known key security.

摘要....................................................................................................................... iv
Abstract................................................................................................................... v
誌謝....................................................................................................................... vi
目次...................................................................................................................... vii
圖目錄................................................................................................................... ix
表目錄.................................................................................................................... x
第一章 緒論.......................................................................................................... 1
1.1 研究背景................................................................................................. 1
1.2 研究動機與目的...................................................................................... 6
1.3 章節概要................................................................................................. 7
第二章 相關密碼學技術介紹............................................................................... 8
2.1 Diffie-Hellman金鑰交換法..................................................................... 8
2.1.1 Diffie-Hellman金鑰交換法概念................................................... 8
2.1.2 Diffie-Hellman金鑰交換演算法................................................... 9
2.1.3 Diffie-Hellman金鑰交換演算法的安全性.................................. 10
2.2 橢圓曲線密碼系統................................................................................ 12
2.2.1橢圓曲線密碼系統簡介............................................................... 12
2.2.2橢圓曲線密碼系統之加密技術......................................................... 15
2.2.3橢圓曲線密碼系統的安全性............................................................. 16
第三章 群組金鑰分配協定相關研究之回顧...................................................... 20
3.1符號定義................................................................................................ 20
3.2 Lee等人的方法...................................................................................... 21
3.3 Biswas的方法........................................................................................ 23
第四章 植基於橢圓曲線密碼系統之多重群組金鑰分配協定一........................25
4.1符號定義.......................................................................................................25
4.2協定一之方法..............................................................................................26
4.2.1架構簡介............................................................................................26
4.2.2 初始階段............................................................................................27
4.2.3 新增成員階段....................................................................................31
4.2.4 成員離開階段....................................................................................36
4.3 安全性分析..................................................................................................38
4.4 效能分析與比較..........................................................................................40
第五章 植基於橢圓曲線密碼系統之多重群組金鑰分配協定二........................43
5.1符號定義.......................................................................................................43
5.2協定二之方法...............................................................................................44
5.2.1 架構簡介............................................................................................44
5.2.2 初始階段............................................................................................45
5.2.3 新增成員階段....................................................................................47
5.2.4 成員離開階段....................................................................................51
5.3 安全性分析..................................................................................................53
5.4 效能分析與比較..................................................................................55
第六章 結論與未來展望..........................................................................................58
6.1 結論.............................................................................................................58
6.2 未來展望.....................................................................................................58
參考文獻.....................................................................................................................60

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