An Efficient Algorithm for Weil/Tate Pairing Based on Radix 2^(2w)+1 Representation

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研究生：	秦茂原
論文名稱：	An Efficient Algorithm for Weil/Tate Pairing Based on Radix 2^(2w)+1 Representation Weil/Tate Pairing 基於 Radix 2^(2w)+1 之快速演算法
指導教授：	孫宏民
口試委員:
學位類別：	碩士 Master
系所名稱：	電機資訊學院 - 資訊系統與應用研究所 Institute of Information Systems and Applications
論文出版年：	2008
畢業學年度：	96
語文別：	英文
論文頁數：	43
中文關鍵詞：	橢圓曲線密碼學
相關次數：	點閱：1 下載：0
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Weil pairing 和 Tate pairing 在許多密碼應用上扮演重要的角
色，因此加速pairing運算成了有趣且重要的議題。近年來，有些應用
所使用的pairing 需要在characteristics大於4並且mod 3同餘2的
supersingular曲線上。目前卻很少有關於在這些曲線上改進效能的研
究。在這篇論文中，我們提供一個有效計算pairing的方法，並適合
characteristics為5的曲線。這個方法在其他characteristics時也有
傑出的效果。我們使用Markov模型分析效能，並且與其他現行的方法
做比較。

Table of Contents ........................................................................................................... I
List of Figures ................................................................................................................ III
List of Tables.................................................................................................................. IV
Chapter 1 Introduction ................................................................................................ 1
Chapter 2 Mathematical Background ......................................................................... 3
2.1 Finite Fields .................................................................................................. 3
2.1.1 Groups........................................................................................... 3
2.1.2 Rings and Fields............................................................................ 4
2.2 Elliptic Curves .............................................................................................. 4
2.2.1 Elliptic Curves properties and group law...................................... 5
2.2.2 Order of Point and Elliptic Curves................................................ 9
2.3 Pairings ......................................................................................................... 9
2.3.1 Divisors ......................................................................................... 9
2.3.2 Weil/Tate Pairing........................................................................... 10
Chapter 3 Computation of Weil/Tate Pairing.............................................................. 13
3.1 Miller Algorithm........................................................................................... 13
3.2 BMX Algorithms .......................................................................................... 13
3.3 LHC Algorithm............................................................................................. 15
3.4 Wu’s Algorithm............................................................................................. 15
Chapter 4 Proposed Scheme ....................................................................................... 24
4.1 Main Idea of Scheme .................................................................................... 24
4.2 Rules, Representation of Lines and Segmentation Algorithm...................... 26
Chapter 5 Performance Evaluation ............................................................................. 35
Chapter 6 Conclusion.................................................................................................. 41

                                

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