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系統識別號 U0026-1007201513093200
論文名稱(中文) 公開金鑰密碼系統上的代數結構
論文名稱(英文) Algebraic structures on public key cryptosystem
校院名稱 成功大學
系所名稱(中) 數學系應用數學碩博士班
系所名稱(英) Department of Mathematics
學年度 103
學期 2
出版年 104
研究生(中文) 張珮娟
研究生(英文) Pei-Juan Chang
電子信箱 L16021098@mail.ncku.edu.tw
學號 L16021098
學位類別 碩士
語文別 英文
論文頁數 48頁
口試委員 口試委員-黃柏嶧
口試委員-陳家駒
指導教授-柯文峰
中文關鍵字 公開金鑰密碼系統  橢圓曲線  圓錐曲線  冪元素  非交換群  多項式環 
英文關鍵字 public key cryptosystem  elliptic curve  conic curve  idempotent element  nonabelian group  polynomial ring 
學科別分類
中文摘要 在這篇論文裡,我們介紹有關每個密碼系統上的操作方式,並進一步分析,討論每個密碼系統可能的優缺點。
英文摘要 In this thesis,we introduce about the operations of each cryptosystem,then give further analysis,discuss possible advantage and disadvantage of each cryptosystem.
論文目次 1. Introduction 1
2. Preliminaries of public key cryptosystem 4
3. Schemes of public key cryptosystem 6
3.1. Matrices over a ring 6
3.2. Elliptic curves over the ring Zn 11
3.3. Conic curves over the ring Zn 14
3.4. Polynomials over noncommutative rings 16
3.5. Polynomials over nonabelian groups 21
3.6. Polynomial rings 26
3.7. Idempotent elements 29
3.8. Circulant matrix 34
3.9. Finite nonabelian groups 39
References 42
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[3] Shanghai Jiao Tong University, Shanghai 200240, P. R. China New Public Key Cryptosystems Using Polynomials over Non-commutative Rings , Department of Computer Science and Engineering.
[4] J. Hastad, "On using RSA with low exponent in a public key network", Proc. of Crypto'B5, pp.403-408 (1985).
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[6] K. Koyama, U. M. Maurer, T. Okamoto, and S. A. Vanstone, “New public-key schemes based on elliptic curves over the ring Zn,in Advances in Cryptology-CRYPTO’91 (Lecture Notes in Computer Science, vol. 576). Berlin, Germany: Springer-Verlag, 1991, pp. 252-266.
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[18] T. El-Gamal, "A public key cryptosystem and a signature sclieme based on the discrete
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[19] Kenneth H. Rosen, Elementary Number Theory and Its Applications, Fifth Edition.
[20] Mukesh Kumar Singh, Texas Instruments Inc. Public Key Cryptography with Matrices,
Proceedings of the 2004 IEEE, Workshop on Information Assurance, United States Military
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[21] P. Nguyen, Cryptanalysis for the Goldreich-Goldwasser-Halevi Cryptosystem form
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