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研究生:楊仁傑
研究生(外文):Jen-Chieh Yang
論文名稱:IDEA區塊演算法的延伸與實作
論文名稱(外文):An Extension of IDEA Block Cipher and Its Implementation
指導教授:葉義雄葉義雄引用關係
指導教授(外文):Yi-Shiung Yeh
學位類別:碩士
校院名稱:國立交通大學
系所名稱:資訊工程系
學門:工程學門
學類:電資工程學類
論文種類:學術論文
論文出版年:2002
畢業學年度:90
語文別:英文
論文頁數:43
中文關鍵詞:IDEA 區塊加密法延伸性不可分割多項式
外文關鍵詞:IDEA Block CipherExtensionIrreducible Polynomial
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在1990年由X. Lai與J. Massey兩位博士所提出的IDEA是比DES更安全的區塊加密法。它利用混合不同的代數群之間的運算來提昇密碼系統的安全性。在本論文中,我們首先簡介IDEA的架構與key scheduling,接下來將IDEA密碼系統的行為數學化,並比較C與JAVA的Performance。接下來,我們擴增子區塊加密從16位元到32位元,故我們必須從新定義基本的function,將乘法同模擴充到32位元並做適當的修改,延伸的IDEA系統將可提高加密的安全性與彈性。

IDEA is invented by Dr. X. Lai and Dr. J. Massey In 1990, which is a more secure block cipher than DES. IDEA use the mixing operations form different algebraic group to improve its security. In this paper, we first introduce the architecture of IDEA and key scheduling, and use mathematical model to describe it. Then we extend the inner sub-blocks from 16 bits to 32bits. So we must redefine and check the basic functions, extend the multiplication of integers to 32bits and do some proper modification. The extended IDEA can enhance the security and flexibility of the cryptography system.

Contents
Acknowledgements ……………………………………………………………i
Abstraction in Chinese ………………………………………………………..ii
Abstraction in English ………………………………………………………..iii
Chapter 1. Introduction ………………………………………………………. 1
1.1 Overview ……………………………………………………….. 1
1.2 Cryptographic System …………………………………………... 2
1.3 Cryptanalysis ……………………………………………………. 3
Chapter 2. Background ………………………………………………………… 6
2.1 Fundamental of Mathematics …………………………………… 6
2.1.1 Algebra …………………………………………………... 6
2.1.2 Modular Arithmetic ……………………………………… 8
2.1.3 Fermat number ……………………………………………9
2.2 The block cipher operating modes ……………………………… 9
2.2.1 ECB(Electronic CodeBook mode) ……………………… 10
2.2.2 CBC(Cipher Block Chaining mode) ……………………..11
2.2.3 CFB(Cipher FeedBack mode) ……………………………11
2.2.4 OFB(Output FeedBack mode) ……………………………12
Chapter 3. The IDEA Block Cipher …………………………………………….14
3.1 The Description of the Algorithm ………………………………..14
3.2 Determination of the key of sub-blocks ………………………….17
3.3 The mathematical model of IDEA ………………………………..20
3.4 C Platform environment ………………………………………….25
3.5 Java Platform environment ……………………………………….25
3.6 Implementation and test …………………………………………..26
3.7 Performance measurement ………………………………………..28
Chapter 4 The Extended IDEA …………………………………………………..31
4.1 Basic function of extend IDEA ……………………………………31
4.2 A suitable irreducible polynomial of extend IDEA ………………..33
4.3 key scheduling ……………………………………………………..37
4.4 Encryption and Decryption algorithm ……………………………..38
Chapter 5 Conclusion …………………………………………………………….41
References ………………………………………………………………………..42
Appendix IDEA Source Code

References
[1] B. Schneier, Applied Cryptography, John Wiley & Sons, 1996.
[2] 賴溪松、韓亮、張真誠,近代密碼學及其應用,松崗電腦圖書資料股份有限公司,台北,民國八十四年。
[3] 張真誠,電腦密碼學與資訊安全,松崗電腦圖書資料股份有限公司,台北,民國七十八年。
[4] Cryptography and Network Security: Principles and Practice by : William Stalling.
[5] NIST Publication 800-17 and 800-2 0 for Monte Carlo tests (http://csrc.nist.gov/cryptval/)
[6] NIST Timing measurement procedure
(http://csrc.nist.gov/encryption/aes/round2/round2.htm)
[7] Handbook of Applied Cryptography by Alfred J. Menezes, Paul C. van Oorschot, and Scott A. Vanstone.
[8] W. Meier, On the Security of the IDEA Block Cipher, Advances in Cryptology - EUROCRYPT’93 Proceedings, Lecture Notes in Computer Science, Springer-Verlag, Berlin 1993, pp. 371-385.
[9] X. Lai and J. L. Massey, A Proposal for a New Block Encryption Standard, Advances in Cryptology - EUROCRYPT’90 Proceedings, Lecture Notes in Computer Science, Springer-Verlag, Berlin 1991, pp. 389-404.
[10] X. Lai, J. Massey and S. Murphy, Markov Ciphers and Differential Cryptanalysis, Advances in Cryptology - EUROCRYPT ’91 Proceedings, Springer-Verlag, 1991, pp. 17-38.
[11] 潘承洞、潘承彪,初等數論,凡異出版社,新竹,民國八十四年。
[12] 聶靈沼、丁石孫,代數學引論,凡異出版社,新竹,民國八十五年。
[13] A. Menezes, P. van Oorschot, and S. Vanstone, Handbook of Applied Cryptography, CRC Press, 1996.
[14] E. Biham and A. Shamir, Differential cryptanalysis of DES-like cryptosystems, Journal of Cryptology, 1991, 4(1):3-72.
[15] A. Curiger, H. Bonnenberg and H. Kaeslin, Regular VLSI-architectures for multiplication modulo (2n+1), IEEE Journal of Solid-State Circuits, July 1976, 26(7):990-994.
[16] L.M. Leibowitz, A simplified binary arithmetic for the Fermat number transform, IEEE Transactions on acoustics, speech and signal processing, 1976, AASP-24:356-359.
[17] I.N. Herstein, Abstract Algebra, Macmillan, 1990.
[18] X. Lai and J. Massey, Hash Functions Based on Block Ciphers, Advances in Cryptology - EUROCRYPT ’92 Proceedings, Springer-Verlag, 1992, pp. 55-70.
[19] http://java.sun.com/products/jdk/1.4/docs/guide/security/CryptoSpec.html

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