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On the Theory and Some Key Techniques of Block Ciphers

Author: GuDaWu
Tutor: XiaoGuoZhen
School: Xi'an University of Electronic Science and Technology
Course: Cryptography
Keywords: block cipher substitution box. substitution-permutation network key schedule algorithm multiple encryption cryptographic mode exponential permutation orthomorphic permutation differential cryptanalysis linear cryptanalysis
CLC: TN918.1
Type: PhD thesis
Year: 1998
Downloads: 540
Quote: 19
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Abstract


The thesis is devoted to the analysis and design of iterated block ciphers. Main contributions of this work are as follows:(1)On the basis of conditional attack and technical attack, we summarize seven items of design principals of a block cipher algorithm. Considering that multiple encryption is the best approach to increase the security of existing algorithms, we propose a ne~v triple encryption scheme NTE.(2)We deepl~?address ourselves to the essence of such cryptographic properties of a substitution box as regularity. algebric degree. nonlinearity, strict avalanche characteristics. propagation characteristics, differential uniformity and robustness, and thus negate a result in open literature. B~?means of spectral techniques we derive the relationship between the regularity and the differential distribution table of a substitution box. Also, we formulate the nonlinearity by linear structures of its nonzero combination functions.(3)We provide a substitution box, exponential permutation which has much measurable security, and give a enumerating result and a fast algorithm of calculating such permutation. An almost perfect nonlinear exponential permutation with high algebric degree is proposed. with some discussion on how to select the parameters of such permutation. The experimental result shows us a conjecture that there exists no such permutation over even dimensional space. As a way of generating substitution boxes, we briefly point out the cryptographic weakness of the exponential functions derived from such permutation. We also present two new cryptographic indexes, fixed point and cyclic structure, on which we investigate the performance of such permutation. Finally, we give a viewpoint about the application of correlation immune functions in designing substitution boxes.(4)Our discussion of the orthomorphic permutations is focused on its classification, properties, enumeration, construction and derivation. We develop a necessary and sufficient condition under which an orthomorphic permutation is linear, and also improve the method available of constructing nonlinear orthomorphic permutations. As the application of orthomorphic permutations in cryptography, we simply emphasize the advantage provided by such permutation in increasing the security of a block cipher. Meanwhile, we design a cryptographic strong boolean function.(5)The design principals of a secure key schedule are also our concern. We present three new practical key schedule schemes based on the triple encryption NTE and stream ciphers respectively.(6)In the case of the design of operation modes of a block cipher, we introduce the security and implementation principals. In view of the famous 搈ultiplicationaddition?structure, we obtain a new secure mode NPCBC, with the discussion of its strength and efficient. The result obtained appears that the NPCBC mode is much stronger than CBC mode.

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