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Differential Cryptanalysis and Linear Cryptanalysis: Theory, Characteristics and Application

Author: ShenJing
Tutor: LiChao
School: National University of Defense Science and Technology
Course: Applied Mathematics
Keywords: differential cryptanalysis linear cryptanalysis S-boxes permutation iterative characteristics Camellia RC6
CLC: TN918.1
Type: Master's thesis
Year: 2004
Downloads: 474
Quote: 1
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Abstract


The design and analysis of block ciphers are the hotspot in the field of information security. Differential cryptanalysis and linear cryptanalysis are the two most effective methods which attack block ciphers at present. This paper discusses basic theory, characteristic , application of the two methods.Block ciphers employ substitution boxes(S-boxes) as important components. We must consider various factors in order to design good S-boxes, for example differential uniform, nonlinearity, degrees of the coordinate Boolean functions and so on. This paper uses the method of Hill Climbing to improve the differential uniform of substitution boxes. We also study the substitution boxes which are differentially 2-uniform. We construct some substitution boxes which have good cryptographic properties according to power functions on finite field.Camellia is one of standard block ciphers algorithms in the NESSIE project. We analyze differential iterative characteristics and linear iterative characteristics, and find how the permutation and its inverse permutation affect 3-round iterative characteristics and 4-round iterative characteristics. We find the best 3-round iterative characteristics and 4-round iterative characteristics at present, and construct r(6≤r≤18) round differential (linear) characteristics of Camellia variant, where the differential probability of 18-round is 2~-296, and the linear bias of 18-round is 2~-141.32.RC6 is a simple and flexible cipher, which is based on RC5. We discuss different fixed rotation’s effect to RC6-I (A variety of RC6 which replace the quadratic function by identity function) at first, and prove that the invulnerability to differential attack is best when the fixed rotation is equal to lgw. Then we study different fixed rotation ’s effect to RC6 and also find when the fixed rotation is equal to lgw the invulnerability to differential attack is best.

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