Component Design And Analysis Of Cryptographic Algorithms

Nowadays the problem of information security protection is increasingly serious. Cryptography has been the basis of the information security, it attracts more attention in recent years. As a hot topic in the cryptography, component design and analysis of cryptographic algorithms play significant roles in steam ciphers and block ciphers. Under this background, this thesis concentrates on the component design theory of cryptographic algorithms and the cryptanalysis methodologies of cryptographic algorithms, and it mainly contains two parts.Cryptographic function, including Boolean function and vectorial Boolean function is an important component of cryptographic algorithms. The cryptographic criteria, such as difference uniformity and algebraic immunity are crucial to the security of cryptographic function. In the first part, we firstly discuss the preimage distributions and the value distributions of exponential sums from perfect nonlinear functions, which is the vectorial Boolean function with optimal difference uniformity on finite fields. Then the enumeration of even-variable Boolean functions with maximum algebraic immunity(MAI) is investigated.Due to their features of high-speed, efficient for both software and hardware implementations, block ciphers are widely used in data encryption, digital signature, etc. In the second part, we focus on some cryptanalytic methods of block ciphers, including Meet-in-the-Middle attack, impossible differential cryptanalysis and integral cryptanalysis. By these methods, the security of two kinds of familiar block ciphers, i.e. Zodiac and RC6 is evaluated.In the domain of component design theory of cryptographic algorithms, the main contents and fruits of this thesis are outlined as follows:(1) We prove that when (?)(x) is DO function or CM function on GF(q~m), the preimage distribution of the perfect nonlinear function tr(a(?)(x)) has just two kinds of values, one kind corresponds to all the elements of quadratic residual on GF(q~m) , and the other kind corresponds to all the non- quadratic residual on GF(q~m) .(2) Based on theory of quadratic forms over finite fields, the value distributions of the exponential sums are determined for three classes of known perfect nonlinear functions (?)(x) from GF(q) to itself. Based on the value distributions of these exponential sums, the correlation distribution between two sequences is calculated for three classes of known perfect nonlinear functions (?)(x) from GF(q) to itself except Coulter-Matthews functions, while we determine the weight distributions of linear codes constructing from the perfect nonlinear functions.(3) Enumeration of even-variable Boolean functions with MAI and 1-resilient Boolean functions with MAI are investigated. As a result, the lower bound on the number of even-variable Boolean functions with MAI was improved. And we also obtain a meaningful lower bound on the number of 1-resilient Boolean functions with MAI for the first time.In the domain of cryptanalytic methods for block ciphers, the main contents and fruits of this thesis are outlined as follows:(1) The security of Zodiac against the meet-in-the-middle attack is discussed. Some new 9-round and 10-round distinguishers of Zodiac are found, and based on which we make some meet-in-the-middle attacks on 15-round and the full 16-round Zodiac. The results show that the full Zodiac-128/192/256 is not immune to the meet-in-the-middle attack.(2) The resistance of RC6 against integral cryptanalysis and impossible differential cryptanalysis is evaluated. The complexities of both integral attack on RC6 reduced to 4 rounds and impossible differential attack on RC6 reduced to 5 rounds are lower than exhaustive search. The result shows that RC6 with more rounds is immune to the two kinds of cryptanalysis since the data-dependent cycle increases the diffusion immensely.