S-box. Block Cipher Design And Safety Analysis

Modern cryptological theory and cryptological technology are important basis of information security. Block cipher is an important branch of cryptology, it has many attractive features such as high rates, easy for standardization, and efficient for both software and hardware implementations. Block ciphers are usually core components in information and Internet security for data encryption, data signature, authentication and key management. S-boxes are the only nonlinear components in many block ciphers. So, their cryptographic properties have determined the security of the whole cipher algorithms. Concentrating on design and security analysis of S-boxes, three principal achievements have been obtained in this thesis.1. First, the construction mechanism of S-box in Rijndael Algorithm was analyzed and the way of transforming generating matrix of S-box to generating polynomial was discussed in this thesis. Then the affine permutation in the process of S-box construction was combined with an inverse mapping in order to construct all kinds of S-boxes, such as 8×8,4×4,6×6 and m×n S-boxes, and the avalanche probabilities of these S-boxes were analyzed in the light of variance, and some rules were obtained from the analysis, which will help to find safer S-boxes. Two methods for constructing m×n S-boxes were proposed in this paper. The results of our experiments indicated that the cryptographic properties of our 6×4 S-boxes constructed with the method used in constructing AES S-box were better than the S-boxes of DES and the ones after evolution. Meanwhile, a large number of m×n S-boxes with good cryptographic properties have been constructed with the methods. The construction and analysis of all kinds of S-boxes are good for further search of S-boxes and these S-boxes provide abundant nonlinear resources for the further design of symmetric cryptographic algorithms.2. After the construction of 8×8 S-boxes satisfying some good cryptographic properties, the ByteSub step in Rijndael algorithm was improved based on the dynamical selection of S-boxes depending on round keys. The improved algorithm has been proved from an example to have stronger ability to resist differential attack. Meanwhile, there was hardly any decrease in the running efficiency of the improved algorithm. Finally, the security comparison of the two algorithms was made from the view of avalanche probability under the conditions that both the key length and block length are 128bits.3. The construction of S-boxes based on genetic algorithm is discussed in this thesis, including heuristic mutation strategy, this mutation operation can both prevent destruction of good gene and guarantee diversity of individuals in the population. Results of the experiments showed that this mutation operation has high searching efficiency and fast convergence speed. Under this method, an effective genetic algorithm for 6×6 S-boxes was provided and a number of S-boxes with high nonlinearity and low difference uniformity could be obtained.