Sokolov A. Synthesis methods of nonlinear multi-byte substitutions for modern ciphers efficiency improvement

Thesis is devoted to the development of methods of synthesis of the non-linear permutations according to the highest standards of cryptographic quality in order to improve the efficiency of modern cryptographic algorithms. In order to create the S-boxes with high quality based on perfect algebraic structures we developed methods of synthesis of complete classes of bent sequences, de Bruijn sequences, and linear recurring sequences of great length on the basis of all isomorphic representations of Galois fields. On the basis of synthesized advanced algebraic structures we built cryptographic S-boxes having a high degree of cryptographic quality: high nonlinearity, the minimum correlation between output and input vectors, respondent to the criteria of distribution, with long periods of return to initial state, and other attractive cryptographic properties. The developed methods allow the synthesis of any length of S-box that can be realized by modern computing devices. Based on de Bruijn sequences we synthesized economical S-boxes that significantly reduced hardware and software implementation and compliance to the basic criteria of the cryptographic quality. It is shown that on the basis of perfect algebraic structures pseudo-random key sequences generators can also be synthesized have not only higher cryptographic and stochastic quality but also allow a faster implementation, which was demonstrated in the process of mathematical modeling.