CRYPTOGRAPHIC PROPERTIES OF S-BOXES CONSTRUCTED BASED ON DYNAMIC CHAOS THEORY WHEN REPRESENTED USING MANY-VALUED LOGIC FUNCTIONS

The S-box is the main cryptographic construction, which largely determines the effectiveness of block symmetric ciphers and hash functions. Several basic requirements are imposed on modern S-boxes based on such criteria of cryptographic quality as distance of nonlinearity, error propagation criterion, and absence of a correlation between the output and input vectors. The theory of dynamic chaos is one of the promising tools for the synthesis of S-boxes, which highly correspond to the specified criteria of cryptographic quality. However, the further development of cryptography and cryptanalysis methods led to the development of new attacks based on the representation of the ciphers using many-valued logic functions, which makes it necessary to research the cryptographic quality of S-boxes not only when they are represented by component Boolean functions, but also for all their possible representations with help of the many-valued logic functions. In this paper, we present the results of the research on modern structures of S-boxes based on the theory of dynamic chaos when they are represented by many-valued logic functions. We distinguished the S-box construction characterized by the highest level of cryptographic quality for all its possible representations, which can be recommended for practical use.