МЕТОД СИНТЕЗУ ВИСОКОЯКІСНИХ S-БЛОКІВ НА ОСНОВІ ФУНКЦІЙ БАГАТОЗНАЧНОЇ ЛОГІКИ.

The cryptographic S-box is the crucial component of modern ciphers which determines their efficiency, cryptographic security, and performance. Today, the development of quantum cryptanalysis, as well as the appearance of possible attacks on cryptographic algorithms by describing them using many-valued logic functions made urgent the task of developing algorithms for the synthesis of S-boxes, which would be characterized by high quality not only when represented by component Boolean functions, but also with any other representation by component functions of many-valued logic. At the same time, most of the existing methods of synthesis of S-boxes presented in the literature are focused only on the research of their cryptographic quality when represented by component Boolean functions. In this paper, on the basis of S-boxes of length N=16, which corresponds to the strict avalanche criterion of component Boolean and 4- functions, we propose a method for synthesis of a set of high cardinality equal to J=117588 of S-boxes of practically valuable length N=256, which simultaneously corresponds the strict avalanche criterion of component Boolean functions, the strict avalanche criterion of component 4-functions, as well as the criterion of correlation immunity of component Boolean functions, i.e., they have ideal matrices of correlation coefficients between output and input vectors. The high cryptographic quality of the developed S-boxes when they are represented by component Boolean and 4-functions makes it possible to recommend them for practical use both in the tasks of increasing the effectiveness of existing cryptographic algorithms and in the development of promising ciphers, while the cardinality of the class of synthesized S-boxes allows them to be used as a long-term key. [ABSTRACT FROM AUTHOR]