Synthesis method for S-boxes satisfying the criterion of correlation immunity of Boolean and 4-functions

Abstract

The improvement of cryptanalysis methods, in particular, using the mathematical apparatus of many-valued logic functions, determines the need to create methods for the synthesis of cryptographic primitives, first of all, S-boxes that satisfy the criteria of cryptographic quality both in the sense of component Boolean functions, and in the sense of their possible representations by functions of many-valued logic. The most important criterion characterizing the ability of the S-box, and hence, of the entire cryptographic transformation in which it is used, to resist attacks of correlation cryptoanalysis, is the criterion of the correlation immunity of component functions. At the moment, there are no methods for the synthesis of S-boxes that satisfy the criterion of correlation immunity both in the sense of component Boolean functions and in the sense of component functions of many-valued logic, which complicates the further development of symmetric cryptographic algorithms, considering their possible representation using many-valued logic functions. In this paper, we propose a method for the synthesis of a full class of S-boxes of length N=16 corresponding to both the criterion of the correlation immunity of component Boolean functions and the criterion of the correlation immunity of component 4-functions. With the help of the developed method, it was possible to construct a set of 18 304 S-boxes that satisfies the criterion of correlation immunity both in the sense of component Boolean functions and in the sense of component 4-functions. The synthesized class of S-boxes can be used to increase the diffusion and confusion of modern symmetric cryptographic algorithms, as well as to increase their protection against promising cryptanalysis attacks based on many-valued logic functions.