Nonlinearity of Many-Valued Logic Component Functions of Modern Cryptographic Algorithms S-boxes

Abstract

Block symmetric cryptographic algorithms are the essential and inalienable element of any information security system. The main component of block symmetric cryptographic algorithms is the S-box, which largely determines the speed and cryptographic quality of the entire cryptographic transformation. The rapid development of cryptanalysis methods, including the development of quantum computers, requires a more careful research of all possible representations of nonlinear elements of block symmetric cryptographic algorithms. In view of the fact that in addition to the mathematical apparatus of Boolean functions used today to estimate the cryptographic quality of S-boxes, a cryptanalyst can apply the mathematical apparatus of functions of many-valued logic, which makes relevant the task of researching and comparing the cryptographic quality of S-boxes of modern cryptographic algorithms, represented by functions of many-valued logic. This paper presents a research and comparative analysis of nonlinear transformations of the cryptographic algorithms AES, Kalyna, BelT, and Kuznechik when represented by functions of many-valued logic. It was found that only the nonlinear transformation of the BelT cryptographic algorithm is characterized by growth when represented by many-valued logic functions, while the Kalyna cryptographic algorithm demonstrates the greatest decrease in nonlinearity when represented by 16-functions among the cryptographic algorithms researched. The results obtained in the paper indicate a significant unused reserve of cryptographic quality, which can be used in the design of new cryptographic algorithms and their structural elements.