Correlation Immunity of Many-Valued Logic Component Functions of Modern Cryptographic Algorithm S-Boxes

Abstract

The development of modern cryptanalysis methods, in particular, with the use of many-valued logic functions, leads to the need for a more detailed research of the correlation properties of Sboxes of modern cryptographic algorithms. In this paper, we introduce indicators for the maximum and integral deviation of a many-valued logic functions on the basis of criterion for the independence of its output from the input variables. These indicators are a convenient tool for comparative analysis of the correlation properties of S-boxes of various lengths when they are represented using the many-valued logic functions with different bases q. The research and comparative analysis of the S-boxes of the AES and Kalyna cryptographic algorithms was performed, which showed a general tendency of a decreasing of their correlation properties with an increase in the value of representation base q, and also made it possible to establish that for all values of the representation base q, the correlation properties of the Kalyna cryptographic algorithm S-box are weaker than the correlation properties of the AES cryptographic algorithm S-box.