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

Bakunina, E. V.; Dykyi, O. V.

doi:10.1080/09720529.2021.2018112

Open Access Research Article

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

^*E. V. BakuninaCorresponding authorelenabakunina72@gmail.comDepartment of Cybersecurity National University “Odessa Law Academy”Odessa, Richelievskaya st., 28, 65011, UkraineView full profile → , O. V. DykyiDepartment of Cybersecurity National University “Odessa Law Academy”Odessa, Richelievskaya st., 28, 65011, UkraineView full profile →

* Corresponding author · click or hover a name for details

pp. 1121–1133Vol. 26Issue 4June 2023DOI: 10.1080/09720529.2021.2018112 Crossmark XML

Received:: 01 Jun 2021
Accepted:: 01 Nov 2021
Published Online:: 29 Mar 2022
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1532
Pages:: 1121–1133

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.

Keywords

Cryptography S-box Correlation immunity Many-valued logic function

Subject Classifications

Classification: (2010) 94A60

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