<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The known method of high nonlinear S-boxes generation based on the gradient descent [Kazymyrov, O. V.: Methods and Techniques of Generation of Nonlinear Substitutions for Symmetric Encryption Algorithms. The thesis for the scholarly degree of candidate of technical sciences, speciality 05.13.21 - - Information security systems, Kharkiv National University of Radioelectronics, Kharkiv, 2014. (In Russian)] requires consecutive applications of several criteria for each formed substitution. This paper presents an improvement of the considered method by the appropriate selection of the criteria application order which decreases the required computational power for S-box generation. The proposed modification allows generation of a byte substitution with nonlinearity 104, algebraic immunity 3 and 8-uniformity within approximately 30 minutes of a single PC running time.</p></abstract>

The known method of high nonlinear S-boxes generation based on the gradient descent [Kazymyrov, O. V.: Methods and Techniques of Generation of Nonlinear Substitutions for Symmetric Encryption Algorithms. The thesis for the scholarly degree of candidate of technical sciences, speciality 05.13.21 - - Information security systems, Kharkiv National University of Radioelectronics, Kharkiv, 2014. (In Russian)] requires consecutive applications of several criteria for each formed substitution. This paper presents an improvement of the considered method by the appropriate selection of the criteria application order which decreases the required computational power for S-box generation. The proposed modification allows generation of a byte substitution with nonlinearity 104, algebraic immunity 3 and 8-uniformity within approximately 30 minutes of a single PC running time.

Optimization of the High Nonlinear S-Boxes Generation Method

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Optimization of the High Nonlinear S-Boxes Generation Method"}

The known method of high nonlinear S-boxes generation based on the gradient descent [Kazymyrov, O. V.: Methods and Techniques of Generation of Nonlinear...

Optimization of the High Nonlinear S-Boxes Generation Method

Published Online: Mar 23, 2018

Page range: 93 - 105

Received: Jul 30, 2015

DOI: https://doi.org/10.1515/tmmp-2017-0020

Keywords
S-box, nonlinearity, algebraic immunity, vectorial Boolean function

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Optimization of the High Nonlinear S-Boxes Generation Method

Published Online: Mar 23, 2018

Page range: 93 - 105

Received: Jul 30, 2015

DOI: https://doi.org/10.1515/tmmp-2017-0020

KeywordsS-box, nonlinearity, algebraic immunity, vectorial Boolean function

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
S-box, nonlinearity, algebraic immunity, vectorial Boolean function