Optimization of The High Non-Linear S-boxes Generation Method

Abstract

n The known method of high non-linear S-boxes generation based on the gradient descent \cite{PhD_thesis} requires a consecutive application 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 computation power for S-box generation. The proposed modification allows
generation of a byte substitution with non-linearity 104, algebraic immunity 3 and 8-uniformity within approximately 10 minutes of a single PC running time.