Improvement of the method for optimal s-boxes generation

Abstract

The known method of high nonlinear S-boxes generation based on the gradient descent requires a consecutive application of several criteria for each formed substitution. This paper presents 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 nonlinearity 104, algebraic immunity 3 and 8-uniformity within approximately 30 minutes of a single PC running time.