A method for generation of high-nonlinear S-boxes based on gradient descent

Criteria based on the analysis of the properties of vectorial Boolean functions for selection of substitutions (S-boxes) for symmetric cryptographic primitives are given. We propose an improved gradient descent method for increasing performance of nonlinear vectorial Boolean functions generation with optimal cryptographic properties. Substitutions generated by proposed method for the most common 8-bits input and output blocks have nonlinearity 104, $8$-uniformity and algebraic immunity 3.