A method for constructing dynamic S-boxes based on fractional transformation

Abstract

This article describes the method for constructing a dynamic S-box based on fractional transformation on a finite field. The article shows the conditions of S-box, such as S-box is bijective. After that, the article describes S-box properties: nonlinearity, linear approximation probability, differential approximation probability, and algebraic degree. The paper proves that some important cryptographic properties of S-box based on fractional transformation are independent of coefficients a,b,c, d. Based on this, we propose an encryption algorithm with a dynamic S-box.