Chaotic S-box: six-dimensional fractional Lorenz–Duffing chaotic system and O-shaped path scrambling

Abstract

This paper is concerned with designing a chaotic encryption system to generate the nonlinear component, substitution box (S-box), of a block cipher system. Many existing S-boxes generation methods employ a single or complicate chaotic systems to yield S-boxes. All of these chaotic systems are integral and have promoted the development of the theoretical research of chaotic S-boxes. However, it is difficult to implement the integral chaotic S-box generation systems that are appropriate for practical engineering applications. In this paper, a six-dimensional fractional Lorenz–Duffing chaotic system and O-shaped path scrambling algorithm (FLDSOP) is developed to yield an S-box with good dynamic characteristics. First, FLDSOP leverages a six-dimensional fractional Lorenz–Duffing chaotic system to construct a preliminary S-box. Second, it designs an O-Shaped path scrambling scheme to disturb the order of elements in the obtain S-box. Experimental results have shown that the chaotic S-box produced by the proposed FLDSOP algorithm can effectively resist to multiple types of cryptanalysis attacks.