An efficient construction of S-box based on the fractional-order Rabinovich–Fabrikant chaotic system

Abstract

For many block encryption algorithms, confusion properties are only related to the substitution box (S-box). The S-box is a crucial component of cryptography. The security of the whole system is affected by the S-box. Consequently, alternative S-box designs and construction methods have been explored in various studies. In this paper, based on the chaotic Rabinovich–Fabrikant fractional order (FO) system, a new method for constructing a strong initial S-box is proposed. To comply with the objective, the numerical results of the FO chaotic Rabinovich–Fabrikant system are provided by using the four-step Runge Kutta method/Adams–Bashforth–Moulton method for a=0.87, b=1.1, and α=0.99. A novel key-based permutation technique is also presented to enhance the functionality of the initial S-box and construct the final S-box. A comparison is made between the performance of the substitution boxes (S-boxes) proposed and that of some other existing chaotic S-box designs. It is perceived that the S-boxes obtained by our proposed methods are stronger. The results of the analysis of the initial and final S-box yield favorable statistics, which make sure of its importance in the use of secure communications. Furthermore, the proposed final S-box’s effectiveness in image encryption applications is evaluated through the majority logic criterion (MLC), resulting in exceptional outcomes.