A Novel Approach for Designing Dynamical S-Boxes Using Hyperchaotic System

In the information security field, the substitution boxes (S-boxes) have been extensively used in many cryptographic systems. This paper presents a novel approach for generating dynamically cryptographically S-boxes using a four-dimensional hyperchaotic Lorenz system. Within the algorithm, the initial condition is employed to drive the hyper-chaotic system to generate a chaotic sequence which is used to construct a chaotic key-dependent S-box. With different system initial conditions, many of distinct S-boxes can be obtained dynamically. Some cryptographic properties for a good S-box such as bijection, nonlinearity, SAC (Strict Avalanche Criterion), BIC (Bit Independence Criterion), and differential approximation probability are found to hold in the obtained S-boxes. The analytic results indicated that all the criteria for designing strong S-boxes can be achieved. The comparison of the proposed method for generating S-boxes with other chaos-based schemes indicates that our S-boxes have a better performance with respect to some properties. Finally, the authors give an example of a digital image encryption algorithm using their S-box and the results of image statistical analysis show that the algorithm has the desirable cryptographic properties.