Exponential sine chaotification model for enhancing chaos and its hardware implementation

Abstract

Chaotic systems have been intensively studied for their roles in many applications, such as cryptography, secure communications, nonlinear controls, etc. However, the limited complexity of existing chaotic systems weakens chaos-based practical applications. Designing chaotic maps with high complexity is attractive. This paper proposes the exponential sine chaotification model (ESCM), a method of using the exponential sine function as a nonlinear transform model, to enhance the complexity of chaotic maps. To verify the performance of the ESCM, we firstly demonstrated it through theoretical analysis. Then, to exhibit the high efficiency and usability of ESCM, we applied ESCM to one-dimensional (1D) and multi-dimensional (MD) chaotic systems. The effects were examined by the Lyapunov exponent and it was found that enhanced chaotic maps have much more complicated dynamic behaviors compared to their originals. To validate the simplicity of ESCM in hardware implementation, we simulated three enhanced chaotic maps using a digital signal processor (DSP). To explore the ESCM in practical application, we applied ESCM to image encryption. The results verified that the ESCM can make previous chaos maps competitive for usage in image encryption.