A Novel 3D Chaotic System with Line Equilibrium: Multistability, Integral Sliding Mode Control, Electronic Circuit, FPGA Implementation and Its Image Encryption

Abstract

This paper announces a novel three-dimensional chaotic system with line equilibrium and discusses its dynamic properties such as Lyapunov exponents, phase portraits, equilibrium points, bifurcation diagram, multistability and coexisting attractors. New synchronization results based on integral sliding mode control (ISMC) are also derived for the new chaotic system with line equilibrium. In addition, an electronic circuit implementation of the new chaotic system with line equilibrium is reported and a good qualitative agreement is exhibited between the MATLAB simulations of the theoretical model and the MultiSim results. We also display the implementation of the Field-Programmable Gate Array (FPGA) based Pseudo-Random Number Generator (PRNG) by using the new chaotic system. The throughput of the proposed FPGA based new chaotic PRNG is 462.731 Mbps. Randomness analysis of the generated numbers has been performed with respect to the NIST-800-22 tests and they have successfully passed all of the tests. Finally, an image encryption algorithm based on the pixel-level scrambling, bit-level scrambling, and pixel value diffusion is proposed. The experimental results show that the encryption algorithm not only shuffles the pixel positions of the image, but also replaces the pixel values with different values, which can effectively resist various attacks such as brute force attack and differential attack.