Analysis and implementation of no-equilibrium chaotic system with application in image encryption

摘要

The study of no-equilibrium chaotic system is one of the recent hot topics. This paper constructs a new no-equilibrium chaotic system by introducing an additional variable and a constant term to a three-dimensional chaotic system. Different from the previous no-equilibrium chaotic system, the new system has period-doubling bifurcation and performs hidden chaotic attractors for a large constant term. The analog circuit and field-programmable gate array (FPGA) implementation are given to illustrate the existence of the system. By utilizing the new system, a chaotic magic cube transformation image encryption algorithm (CMCT-IEA) is proposed, which has a classical permutation-diffusion structure. A new permutation method is designed to scramble image pixels in three-dimensional space, and a diffusion method is developed to diffuse small pixel changes of the original image to all pixels in three-dimensional space. A dynamic key is also designed to improve the security of the encryption algorithm. We also analyze the security of CMCT-IEA in terms of computational complexity, statistical properties, and the ability to defend against several common attacks. Compared with several advanced algorithms, the CMCT-IEA exhibits excellent security characteristics.