Design Of Chaotic System And Its Application In Image Encryption

Chaos is an important branch of nonlinear dynamic system,which has very complex dynamic behavior.In recent years,the study of chaos theory and its application research have become one of the frontier scientific research topics in current nonlinear science.Chaos systems have many similarities with encryption systems due to their initial value sensitivity,boundedness,ergodicity,pseudo-randomness,fractal dimension and other characteristics,so chaotic systems are widely used in the field of image encryption.The construction of new chaotic system and the application of chaotic image encryption algorithm have gradually become popular research topics.Based on the construction of chaotic systems,this paper designs two image encryption algorithms for color images,and evaluates their security performance.The specific work is as follows:(1)A four-dimensional chaotic system with dual memristors is designed using the loadcontrolled and generalized voltage-controlled memristor models,and the mathematical model of the system is established.It is found that the system has abundant dynamic behaviors and is very suitable for secure communication applications.The MULTISIM electronic circuit of the dual memristive chaotic system is realized by using integrated operational amplifiers and common electronic devices.The circuit experimental results are consistent with the numerical simulation results,which confirms the physical realizability of the system.(2)Combining the dual memristive four-dimensional chaotic system with Logistic mapping and dynamic DNA coding,a new block image encryption algorithm is proposed.The encoding and decoding methods of each sub-block and the DNA operation rules between subblocks are randomly determined by the chaotic sequence,which improves the complexity and security of the algorithm.The simulation results verify the effectiveness and efficiency of the image encryption scheme.(3)A new laser complex chaotic system is designed based on the four-dimensional laser real chaotic system model.The basic dynamics characteristics of the system are studied by the conventional dynamics analysis method and MATLAB simulation software,such as dissipation,equilibrium point,Lyapunov exponential spectrum,phase diagram and bifurcation diagram.The simulation results show that the system has rich dynamic behavior and has bow-tie chaotic attractor under certain parameters,which is very suitable for the field of chaotic encryption.(4)Based on the constructed seven-dimensional laser chaotic system,a new image encryption algorithm is designed.In the scrambling and diffusion stages,the improved Logistic map and fractional Fourier transform are introduced to broaden the selection range of keys.Simulation results show that the proposed algorithm has unique advantages in key space and key sensitivity,and has good randomness and security.