Chaotification Control And Analysis Of Higher-Dimensional Dynamic Systems And Its Application In Image Encryption

Chaos theory is an important research branch of nonlinear dynamics.Chaos commonly exists in nonlinear systems,and it has high sensitivity to initial values,long-term unpredictability,and trajectory ergodicity.Compared to low-dimensional chaotic systems,the higher-dimensional hyperchaotic systems have more complex chaotic characteristics,and the hyperchaotic systems have been widely investigated and applied to the design of information encryption.The encryption algorithms have larger key space and excellent security based on higher-dimensional hyperchaotic systems.The main work of this paper is given as follows:A higher-dimensional hyperchaotic system with a maximum number of positive Lyapunov exponents is constructed.By designing asymptotically stable nominal linear systems and uniformly bounded controllers,a higher-dimensional hyperchaotic system with multiple control positions that can generate a maximum number of positive Lyapunov exponents is presented.At the same time,the multiple pseudo random sequences generated by the hyperchaotic system are preprocessed,and some pseudo random sequences are selected for multiple round scrambling encryption of the image,and the remaining pseudo random sequences are used for diffusion encryption of image pixels.Through numerical simulation experiments and security analysis,it is verified that the higher-dimensional hyperchaotic encryption algorithm combined with multiple pseudorandom sequences has good confidentiality and security,and can resist differential attacks,chosen-plaintext attacks,and cropping attacks.A combined control method with multiple controllers is proposed to design higher-dimensional hyperchaotic systems with a maximum number of positive Lyapunov exponents.At the same time,an information encryption algorithm with a scrambling sequential diffusion reverse diffusion structure is designed based on the hyperchaotic system,and simulation experiments verify the feasibility and effectiveness of the proposed algorithm.Through security analysis such as key sensitivity,differential analysis,and NIST testing,encryption algorithms based on higher-dimensional hyperchaotic systems have good security and sufficient key space to resist selective plaintext attacks,differential attacks,and so on.A chaotic method for higher-dimensional dynamic systems with non-smooth controllers is proposed,which combines the theory of chaotic systems anti-control to control higher-dimensional linear systems so that the controlled system can generate complex chaotic attractors.The stability of the equilibrium point of the controlled system is analyzed.The pseudo-random sequences generated by the new chaotic system are designed for chaotic secure communication,so that the chaotic pseudo-random sequences can pass NIST test.At the same time,based on the pseudo-random sequence generated by the chaotic system,an encryption algorithm combining block row scrambling,block column scrambling,and XOR diffusion in a "Z" shape is designed.The feasibility and effectiveness of this method are verified by the encryption of image information.Through numerical simulation experiments and algorithm security performance analysis,it is further demonstrated that the chaotic encryption algorithm has sufficient key space,can resist common attack methods,and enhances the security of information transmission.