Circuit Design Of Multistage Chaotic System And Its Application In Image Encryption

Chaos phenomenon is a random phenomenon in nonlinear system.Chaos characteristic is extremely sensitive to the initial conditions of the system.The results show that chaos not only has a very rich theoretical research basis,but also has a very close relationship with engineering problems,so it has a wide range of application prospects in many fields.The image encryption technology based on chaotic system is more secure than the traditional image encryption algorithm.Therefore,it is very important to construct chaotic systems that can produce more complex topologies.One of the ways to construct chaotic system with high complexity is to increase the order of chaotic system on the basis of original chaotic system.It is also possible to introduce appropriate piecewise function into the system equation and enrich the dynamic behavior of the system.With the development of chaos theory and its application,many digital image encryption algorithms based on chaos have been proposed by experts and scholars.This paper mainly studies the construction method of multi-order chaotic systems and the design of the simulation circuit of the constructed system,and applies these high order chaotic systems to the field of image encryption.The general work content is divided into the following parts:(1)Construct a new fifth-order Lorentz-like chaotic system and apply it to the field of image encryption.A new fifth-order chaotic system is constructed by adding a onedimensional linear controller to a fourth-order Lorentz-like chaotic system.By analyzing the bifurcation diagram,phase trajectory diagram and Lyapunov exponential spectrum of the fifth-order system,the chaotic characteristics of the system are verified.The circuit is simulated by Multisim software.The FPGA hardware realization part is added on the basis of the simulation circuit.This system has more complex dynamic characteristics than fourth-order Lorentz class systems,and can observe more abundant chaotic attractors than fourth-order chaotic systems,so it has more application value than fourth-order chaotic systems.(2)A new five-order multi-wing chaotic system is constructed: On the basis of a four-wing circuit,the system is modified to increase the number of wings.The chaos and dynamic phenomena of the system are analyzed by using dynamic analysis methods such as planar phase orbit diagram,Lyapunov exponential spectrum,0-1 test and system complexity.It is found that the fifth-order system has rich dynamic behavior,and when the system parameters change,The system has a number of different states of coexistence attractors.Then the integer function with cosine function is introduced to realize the wing number control of the multi-wing chaotic attractor.After introducing the function,the system only needs to change one parameter value to achieve the effect of controlling system wing number.The function can be introduced into different directions to change the direction of the system wing number.Then the circuit simulation part and FPGA hardware realization part are completed to verify the realization of the system.(3)The five-order eight-wing chaotic system is combined with scrambling algorithm and diffusion algorithm,and applied to the image encryption system.The encryption system includes a variety of encryption algorithms for image secondary encryption,including Arnold scrambling algorithm and no repeat scrambling algorithm.The diffusion algorithm includes the modulus diffusion algorithm based on GF(257)domain and the diffusion algorithm based on multiplication.After a series of analysis of the encryption performance of the system,such as image histogram,image entropy,key sensitivity and key space,it is proved that the encryption system has good security effect and has great application value in the field of image encryption.In conclusion,this paper has some reference value in the construction of high order chaotic systems,and a method to control the wing number of systems is proposed.It also provides a new idea for the application of high-order chaotic system in image encryption field.