Research On A Novel Memory Resistive Chaotic System And Its Application In Image Encryption

Chaotic systems have characteristics such as initial value sensitivity,boundedness,ergodicity,and randomness,and can generate complex dynamic behaviors.In recent years,they have attracted extensive attention from scholars at home and abroad,becoming one of the important topics in the field of nonlinear research.As a nonlinear element with memory characteristics,memristors can be used to construct more complex and multistable chaotic systems,obtain chaotic signals with stronger chaotic and random characteristics,and correspondingly enhance the application value in fields such as image encryption and secure communication.In order to improve the security of image information transmission,it is necessary to design a more secure image encryption algorithm based on chaotic systems.In this thesis,a newly designed generalized memristor model is introduced into chaotic systems to obtain a new type of memristor chaotic system.Its complex dynamic behavior is studied,and its memristor chaotic circuit is built.Finally,a designed image encryption algorithm based on the new type of memristor chaotic system and DNA encryption is proposed.The specific work is as follows:(1)Based on the general memristor model,a new generalized memristor is designed,and a new type of fourth order memristor hyperchaotic system based on this generalized memristor is constructed,with adjustable parameters and easy to observe.The dynamic behavior of the system is studied.Firstly,by analyzing the dynamic characteristics of the system,such as dimensions,divergence,equilibrium points,stability,Poincare cross section,Lyapunov exponent,and power spectrum,it is found that the system has endless equilibrium points and is more complex and chaotic than the original system.Secondly,under the condition of varying parameters and initial values of the memristor,the newly emerging transient chaos and coexistence of multiple attractors in the system are studied through bifurcation characteristics and Lyapunov exponential spectrum.Finally,the circuit of the memristor chaotic system is designed to verify the feasibility of the system.The consistency between the circuit waveform and the system numerical simulation results is verified,laying a foundation for the practical application of the memristor chaotic system.(2)A newly designed memristor chaotic system is applied to image encryption,and an image encryption algorithm based on memristor chaotic system and DNA coding is proposed.Aiming at the problem of insufficient ability of image to resist differential attacks,an algorithm that combines hash functions,RSA encryption,and initial values of plaintext and memristor chaotic systems is proposed to enhance the ability to resist statistical attacks.Aiming at the strong correlation between pixels and the insufficient ability to resist statistical attacks,a multiple scrambling and diffusion algorithm combining Arnold scrambling,bit diffusion,and Zig Zag scrambling is proposed.Secondly,a new dynamic DNA coding rule and arithmetic rule combined with hash value is proposed to solve the problem of the simplicity of traditional DNA coding and arithmetic algorithms.Finally,through histogram,information entropy,key space,key sensitivity,plaintext sensitivity and other analysis methods,it is concluded that the algorithm has good security performance.