Research On Generation Of Several Chaotic System And Its Application In Image Encryption

Nonlinear dynamics theory and method have been widely used in various engineering technologies,such as aerospace,machinery,transportation,chemical industry,electronics,and life sciences.Related research results not only explain many of the complex phenomena in practical engineering,but also provide theoretical guidance in solving many problems.As a branch of nonlinear dynamics,chaos reveals the unity of certainty and randomness,order and disorder,and simplicity and complexity in nature.In particular,the pseudo-randomness of chaotic sequences and their sensitivity to initial conditions provide new ways to encrypt digital images.The generation of chaotic systems and the encryption of the images are independent but interrelated research topics.These topics are of high interest in chaos research having important theoretical significance and practical value in applications.Given the practical requirements of chaos theory technology and engineering applications,this paper conducts an in-depth and detailed analysis of characteristics,then designs and analyzes several image encryption schemes based on the chaotic system.The main content and achievements are summarized as follows:(1)In order to obtain more complex dynamic characteristics,the hyperbolic chaotic systems are generated separately by the hyperbolic sine and hyperbolic cosine functions.First,the hyperbolic sine function and the absolute value function are used to construct the nonlinear term,and a third-order hyperbolic sinusoidal chaotic system is proposed by transforming the chaotic Jerk system.The Hopf bifurcation condition of the system at the equilibrium point is proved from theory.The basic dynamics,anti-monotonicity,basins of attraction,dynamics map,and period-doubling bifurcation are analyzed.Coexisting attractors controlled only by initial values are found.Then,a fourth order hyperbolic cosine chaotic system is generated by introducing linear feedback control and hyperbolic cosine function.The dynamic behavior of this system is analyzed.For the chaotic,periodic,and hyperchaotic systems,three kinds of coexisting hidden attractors are studied using the bifurcation and phase diagrams,The feasibility and complexity of the proposed system were verified by the numeric simulations,and the complex nonlinear systems can be widely used for image encryption.(2)Two piecewise linear chaotic systems are generated using chao anti-control method based on a linear system.First,the heteroclinic orbit is designed in accordance with the Shilnikov theorem,and a heteroclinic loop is constructed between its two equilibrium points generating a third-order piecewise linear chaotic system.The mechanism underlying the formation of the chaotic attractor is analyzed,and the existence conditions of the heteroclinic loop are proved.Then,a fifth order piecewise linear chaotic system is generated and its complex dynamic characteristics are analyzed using the step function to extend the equilibrium points of the system,thereby generating highdimensional grid multi-scroll chaotic attractors.(3)In order to enhance the unpredictability of the system,a chaotic system model is proposed based on the switching control of nonlinear systems.First,an asymmetric third-order chaotic subsystem is designed by transforming the chaotic Jerk system.Its basic dynamic behavior is analyzed,its anti-monotonicity is observed,and three full Feigenbaum remerging trees in series are observed,which is an especially rare phenomenon in autonomous systems.We then designed a switching plane,and combined the system with the hyperbolic sinusoidal chaotic system to synthesize a new nonlinear switching system.In studying the influence of the switching plane on system performance and analyzing the dynamic behavior and attractors production mechanism of the nonlinear switching system,multiple coexisting attractors are found.The simulation results verified the valisdty and unpredictability of the proposed system.(4)All of the chaotic systems constructed in this paper were realized physically.First,from ideas stemming from chaotic circuit modular design,a circuit structure was optimized based on circuit simulations,and a third-order piecewise linear chaotic system was simulated using the analog system.Then,the Euler method was used to discretize the chaotic system,using the SOPC technology to implement the switching-controlled chaotic system,the hyperbolic sine chaotic system,the hyperbolic cosine chaotic system,and the fifth-order piecewise linear chaotic system on the FPGA platform.The experimental results are entirely consistent with the simulation results,thus verifying the validity and feasibility of the constructed chaotic system.(5)In application of the constructed chaotic system to image encryption,we propose two image encryption schemes based on the chaotic system.First,the chaotic sequences are generated using the fifth-order multi-scroll chaotic system.A new image encryption algorithm based on the chaotic sequences is designed,which has the "scrambling and diffusion" structure,large information entropy and key space,simulation results verify the effectiveness and security of this algorithm.Then after designing an image encryption algorithm based on the S-box,we combined the five chaotic systems constructed in this paper with the S-box for image encryption,and compared the performances of the five encryption schemes and analyzed the causes of the differences in performance,it is verified that the complex chaotic system dynamics has a positive effect on image encryption.The simulation results show that all five algorithms are of good encryption effects and good anti-attack capability.