| Nonlinear science is the frontier and hotspot of the world science,and chaos theory and applied research is an important branch of nonlinear science.Due to the extreme sensitivity of initial value and pseudo-randomness of chaotic system,it has great application of image encryption and secure communication.In particular,the conservative chaotic system has greater advantages in image encryption,which has attracted the investigation from domestic and foreign scholars.This paper explores the construction and analysis of conservative chaotic and dissipative systems,as well as their image encryption algorithms and hardware implementation.1.This paper proposes a four-dimensional conservative chaotic system and implements a five-dimensional conservative hyperchaotic system proposed by Wu.Dynamic analysis of these two conservative systems,including equilibrium stability analysis,Poincare mapping analysis and etc.On this basis,the circuit simulation experiment design and implementation of two conservative systems are conducted,and the simulation experiment results are consistent with the numerical analysis results.2.This paper also proposes a four-dimensional dissipative chaotic system.The dynamic characteristics of the system are analyzed from the aspects of initial value sensitivity,dissipation and symmetry,equilibrium point,Lyapunov exponent diagram and bifurcation diagram and Poincare mapping.The experimental results from the designed analog circuit system show that the simulation results are consistent with the numerical analysis,indicating the existence and realizability of the chaotic attractor of the system can be verified from the physical level.In addition,FPGA design and implementation of system and system synchronization with the same structure are also performed.The FPGA implementation results of the system are consistent with the circuit simulation results and numerical analysis results,and the FPGA implementation results of the system synchronization with the same structure are consistent with the theoretical derivation and numerical simulation,and further verify the hardware achievability of the chaotic system and chaotic system synchronization.3.Based on the theory of chaotic image encryption,this paper presents a chaos-based image encryption and decryption algorithm,including pixel-level scrambling and bit-level scrambling.Then the four-dimensional dissipative chaotic system is applied to the algorithm.And evaluate the performance of key space,adjacent pixel correlation,information entropy and so on.Furthermore,the proposed encryption algorithm is compared with another commonly used encryption algorithm.The analysis results show that the proposed algorithm given has outperformed in terms of security.Finally,the five-dimensional conservative hyperchaotic system is applied to the image encryption algorithm,and compared with the image encryption performance of a five-dimensional dissipative chaotic system.The results show that the image encryption algorithm of the conservative chaotic system is better than the dissipative chaotic system.4.Based on the previous mentioned work,this paper designs an FPGA-based chaotic image encryption system,designs the framework of the image encryption system and its various modules,and completes the data communication of each module,and then the algorithm proposed in this paper is encrypted and decrypted by FPGA development board.The FPGA experimental results show that the chaotic image encryption and decryption algorithm presented in this paper has hardware achievability.The work of this paper can provide a certain research basis for the implementation of FPGA hardware for conservative chaotic and dissipative systems and their image encryption. |
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