| Internet communication has become the main means of daily communication for people gradually with the rapid development of network technology,so the issue of information security becomes more and more important.As a way of information carrier,images have the inherent characteristics of large data volume and strong correlation,and the use of general data encryption standard(DES),advanced encryption standard(AES)and RSA encryption algorithm can not meet the security requirements of image encryption.In contrast,chaotic systems are used in image encryption algorithms widely for their high sensitivity to initial values,unpredictability,acyclicity,and random-like properties.Therefore,the study of digital image encryption algorithms is of great practical importance.The specific research in this paper is as follows:1.A new four-dimensional memristor system is constructed on the basis of the memristor circuit,and it is found that the system has an equilibrium point line composed of infinite equilibrium points by analyzing its equilibrium points,so its attractors belong to the category of hidden attractors.Based on Lyapunov stability theory,different synchronization error systems are constructed and suitable controllers are designed to realize different synchronization methods,such as complete synchronization,inverse synchronization,misaligned generalized projection synchronization and uniform generalized projection synchronization,etc.,and their effectiveness is verified by MATLAB numerical simulations.2.The dynamics of the above four-dimensional memristor system is investigated in depth in terms of phase diagram,bifurcation diagram,Lyapunov exponential spectrum and complexity.It is found that the memristor system exhibits a chaotic state over a wide range of parameters,indicating that the chaotic system is more random and thus more beneficial for application in chaotic digital image encryption.In order to verify the application of this system in image encryption algorithm,the image encryption algorithm in GF(257)domain is proposed.Firstly,the chaotic sequences generated by the amnestic chaotic system are used to disarrange the plaintext images in combination with the one-dimensional vectorless repetition disarrangement algorithm.Then the GF(257)algorithm is used to diffuse the scrambled image to obtain the encrypted image.Finally,the analysis of information entropy,key space,histogram,correlation,key sensitivity and noise attack verifies that the proposed encryption algorithm can effectively encrypt the image and has high security performance.3.Usually,the signal propagation is non-instantaneous,and the introduction of time lag can reflect the real state more realistically.Here,the existence and stability of Hopf bifurcation in time-lag systems are explored by using the central manifold theorem,and the corresponding numerical simulation results are presented.In addition,to facilitate the comparison of the effect of time lag on the encryption results,the same encryption algorithm as that of the amnestic chaotic system is still used,and the designed encryption scheme is thoroughly tested for security by information entropy,key space,histogram,correlation,key sensitivity,and noise attack analysis. |
