Analysis Of High Complexity Chaotic Dynamic System And Its Application In Cyberspace Security

Since the British mathematician Matthews introduced the concept of "chaotic code" in the late 1980 s,many studies have confirmed that chaos technology has great potential in cyberspace security.Due to the good statistical properties of chaotic systems,such as initial value-sensitive dependence,topological transitivity,aperiodicity and orbital density,the performance of encryption systems can be effectively improved.Therefore,the research based on chaotic system has attracted the attention of many researchers,especially the combination of image encryption and chaotic system is favored by many researchers.However,many of the existing chaotic systems have relatively narrow parameter space and cannot generate highly random and evenly distributed sequences,which may reduce the reliability of cryptosystems.Therefore,this paper constructs a new chaotic system model with good pseudo-random properties,and designs a new image encryption algorithm based on the chaotic model.Firstly,the periodic bifurcation points of a one-dimensional Sine cascade chaotic system are approximately derived by using Taylor’s expansion of sinusoidal mapping.The cascade can increase the fixed points of the system,and it is pointed out that the increase of the fixed points is the internal cause of the extremely complex chaotic system.The more fixed points,the higher the complexity of the system.On the contrary,the fewer fixed points,the lower the complexity of the system.Then,by using Lyapunov exponent,information entropy,sample entropy,spectral entropy and other methods,the dynamic performance of one-dimensional sinusoidal cascade chaotic system is studied.Secondly,in this paper,we proposed a novel framework for nonlinear dynamical systems that can generate extremely large Lyapunov exponents(LE>60),i.e.,onedimensional arcsine chaotic map(1-DACM)system.The system adopts the arcsine function and the cascade method to generate more complex attractor structures,which greatly improves the inherent complexity of the system.At the same time,the phase space structure of the cascaded chaotic system is perturbed by using the arcsine function as the nonlinear feedback function,so that the output state value of the system is evenly distributed in the whole phase space.The paper focuses on three nonlinear dynamical system properties using this structure.The performance analysis shows that the chaotic time series generated by the 1-DACM system has good aperiodic and uniform distribution characteristics on the basis of maintaining chaos,which meets the high requirements of cryptosystems.Finally,with the proposed chaotic system as the core,an image encryption algorithm based on position scrambling,cyclic pixel coding,pixel diffusion and N-fold cyclic structure is constructed.The key structure of the encryption algorithm is closely related to the plaintext,and then the relationship between each pixel is established through cyclic pixel coding.Therefore,the encryption algorithm has strong sensitivity and excellent resistance to differential attacks.The effectiveness and feasibility of the encryption scheme are verified through a large number of experiments,so the encryption scheme has a good application prospect.