Research On Image Encryption Algorithm Based On Hyper-chaotic And Multi-scroll Chaotic Systems

At present,research based on chaos has attracted more and more attention,and many aspects of real life also urgently need to use the unique properties of chaotic systems.Using various memristor models to improve existing chaotic systems can create chaotic systems with more complex dynamics.The randomness and unpredictability of chaotic systems are inseparable from cryptography.Image encryption algorithms based on chaotic sequences have higher security.First,by analyzing the definition and basic characteristics of chaos,a method for judging chaos is obtained,and the feasibility and superiority of digital image encryption algorithm based on chaotic systems are described.In the method of experimental simulation and numerical analysis,this thesis proposes a new hyper-chaotic system based on memristor and a multi-scroll chaotic system.In addition,basic numerical simulation and theoretical analysis were carried out on the two systems respectively.At the same time,a new digital image encryption algorithm was designed.The specific work content is as follows:(1)A new hyper-chaotic system is designed based on the flux-controlled memristor.This system has a simple structure and is easy to implement and exhibits rich dynamic behaviors.Afterwards,the chaotic characteristics of the system are analyzed through the system's balance point,Poincare maps,the Lyapunov exponents and other results.In addition,the circuit of the system is realized by the circuit software SPICE.The consistency of SPICE simulation and numerical analysis proves the feasibility of the system.Finally,an image encryption algorithm including two encryptions is designed.The classic three-dimensional Lorenz system is used for the first encryption,and the hyper-chaotic system is used for the second encryption,and use Matlab simulation software to numerically analyze the performance of the encryption algorithm.(2)A new three-dimensional chaotic system is designed based on the nonlinear term of the sine function,which can generate chaotic attractors with different scrolls.By setting different initial values,three-scroll,four-scroll and five-scroll attractors can be obtained respectively.The results of numerical simulations such as the Lyapunov exponents and power spectrum of the system prove that the multi-scroll chaotic system has the ability to generate chaos.In addition,the random sequence generated by the iterative system can pass all the items of the FIPS 140-2 random number test.Finally,a color image encryption algorithm is designed.This scheme mainly includes two steps of scrambling and diffusion,and can realize encryption for color images of different sizes.Using statistical methods such as histogram analysis and correlation analysis,the security of the encryption algorithm is verified.The application of chaotic systems with rich dynamics to digital image encryption algorithms has great research value in the field of information security.