Design Of Novel Discrete Chaotic System And Its Applications In Image Encryption And Digital Watermarking

The design and applications of discrete chaotic maps are one of the research hotspots in the field of chaos.Through theoretical analysis and numerical simulation,this paper studies the construction method of the new discrete chaotic map model and applies the novel discrete chaotic map to image encryption and digital watermarking algorithm,which has important theoretical significance and engineering value.The novel discrete chaotic maps are proposed in this paper.Firstly,the general voltagecontrolled discrete memristor model was derived from the circuit perspective,and new types of discrete memristors were constructed.Then,the new type of discrete memristor was introduced into the typical discrete chaotic map.The discrete memristor-based Chebyshev map,the discrete memristor-based Logistic map,the discrete memristor-based Henon map and the discrete memristor-based Ikeda map are constructed.For another,based on the method of coupling and dimension expansion,improve the typical discrete chaotic maps.And the three-dimensional discrete map based on Sine map and the three-dimensional Henon map are proposed.Finally,the system characteristics of the novel chaotic maps were analyzed from the aspects of trajectory diagram,complexity,Lyapunov exponent spectrum and bifurcation diagram.The experimental results show that the novel discrete chaotic maps have complex dynamic behavior,large complexity and good uniform distribution characteristics,which lays the model foundation for the application of chaotic cryptography.As the applications of discrete chaotic map,this paper proposed two novel image encryption algorithms and a zero-watermarking algorithm.In the image encryption algorithms,the novel scrambling algorithms are designed to improve the security of encryption.And using wavelet transform,only low-frequency coefficients are operated,improving the efficiency of the algorithm.The simulation results show that the encryption algorithm in this paper has security,efficiency and anti-attack,and has broad application prospects in image security.In the design of zero-watermark algorithm,Shearlet transform,discrete cosine transform and Hu moments are used to construct the feature matrix.The watermark image is encrypted before constructing zero watermark to ensure security.Simulation experimental results show that the algorithm not only has perfect invisibility,but also can resist attacks and combined attacks.It has a good application prospect in digital watermarking.