Non-linear Theory And Application In Information Security

Non-linear theory contains three important parts: Fractal, Chaos and Soliton theory. They are theoretical foundation of non-linear theory.Based on non-linear theoretical analysis, the research has studied some chaotic and fractal problems and application in information security as follows:The paper develops Baker, Devaney and Romera's studies, constructs a series of generalized Mandelbrot-Julia sets, presents the theoretic proof in the exploration of the generalized J set for the complex exponent, theoretically analyzes the nature of symmetry and period of the generalized Mandelbrot-Julia sets.The nature of the fixed points of the coupled Logistic map is studied analytically, and the boundary equation of the first bifurcation of the map in the parameter space is derived. By phase plot, bifurcation plot, power spectra, Lyapunov exponent and fractal dimension, the paper reveals the general features of coupled Logistic map transforming from regularity to chaos.In this paper two kinds of watermarking algorithm is proposed.One is an image authentication algorithm based on feature of original image and hyperchaotic iteration, the other is a asymmetric digital watermark scheme using the robust character against geometric distortion of IFS. The experimental results show they are robust to noise adding, filtering, compression, rotation.Based on the theory of stability of the linear system, a strategy of the Rossler's chaotic system tracking control is presented. This strategy can track all kinds of reference signals. It is also proved that the strategy can make the system approach to any desired smooth orbit at an exponent rate. Numerical simulations have shown the proposed strategy is effective.This paper develops Peitgen, Pickover and Carlson's technique. A series of pseudo-3D generalized Mandelbrot-Julia sets are constructed. The paper studies the structure topological inflexibility and the fission of evolution law for pseudo-3D generalized Mandelbrot-Julia sets.Some studies have been published in Progress in Natural Science, Journal of Computer Researchand Development and Chinese Journal of Applied Mechanics.