Nonlinear Theory In Information Security And Landscape Simulation

Non-linear theory can be divided into three parts: Chaos theory, Fractal theory and Soliton theory. The research of non-linear theory is more focus on theoretical analysis. Not only theoretical analysis but also chaotic security and fractal simulation are studied in this dissertation.The nature of the fixed points of the compound Logistic Map is researched and the boundary equation of the first bifurcation of this map in the parameter space is given out. Using the quantitative criterion and rule of chaotic system, this dissertation reveal the general features of the compound Logistic Map transforming from regularity to chaos, the following conclusions are shown: ?chaotic patterns of the map may emerge out of double-periodic bifurcation; ?the chaotic crisis phenomena and the reverse bifurcation are found in the compound Logistic Map. At the same time, we analyze the orbit of critical point of the compound Logistic Map and put forward the definition of Mandelbrot-Julia set of compound Logistic Map. We construct a series of Mandelbrot-Julia sets of compound Logistic Map. The symmetry of Mandelbrot-Julia set is investigated in this dissertation. The iterated function systems (it is called IFS for short) theory and the random iteration algorithm are expounded. By the theoretical analysis, the method by which the boundary of a class attractors of IFS using two affine maps can be evaluated is given out.The algorithm of determining the Lyapunov exponent and the correlation dimension of the attractors of IFS is introduced.Utilizing the computer simulated a class two dimensional, three dimensional attractors of IFS,the boundary, the Lyapunov exponent and correlation dimension of the attractors of IFS are calculated, and the dynamic characteristics of the attractors of IFS are analyzed.A searching based chaotic cryptographic algorithm using Logistic Map and He'non map is put forward in this dissertation. Using these arithmetics, all kinds of files (such as Txt, Bmp, Wav and so on) are encrypted and decrypted. The research indicates that the security of chaotic encryption arithmetic based on searching is intensified. A kind of known-plaintext attack method decrypting these algorithms is put forward in this dissertation. The security of the cryptographic algorithm is analysed and this dissertation presents a remedy to resist known-plaintext attack.This dissertation generalizes the theory of 2 dimensions Iterated Function System (IFS) to 3 dimensions IFS. Some nature scene based on the 3-D IFS model are put out in this dissertation.Based on the theory of color space and IFS, the author put forward the ΦΩΨ-IFS model (?respectively represent RGB , CMY, YIQ, HSV or HLS) and construct a series of 2 dimension and 3 dimension ΦΩΨIFS attractors (true color attractors) on the computer.