| Many properties of chaotic systems, such as ergodic, mixing, deterministic features andsensitive dependence on initial conditions, are related to diffusion and confusion of cryptography, which satisfied the basic requirement of secure communication. Therefore, chaotic secure communication and its related research is a research focus in secure communication. Unpredictability, is one of the most important characters of chaotic systems, is also the basic requirement of the signals in the secure communication. The research on applying the unpredictable chaotic systems on secure communication, especially the methods of generating, testing and analysing the signals from unpredictable chaotic systems and construction of the relative secure communication systems, is very important.Cell model of chaotic attractor and periodic orbit theory enhanced the kownledge of chaos mechanisms and also give a new thinking of the reseach of chaos mechanisms, provide the theoretical foundmental of the engineering applications. The signals of chaos systems used in the chaos secure communication researches can be divided into two classes, simulation chaos and physical chaos. Most of the researches are based on simulation chaos. Simulation chaos refers to the chaos sequences generated from the discrete chaos mappings or the integral operation of continuous functions of chaotic systems. Its features are reproducible, noise-like, sensitive to initial conditions etc. Physical chaos refers to the real chaotic systems or chaotic circuits, which is considered to be the unpredictable chaotic systems. Generating signals using physical chaos and some related methods of testing and analyzing the signals are the key problems for applying physical chaos to secure communication, which are comparatively less studied. The dissertation also tries to construct a hardware circuit of the secure communication experiment platform using the unpredictable physical chaotic systems. The work has important theoretical interest and application prospects for the practical application of chaos theory.Firstly the dissertation introduces the basic theory of chaos, which ralted to the statistical test of unpredictability and its related theory. Then it focuses on several key issues about test and analysis of physical chaotic signals and design of secure communication systems using physical chaotic signals. The main contributions of the dissertation include: 1. Some simulation issues about the method to analysis some statistical properties of chaotic attractors based on the cell model of chaotic attractor are discussed. The simulation issues discussed include:time serial length, choice of the start point, distinction of direct motion and spiral motion, ε and simulation steps size, fundermental frequency and minimum distance of periodic orbits, etc. In-depth discussion of these statistical properties analysis method will be helpful for better understanding the structure of chaos attractor and chaos mechanism, which can help us better apply the theory to real systems and solve practical engineering problems.2. Generation and statistical test and analysis of unpredictable physical chaos random sequences are discussed. Random sequences which can be used in chaos encryption communication systems is generated by physical chaos. And the randomness properties of the random sequences generated by several typical physical chaotic systems, including Chua’s circuit, Lorenz system, Chen’s system, are analyzed using NIST(National Institute Standards and Technology)’s STS(standard test suite) randomness test suite. Five tests, which are the monobit test, the runs test, the discrete Fourier transform test, the approximate entropy test, the cumulative sums test, are performed to compare pseudorandom properties of those chaotic sequences. Experiment results show that the randomness properties of the sequences generated by physical chaos are better than by simulation chaos, and NIST’s STS randomness test suite is able to distinguish the randomness of different chaos sequences.3. Design a new S-box based on chua circuit. Linear attacks and differential attack can successfully crack the the DES cipher system. While the S-box in the DES encryption algorithm is the only nonlinear part is to resist linear cryptanalysis and differential attacks and is the core component for the DES algorithm. So we design a new S-box based on chua circuit.4. A novel scheme of chaotic synchronization encryption system is proposed.The experimental results show that the new system scheme can realize chaotic synchronization.Finally, the dissertation is concluded and future work is stated. |
