Design And Application Of Random Sequence Generator Based On Chaotic Systems

In modern engineering practice, random sequence (RS) has been widely applied in many fields such as information security, digital communication, radar, cryptography, automation, acoustical measurement, optical measurement and fault detection in digital network system. With the fast development of information technology, random sequence generators (RSGs) have been required more. How to generate RS featuring high quality and performance has been a pop research which arrests world wide attentions of institutions and scholars.Chaos is a complex motion which limits to finite region all along and generates non-repeated trajectories in nonlinear dynamic systems. Due to the properties of chaotic system such as extreme sensitive dependence on their initial conditions and control parameters, wide frequency spectrum and noise-like, it provides a good research model for generating high-performance RS. In this dissertation, RSGs are designed based on chaotic system and analyzed comprehensively. The main research contents are mentioned as follows:1. The methods of generating RS and developing process are generalized. The merits and drawbacks of common methods are analyzed simply. Then the basic concepts of chaos are introduced. It indicates that chaotic systems are natural high-performance research models of RSGs by analyzing the relation and distinguish between chaotic sequence and RS.2. Simple one-dimensional Logistic chaotic map is analyzed theoretically. Aiming at its drawbacks such as few keys, unsafety, attacked easily, a method of generating random binary sequence based on a couple of Logistic map models is presented. It's shown that the method can generate high-performance RS by analyzing random performance. The digital hardware of the RSG on programmable arrays FPGA is designed with VHDL. It has the advantages of simplification, convenience, stabilization, reliability and high speed. At last the RSG is used in binary image encryption. And the safety is simply analyzed.3. The time-frequency characteristic of the output sequence produced by complex three-dimensional continuous Chen's chaotic system is analyzed in detail. Aiming at its inherent limitations in time and frequency domains, the disposals and improvements on algorithm are given. Moreover, the algorithm overcomes the problem of finite precision and can generate high-quality RS. The digital hardware of the RSG based on Chen's system on FPGA is designed with System Generator software which is a new design tool produced by Xilinx Company. The software has the advantages of great reduction of system's developing time, flexible design, easy and convenient operation, stabilization and reliability. Take image encryption for example, the RS has the advantages of having a large space of the key, security enough and strong resistance to estimation, which can be validated by analyzing security performance.4. Hyperchaos has extraordinarily complex dynamic behavior and good randomness because it has at least two positive Lyapunov exponents. Hence it has promising future in designing RSG. However, through analyzing time-frequency characteristic, hyperchaotic L u system also has some limitations in time and frequency domains. Its sequence can't substitute for RS directly. In order to overcome this defect, a novel RSG design based on two chaotic systems—hyperchaotic Lu system and Logistic map is presented. The RS generated by the RSG can be used to substitute for white noise because it has wide frequency spectrum. At last the RSG is applied into the analysis of system characteristic.