Chaos Control And Its Applications In Cryptography

Since the 1990s of 20th century, the idea of using chaotic systems to the secure communication has attracted more and more attention. The use of chaos in the secure communication depends on the natural connection between the two research areas. Some characteristic of chaos satisfies that of the secure communication. Whereas, the secure characteristic of the communication requires the secure system possesses the chaotic character. As for the application of chaos in secure communication, there are two different kinds. One is the chaotic secure communication based on the analog system( mainly based on the idea of the chaotic synchronization) The other is the chaotic cryptology based on the digital system.The chaotic system has nice characteristic of secure communication, such as randomness, the extreme sensitivity to the parameter and the initial value. Meanwhile, the chaotic system can be controlled. Thus, from the point of view of control theory, the H robust control for a class of linear singular systems with state and input delay is studied in this paper. And the adaptive observer for a class of chaotic system and the application of the chaotic system in digital system are discussed, too. Concretely, the content of this paper includes the following three aspects:1. In the normal study of local properties of dynamical systems, a nonlinear system is often linearized at one point, and studies its property at this point. Thus, the study of linear systems has high reference value to the nonlinear ones( a lot of problems are studied in this way ). In the prepare form of this article, the H robust control for a class of linear singular systems with state and input delay is discussed. In terms of the method of linear matrix inequalities, a sufficient condition is given which ensures that the system is regular, impulse free, stable, and satisfying H performance. Meanwhile, a necessary and sufficient condition to the robust stabilization systems is shown.2. For the chaotic synchronization, the nonlinear observer for adaptive synchronization of a class of special chaotic system is studied. By advising the estimate equation, the state of receiver is synchronizes to that of transmitter.3. In the field of applying the chaotic system to digital secure communication, the usualmethod is utilizing the extremely sensitivity of chaotic system to the parameter and the initial value to advise a new cryptological scheme. The idea of chaotic synchronization is seldom involved. In this paper, we advise a kind of chaotic scheme based on the chaotic synchronization that can be used to digital secure communization. Only transmitting the drive signal, the transmitted signal could be recovered at the receiver even if the initial values at receiver and transmitter are different.