一个新五维超混沌电路及其在保密通讯中应用

A New Five Dimensional Hyper-Chaotic Circuit and Its Application in Secure Communication

摘要: 超混沌系统比普通混沌系统的动态行为更加难以预测，因此在保密通讯中具有更重要的应用价值。本文在Chen混沌系统中引入两个状态变量和一个反向控制器构造了一个新的五维超混沌系统。首先讨论了新系统的定点稳定性及其相空间动力学行为，发现新系统有3个正的Lyapunov指数。设计了该系统的模块化电路，示波器观测结果与数值模拟结果一致。其次采用驱动响应式同步方式实现了新系统的混沌同步，并数值模拟了方波信号的混沌保密通讯过程，利用混沌掩盖法完成了新系统方波信号的混沌保密通讯电路。最后，分别采用混沌信号加入到图片中和图片数字化加入到混沌信号中两种不同的方式实现图片的混沌保密通讯过程。对比研究表明后者的加密效果更好，具有更高的信息还原度。

Abstract: The dynamic behavior of a hyper-chaotic system is much more difficult to be predicted than that of a normal chaos system. Therefore, it becomes very useful in the secure communication. This paper constructed a new five dimensional hyper-chaotic circuit based on Chen system when the two state variables and an inverse controller are introduced. First, the stability of the fixed points and dynamic behavior of the phase space of the new system are discussed, and three positive Lyapunov exponents are found. Modular circuit of the system is designed. The results of circuit simulation are in agreement with the numerical simulation. Then chaos synchronism of the system is achieved with drive-response synchronization method. Numerical simulation of the secure communication process for the square wave signal is given, and chaotic masking method is used to realize the secure communication circuit with square wave voltage signal of the system. Finally, two ways to deal with secure communication are discussed; one is the chaotic signal mixed with the image, and the other is chaotic signal added to the digital image. It is shown that the latter is better than the former in the effect on secure communication, and is more suitable for information reversion.