混沌同步理论及在密码学中的应用

【作者】 蔡敏；

【导师】 徐赐文； 朱正元；

【作者基本信息】 中央民族大学 ， 基础数学， 2007， 硕士

【摘要】 从上世纪90年代开始，混沌在保密通信中的应用受到了越来越多的关注，这是因为混沌与保密通信有着天然的联系，混沌动力系统的某些特性对应于保密通信中的安全特性，反之，保密通信中的安全特性又要求保密系统有相应的混沌特性。关于混沌在保密通信中的应用，一般而言，目前存在两种不同形式的模式：一种是基于模拟信号的混沌保密通信系统(主要是基于混沌同步的概念)；另一种是基于计算机数字通信的混沌加密系统。混沌系统有很好的保密通信特性，例如内在随机性、对初值和参数的极端敏感性等等。同时，混沌系统也是可以控制的，即混沌同步。本文共分四个章节，主要内容是：研究了一种新的混沌同步方法，并将该方法应用于混沌掩模保密通信，验证了其有效性和可行性。首先，介绍了混沌学的发展过程和意义，阐述了通信系统的一般要求和混沌在保密通信中的应用潜力，综述了国内外现有的混沌同步保密通信方法，其中包括：混沌掩盖、混沌切换，混沌调制等等。接着，对实现混沌同步的各种方法进行了深入的研究，Pecora—Carroll同步，因为该方法对有些系统是失效的，所以提出了实现混沌同步的另外一种驱动—响应同步，实现了Pecora—Carroll方法所不能实现的混沌同步；自适应同步，给出了自适应同步的定义，讨论了吕系统的自适应同步，并进一步讨论了未知参数的自适应同步；反馈同步，对Lorenz系统实现反馈同步须满足的条件进行了研究；耦合同步，讨论了单变量的耦合同步；并对各种同步方法进行了比较，给出了混沌同步的研究方向和发展前景。然后，在分析了现有混沌同步方法的特点后，提出了一种新的混沌同步方法，该方法具有以下优点：既可以实现同构混沌系统的同步，也可以实现异构混沌系统的同步，既可以应用于连续系统也可以应用于离散系统，同步时不需要考虑初始条件，也不需要计算条件Lyapunov指数。大量的仿真结果表明了该方法的有效性。最后，将这种新的混沌同步方法应用于混沌掩模保密通信系统中，进行了保密通信的仿真研究，大量仿真结果表明了该方法的有效性和可行性。更多还原

【Abstract】 Since the 1990s of 20^th century, the idea of using chaos 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, chaotic system can be controlled, Chaotic Synchronization.The article contains 4 parts. The main content is that we analyzed a new method of Synchronization, and this method is applied to chaos masking secure communication system.Firstly the development and significance of chaos are introduced. The general requirement of communication system and the application potential in secure communication are expatiated. The chaotic synchronization secure communication methods home and abroad arealso summarized, including: chaotic masking, chaotic switching, chaotic modulation, and so on.Secondly, we deeply discussed various chaos synchronization methods. The main results are （1） the methods to obtain synchronization: Pecora-Carroll synchronization, driving-response synchronization, feedback synchronization, self-adept synchronization and couple synchronization. We also introduce the way that chaos synchronization is put into use and point out some problems should be solved.Then the features of existing chaos synchronization methods are analyzed. A novel chaos synchronization methods is presented, which has the fellow advantages: synchronization can be realized for not only alike-structure chaos system but also different- structure chaos system, not only applying to continuous system but also to discrete system, it is not necessary to consider the initial conditions in synchronization, and no necessary to calculate conditionally Lyapunov exponent. A lot of simulation results indicate the effectiveness of the method.Finally the novel chaos synchronization method is then applied to chaos masking secure communication system and simulation is performed. Many simulations indicate the validity of the method.更多还原