Research of Digital Chaos Synchronization

在本研究中，我们研究了有限位长存储器的混沌调制解调器系统出现的各种问题，并探讨了防止混沌性质退化的措施。用实数表示混沌信号时，混沌信号可以表现出其原有的非周期随机性。然而，在实际工程应用中，特别是在数字系统中，数字通常用有限位数表示。用有限位数计算混沌时，会出现什么样的信号？一般来说，当混沌用有限位数表示时，它就变成了一个长周期信号（这被称为“伪混沌”）。这种伪混沌具有类似于一个周期内的混沌的性质，使得附近的轨道敏感地依赖于初始条件，并且自相关和互相关函数随时间趋于零。利用这些特性，我们可以通过同步伪混沌发送器和伪混沌接收器来实现具有一定安全性的混沌调制解调器系统。我们假设一个实用的16位数字信号处理器，在计算中，通过一定的方法将32位累加器压缩成16位。我们利用美国佛罗里达州立大学研究人员提出的Diehard检验方法来验证伪周期信号的随机性。结果，我们成功地获得了几个具有良好随机性的参数集。

In this research, we examine various problems which appear for the chaos modem system with finite bit length memory, and investigate measures to prevent degradation of chaotic nature. A chaos signal can show its original non-periodic random nature when it is expressed by a real number whose expression needs infinitely many digits. However, in practical engineering applications, in particular, for digital systems, a number is expressed naturally with finite digits. What kind of signal will appear when chaos is computed by finite digits? In general, when chaos is expressed by finite digits, it becomes a long periodic signal (this is called "pseudo chaos"). This pseudo chaos has properties similar to chaos within one period such that nearby orbits depend sensitively on initial conditions, and auto-correlation and cross-correlation functions tend to zero with time. From such properties we can realize a chaos modem system having some amount of security by synchronizing a pseudo chaotic transmitter and a pseudo chaotic receiver. We assume a practical 16 bit digital signal processor, and in the calculation, 32 bit accumulator is compressed into 16 bits via a certain method. We verify the randomness of the pseudo-periodic signal by using Diehard test which is proposed by a researcher in Florida State University. As a result, we have succeeded to obtain several parameter sets which have a good random nature.