将混沌序列变换成均匀伪随机序列的普适算法

A universal algorithm for transforming chaotic sequences into uniform pseudo-random sequences

提出了一种将混沌序列变换成均匀伪随机序列的普适算法.这种算法基于计算机浮点数表示的bit位操作,不针对任何具体对象,可将任意连续或分段连续分布的实型随机变量转换成均匀分布的随机变量.理论分析表明,这种算法源于实型随机变量中普遍存在着的沿bit位以指数规律增强的均匀化趋势.任何实型的混沌序列,不论来自混沌映射系统还是混沌微分动力系统,都可以在同一个标准算法下变换成均匀分布的伪随机序列,因而是混沌伪随机数发生器标准化模块设计和硬件实现的关键技术基础.

We present a universal algorithm for transforming chaotic sequences of either chaotic map systems or chaotic differential dynamic systems into uniform pseudo-random sequences. Theoretically, the algorithm is based on bit-operations represented by floating-point algorithm, not aiming at any definite physical chaotic systems. It has been proved that, any real random variable generally has a type of natural tendency of homogenization which exponentially increases bitwise with random variable. As a result,any real chaotic sequence can be completely transformed into the pseudo-random sequence having uniform identical independent distribution. Adopting logistic map,Hrnon map and Lorenz system as examples to test the universal validity of the algorithm, respectively, the experiments demonstrate that the algorithm is correct. We can reasonably expect that the universally valid algorithm should become the technological basis of standardized modular design of chaotic pseudo-random sequence generator in hardware implementation.