Abstract: In this paper, a class of quadratic polynomial chaotic maps topologically conjugating Tent mapping is established. These maps have three system parameters and their probability density functions are given. Then, according to the corresponding probability density function, an inverse sine function is designed. By means of the inverse sine function transformation, the random number generated by the quadratic polynomial chaotic maps is uniformly distributed in the interval（-0.5, 0.5）. Finally, a pseudo random number generator capable of generating{0, 2m-1} is designed by interval division. Theoretical analysis and experimental results show that the random sequence generated by the random number generator is sensitive to initial values, has good self-cross correlation properties and passes the NIST SP800-22 random number testing.

Key words: quadratic polynomial chaotic maps, probability density function, self /cross correlation properties, NIST SP800-22 testing

摘要： 构造了一类与Tent 映射拓扑共轭的二次多项式混沌映射，该二次多项式混沌映射具有三个系统参数，并给出了该类混沌映射的概率密度函数。根据对应的概率密度函数，设计了一个反正弦函数，通过反正弦函数变换，使二次多项式混沌映射生成的随机数在区间（－0.5，0.5）上服从均匀分布，利用区间划分的方法设计了一个能生成{0，2m－1}的伪随机数发生器。理论分析和实验结果表明该随机数发生器生成的随机序列具有较好的初值敏感性、自/互相关特性，并通过了NIST SP800-22 随机数检测。

关键词: 二次多项式混沌映射, 概率密度函数, 自/互相关特性, NIST SP800-22检测