基于直方图均化法的改进Logistic映射伪随机数发生器设计及性能研究

A Study of an Improved Pseudo Generator Design of Random Number and Performance on the Basis of a Logistic Map of Histogram Homogenization Method

Logistic映射伪随机数发生器(LM-PRNG)可用于生成均匀分布的伪随机数,但直接生成随机数的数据分布均匀性不佳.为此,文中根据LM-PRNG直接生成随机数数据分布的特性,设计了一种基于直方图优化法的改进Logistic伪随机数发生器(ILM-PRNG),并利用参数检验、均匀性检验及独立性检验分析了LM-PRNG和ILM-PRNG的性能.3种数据规模下的测试结果表明:在显著水平α=0.05下,LM-PRNG生成伪随机数序列的一阶矩在数据规模N=10~3和N=10~4时可以通过检验,在N=10~5时通过检验的比例为60%,其二阶矩、方差和均匀性在本次实验中均未通过检验,通过独立性检验的样本数占本次研究样本数的93.3%;ILM-PRNG生成的均匀分布伪随机数均通过参数检验、均匀性检验和独立性检验,其参数性与均匀性均随着生成数据规模的扩大而不断提高,独立性与数据规模的关系不大;ILM-PRNG可以克服LM-PRNG的不足,生成更良好的均匀分布伪随机数,是一种性能良好的新型伪随机数发生器.

The logistic map can be used to generate pseudo random numbers. However,the data generated directly cannot take on a good uniformity. Based on the characteristic of random numbers generated directly by the logistics map pseudo random generator（ LM-PRNG）, an improved pseudo random number generator（ ILM-PRNG） is designed based on a histogram homogenization method, and the performance of LM-PRNG and ILM-PRNG is researched by parameters tests,uniform test and unique test. At 0. 05 level,the results of three kinds of number scales show that the first moment of random numbers generated by LM-PRNG can pass the tests when N = 10^3,N =10^4 and 60% N = 10^5. The second moment,variance and uniform failed in the test. 93. 3% of the samples can pass the unique test. Meanwhile,random numbers generated by ILM-PRNG can pass all the tests in this research.The parameter and uniform characters are getting better with the numbers getting larger. As a new kind of PRNG,the ILM-PRNG can overcome the lack of the original logistic generator and can be used to generate uniform pseudo random numbers more satisfactorily.