混沌二进制序列的伪随机性和复杂性分析  

Analysis of pseudorandomness and complexity of chaotic binary sequences

作　　者：刘年生[1] 郭东辉[2] 

机构地区：[1]集美大学计算机工程学院,福建厦门361021 [2]厦门大学电子工程系,福建厦门361005

出　　处：《计算机工程与应用》2008年第2期16-19,共4页Computer Engineering and Applications

基　　金：国家自然科学基金(the National Natural Science Foundation of China under Grant No.60076015);福建省自然科学基金(the NaturalScience Foundation of Fujian Province of China under Grant No.A0640009);福建省青年创新项目(No.2005J034);福建省教育厅科技项目(No.JA05293);集美大学优秀青年骨干教师基金(No.2006B003) 。

摘　　要：分析和讨论了由经典的Lorenz混沌系统和Chebyshev映射所生成的二进制序列的伪随机性和复杂性,采用T.Kohda混沌二进制量化算法,将混沌系统所产生的实数序列转换为相应的二进制序列;从统计检验、自相关性、频谱、Lempel-Ziv复杂度和近似熵等多方面对序列的伪随机性和复杂性进行定量分析。统计分析结果表明对由混沌系统所产生的有限二进制序列逼近Lem-pel-Ziv意义的随机序列,它具有较高的伪随机性、复杂性和非周期性,但是序列的伪随机性和复杂性并不随序列长度的增加而提高,在近似熵评价指标中呈显出降低的趋势。同时,作为伪随机源,Lorenz混沌系统略比Chebyshev映射好。The pseudorandomness and complexity of binary sequences generated by typical Lorenz chaotic system and Chebyshev map are analyzed and discussed.The binary, sequences are obtained from the chaotic real-valued sequences generated by chaotic systems by using T.Kohda binary quantification algorithm.The statistical test,correlation function,speetral analysis,Lempel-Ziv complexity and approximate entropy are regarded as quantitative measures to characterize the pseudorandomness and complexity of binary＂ sequences.The experimental results show the finite binary＂ sequences generated by chaotic system approach the random sequences of Lempel-Ziv level.They are of good properties in the pseudorandomness,complexity and nonperlodicity.However,thelr pseudorandomness and complexity do not enhance with the sequence length increased,but degrade in the criterion of approximate entropy.Furthermore,the results of data statistics analysis show that the Lorenz system is better than Chebyshev map as the source of pseudorandomness.

关 键 词：混沌系统 有限二进制序列 序列伪随机性 序列复杂性 

分 类 号：TP301.5[自动化与计算机技术—计算机系统结构] TP309.2[自动化与计算机技术—计算机科学与技术]