二维新混沌系统和伪随机数生成器的设计  

Design of 2-dimensional novel chaotic system and pseudo-random number generator

作　　者：张丽姣[1] 闵乐泉[1,2] 韩双霜[2,3] 

机构地区：[1]北京科技大学数理学院,北京100083 [2]北京科技大学自动化学院,北京100083 [3]武警北京指挥学院信息管理中心,北京100012

出　　处：《计算机工程与设计》2014年第4期1178-1182,1197,共6页Computer Engineering and Design

基　　金：国家自然科学基金项目(61074192;61170037)

摘　　要：为设计性能较好的伪随机数发生器,提出了一个满足修正的马罗驼(Marotto)定理的新二维离散混沌系统(2DCS)。利用离散广义混沌同步理论和2D-CS构造了一个广义同步混沌系统(2D-GCS);通过一个实数域到整数域的变换设计了一个混沌伪随机数生成器(CPRNG);利用美国联邦信息处理标准(federal information processing standards,FIPS)提出的FIPS 140-2检测包分别对CPRNG和RC4算法产生的1000个二进制序列的随机性进行检测,结果均通过了检测。检测结果的平均值和方差对比表明CPRNG和RC4算法产生的伪随机序列随机性能相当,相关性检测结果表明该CPRNG在不同的密钥扰动下产生的密钥各组序列几乎完全独立,设计的CPRNG能产生性能良好的伪随机数。To design a good performance pseudo-random number generator, a novel 2-dimensional discrete-time chaotic system （2D-CS） is introduced based on a modified Marotto＇s theorem for discrete-time chaotic systems. Combining the 2I）-CS with the theorem of generalized synchronization, a generalized chaos synchronization system （2D-GCS） is designed. By transforming the real number set to the integer set, a chaos-based pseudo-random number generator （CPRNG） is designed. Using the FIPS 140- 2 suite tests issued by the federal information processing standards （FIPS） to test the randomness of the 1000 binary number se- quences generated via the CPRNG and the RCA algorithm respectively, of which results have all passed the tests. The means and variances of the tested results show that the statistical properties of the randomness of the sequences generated via the CPRNG and the RCA have no significant differences. Correlation detections show that the CPRNG can produce almost independent key se- quence under different key disturbation. The CPRNG is able to generate sound random sequences.

关 键 词：修正的马罗驼定理 混沌系统 广义同步定理 伪随机数发生器 检测 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]