一种整数混沌映射的伪随机数生成器  

A Pseudo-Random Number Generator for Integer Chaotic Map

作　　者：王永[1,2] 龚建[1] 王明月 江功坤 WANG Yong;GONG Jian;WANG Mingyue;JIANG Gongkun(College of Computer Science and Technology,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;Guangxi Key Laboratory of Cryptography and Information Security,Guilin University of Electronic Technology,Guilin 541004,China)

机构地区：[1]重庆邮电大学计算机科学与技术学院,重庆400065 [2]桂林电子科技大学,广西密码学与信息安全重点实验室,桂林541004

出　　处：《北京邮电大学学报》2022年第1期58-62,共5页Journal of Beijing University of Posts and Telecommunications

基　　金：国家自然科学基金项目(71901045);重庆市自然科学基金项目(cstc2021jcyj-msxmX0557);广西密码学与信息安全重点实验室基金项目(GCIS201908)。

摘　　要：为了改善浮点数混沌系统在迭代中状态值精度丢失导致的安全性问题,对分段Logistic映射进行了整数化处理,提出整数化的分段Logistic。利用有限精度下暂态数据具有更好均匀性的特点,重新定义了该整数化的乘法运算,使得输出的状态值具有更均匀分布的概率密度并且保证了其安全性。在此基础上,提出了一种伪随机数生成器算法。该算法结合一维元胞自动机和S盒的替换机制,降低了状态值间耦合性、提高了算法的复杂性。性能分析和仿真实验表明,所提算法采用的整数混沌映射拥有均匀的概率密度分布和复杂的动力学行为,产生的伪随机序列具有复杂性高、安全性好和效率高等特点,在数据安全领域有很好的应用前景。To mitigate the safety issue caused by the loss of precision of the state value of the floating-point number during the iteration, an integer piecewise Logistic map is proposed by integer processing. The proposed method redefines the multiplication operation of the integer utilizing the uniformity of transient data in the finite precision, which makes the output state values of the model having more uniform distribution probability density and ensure its security. Furthermore, a pseudo-random number generator algorithm is proposed. The proposed algorithm combines the one-dimensional cellular automata with the S-box substitution mechanism, which reduces the coupling between state values and improves the complexity of the algorithm. Performance analysis and simulation experimental results show that the integer chaotic map used in the scheme has uniform probability density distribution and complex dynamic behavior, and the pseudo-random sequences generated by the proposed scheme has high complexity, strong security, and good efficiency. Therefore, the proposed scheme has good application prospects in the field of data security.

关 键 词：整数混沌系统 分段Logistic映射 伪随机数生成器 数据安全 

分 类 号：TP391.1[自动化与计算机技术—计算机应用技术]