基于m序列和球腔体的二维动态耦合映像格系统及其特性  

Two-dimensional Dynamic Coupled Mapping Lattice System Based on m-sequence and Spherical Cavity and Its Characteristics

作　　者：马英杰 田彦 赵耿 杨亚涛 覃晶滢 洪辉 MA Yingjie;TIAN Yan;ZHAO Geng;YANG Yatao;QIN Jingying;HONG Hui(Department of Electronic and Communication Engineering,Beijing Electronic Science and Technology Institute,Beijing 100070,China;Department of Cyberspace Security,Beijing Electronic Science and Technology Institute,Beijing 100070,China)

机构地区：[1]北京电子科技学院电子与通信工程系,北京100070 [2]北京电子科技学院网络空间安全系,北京100070

出　　处：《计算机科学》2025年第4期381-391,共11页Computer Science

基　　金：中央高校基本科研业务费(328202258,3282024060);国家自然科学基金(62441208)。

摘　　要：为解决现有时空混沌系统中动力学复杂性较低和生成序列之间相关度较高的问题,提出了一种基于m序列和球腔体的二维动态耦合映像格系统。利用改进的m序列来构建迭代矩阵,用于确定每个格点在迭代过程中耦合对象的索引和扰动符号,采用球腔体构造的分段混沌映射对混沌序列引入强度可控的扰动。通过分岔图、回归映射、Lyapunov指数和K熵评估系统的动力学特性,并对生成序列的相关性、均匀性、随机性以及系统的计算复杂度进行测试与验证。仿真实验与对比分析表明,该系统呈现出丰富的非线性动力学行为和优越的性能指标,包括周期倍增和分叉现象,在数据加密、图像加密和S盒生成领域具有潜在的应用前景。In order to solve the problems of low dynamic complexity and high correlation between generated sequences in existing spatiotemporal chaotic systems,two-dimensional dynamic coupled map lattices system based on m-sequences and spherical cavity is proposed.The improved m-sequence is used to construct an iterative matrix,which is used to determine the index and perturbation symbol of the coupled objects of each lattice in the iterative process.The piecewise chaotic mapping constructed through a spherical cavity introduces controllable perturbations to the chaotic sequence.The dynamic characteristics of the system are evalua-ted by bifurcation diagram,regression mapping,Lyapunov exponent and K-entropy,while the correlation,uniformity,random-ness of the generated sequence and the computational complexity of the system are tested and verified.Simulation experiments and comparative analysis show that the system exhibits rich nonlinear dynamical behavior and superior performance metrics,including period doubling and bifurcation phenomena,with potential applications in data encryption,image encryption,and S-box generation.

关 键 词：混沌系统 二维耦合映像格 M序列 动力学特性 球腔体 

分 类 号：TN918[电子电信—通信与信息系统]