计算机科学

计算机科学 ›› 2025, Vol. 52 ›› Issue (4): 381-391.doi: 10.11896/jsjkx.240100008

• 信息安全 • 上一篇    

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

马英杰1, 田彦2, 赵耿2, 杨亚涛1, 覃晶滢1, 洪辉2   

  1. 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
  • 收稿日期:2024-01-02 修回日期:2024-05-23 出版日期:2025-04-15 发布日期:2025-04-14
  • 通讯作者: 田彦(ty19991103@163.com)
  • 作者简介:(myj@besti.edu.cn)
  • 基金资助:
    中央高校基本科研业务费(328202258,3282024060);国家自然科学基金(62441208)

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

MA Yingjie1, TIAN Yan2, ZHAO Geng2, YANG Yatao1, QIN Jingying1, HONG Hui2   

  1. 1 Department of Electronic and Communication Engineering,Beijing Electronic Science and Technology Institute,Beijing 100070,China
    2 Department of Cyberspace Security,Beijing Electronic Science and Technology Institute,Beijing 100070,China
  • Received:2024-01-02 Revised:2024-05-23 Online:2025-04-15 Published:2025-04-14
  • About author:MA Yingjie,born in 1979,Ph.D.Her main research interests include communication system and chaotic secure communication.
    TIAN Yan,born in 1999,postgraduate.His main research interests include secure communication and chaotic block cipher.
  • Supported by:
    Fundamental Research Funds for the Central Universities(328202258,3282023054) and National Natural Science Foundation of China(62441208).

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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。

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

Abstract: 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.

Key words: Chaotic system, Two-dimensional coupled map lattices, m-sequence, Dynamic characteristics, Spherical cavity

中图分类号: 

  • TN918
[1]ZHENG J,HU H P.A highly secure stream cipher based onanalog-digital hybrid chaotic system[J].Information Sciences,2022,587:226-246.
[2]PENG J J,ZHU C X,JIANG D H.A new 2D-ASC chaotic system and its image encryption applications[J].Modern Physics Letters B,2023,37(10):2350009.
[3]QIN M H,LAI Q.Extreme multistability and amplitude modulation in memristive chaotic system and application to image encryption[J].Optik,2023,272:170407.
[4]ZHOU Z Q,XU X M,YAO Y X,et al.Novel multiple-image encryption algorithm based on a two-dimensional hyperchaotic modular model[J].Chaos,Solitons & Fractals,2023,173:113630.
[5]ZHOU S,QIU Y Y,QI G Y,et al.A new conservative chaotic system and its application in image encryption[J].Chaos,Solitons & Fractals,2023,175:113909.
[6]WANG Y,MA J B,CHEN Y,et al.New pseudorandom number generator based on spatiotemporal chaos[J].Computer Engineering and Applications,2018,54(11):97-102.
[7]ZHAO G,MA Y J,CHEN L,et al.Design of Dynamic S-Box Based on Perturbed Spatiotemporal Chaotic System[J].Acta Electronica Sinica,2022,50(8):2037-2042.
[8]ZHOU S,QIU Y Y,WANG X Y,et al.Novel image cryptosystem based on new 2D hyperchaotic map and dynamical chaotic S-box[J].Nonlinear Dynamics,2023,111(10):9571-9589.
[9]DA SILVA S S,CARDOSO M,NARDO L,et al.A New Chaos-Based PRNG Hardware Architecture Using the HUB Fixed-Point Format[J].IEEE Transactions on Instrumentation and Measurement,2023,72:1-8.
[10]LIU H F,ZHOU X F,LIANG X L,et al.Image encryption algorithm based on multiple chaotic systems[J].Journal of Shaanxi University of Science & Technology,2022,40(1):188-195.
[11]FLORES V A,GARCÍA G E E,INZUNZA G E,et al.Implementing a chaotic cryptosystem in a 64-bit embedded system by using multiple-precision arithmetic[J].Nonlinear Dynamics,2019,96(1):497-516.
[12]LAI Q,YANG L,CHEN G.Design and Performance Analysis of Discrete Memristive Hyperchaotic Systems With Stuffed Cube Attractors and Ultraboosting Behaviors[J].IEEE Transactions on Industrial Electronics,2023,71(7):7819-7828.
[13] NING H,ZHAO G,LI Z Y,et al.A novel method for constructing dynamic S-boxes based on a high-performance spatiotemporal chaotic system[J].Nonlinear Dynamics,2024,112(2):1487-1509.
[14]ZHANG Y Q,HE Y,WANG X Y.Spatiotemporal chaos inmixed linear-nonlinear two-dimensional coupled logistic map lattice[J].Physica A:Statistical Mechanics and its Applications,2018,490:148-160.
[15]KANEKO K.Spatiotemporal Intermittency in Coupled MapLattices[J].Progress of Theoretical Physics,1985,74(5):1033-1044.
[16]ZHAO G,PAN Z,MA Y J,et al.A Novel One-Dimensional Migration-Coupled Mapping Lattice System and Its Dynamic Characteristics[J].Application Research of Computers,2023,40(11):3289-3293.
[17]AZAM N A,MURTAZA G,HAYAT U.A novel image encryption scheme based on elliptic curves and coupled map lattices[J].Optik,2023,274:170517.
[18]DONG Y H,ZHAO G,MA Y J,et al.A novel image encryption scheme based on pseudo-random coupled map lattices with hybrid elementary cellular automata[J].Information Sciences,2022,593:121-154.
[19]LV Z W,SUN F Y,CAI C X.A new spatiotemporal chaotic system based on two-dimensional discrete system[J].Nonlinear Dynamics,2022,109(4):3133-3144.
[20]ZHOU P Z,DU J X,ZHOU K,et al.2D mixed pseudo-random coupling PS map lattice and its application in S-box generation[J].Nonlinear Dynamics,2021,103(1):1151-1166.
[21]LIU Z,LIU J Y,ZHANG L Y,et al.Performance of the 2DCoupled Map Lattice Model and Its Application in Image Encryption[J].Complexity,2022(2):1-18.
[22]NING H,ZHAO G,DONG Y H,et al.A Novel Two-Dimensional Dynamic Pseudo-Random Coupled Map Lattices System Based on Partitioned Elementary Cellular Automata[J].Applied Sciences,2022,12(23):12399.
[23]LAI Q,YANG L,LIU Y.Design and realization of discretememristive hyperchaotic map with application in image encryption.[J].Chaos Solitons Fractals,2022(165):112781.
[24]KANEKO K.Spatiotemporal chaos in one- and two-dimensional coupled map lattices[J].Physica D:Nonlinear Phenomena,1989,37(1/2/3):60-82.
[25]WANG X Y,ZHAO M C,FENG S J,et al.An image encryption scheme using bit-plane cross-diffusion and spatiotemporal chaos system with nonlinear perturbation[J].Soft Computing,2023,27(3):1223-1240.
[26]ZHANG G F,ZHENG L L,SU Z P,et al.M-Sequences and Sliding Window Based Audio Watermarking Robust Against Large-Scale Cropping Attacks[J].IEEE Transactions on Information Forensics and Security,2023,18:1182-1195.
[27]DOU Y Q,LI M.An Image Encryption Algorithm Based onCompressive Sensing and M Sequence[J].IEEE Access,2020,8:220646-220657.
[28]ZHANG Y Q,HE Y,LI P,et al.A new color image encryption scheme based on 2DNLCML system and genetic operations[J].Optics and Lasers in Engineering,2020,128:106040.
[29]KANTZ H.A robust method to estimate the maximal Lyapunov exponent of a time series[J].Physics Letters A,1994,185(1):77-87.
[30]LI S L,LIU Y Z,REN F Y,et al.Design of a High Throughput Pseudorandom Number Generator Based on Discrete Hyper-Chaotic System[J].IEEE Transactions on Circuits and Systems II:Express Briefs,2023,70(2):806-810.
[31]SHAO S W,LI J,SHAO P,et al.Chaotic Image Encryption Using Piecewise-Logistic-Sine Map[J].IEEE Access,2023,11:27477-27488.
[32]WOLF A,SWIFT J B,SWINNEY H L,et al.Determining Lyapunov exponents from a time series[J].Physica D:Nonlinear Phenomena,1985,16(3):285-317.
[33]WANG X Y,YANG J J,GUAN N N.High-sensitivity imageencryption algorithm with random cross diffusion based on dynamically random coupled map lattice model[J].Chaos,Solitons & Fractals,2021,143:110582.
[34]ZHANG Y Q,WANG X Y.Spatiotemporal chaos in Arnoldcoupled logistic map lattice[J].Nonlinear Analysis:Modelling and Control,2013,18(4):526-541.
[35]DONG Y H,ZHAO G,MA Y J.Two-dimensional pseudo-random coupled map lattices system based on partitioned elementary cellular automata and its dynamic properties [J].Journal on Communications,2022,43(1):71-82.
[36] BASSHAM I L E,RUKHIN A L,SOTO J,et al.A Statistical Test Suite for Random and Pseudorandom Number Generators for Cryptographic Applications[R].National Institute of Stan-dards and Technology,2010.
[37]SU Y Y,TONG X J,ZHANG M,et al.Efficient image encryption algorithm based on dynamic high-performance S-box and hyperchaotic system[J].Physica Scripta,2023,98(6):65215.
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