基于多层元胞自动机的动态随机耦合映像格系统性能分析

赵耿; 吴锐; 马英杰; 董有恒; 黄思婕

doi:10.12263/DZXB.20230134

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基于多层元胞自动机的动态随机耦合映像格系统性能分析

学术论文 | 更新时间：2025-12-08

- 基于多层元胞自动机的动态随机耦合映像格系统性能分析
- Performance Analysis of Dynamic Random Coupled Map Lattices System Based on Multilayer Elementary Cellular Automata
- 电子学报 2024年52卷第9期页码：3111-3122
- 作者机构：
  
  1.西安电子科技大学，陕西西安 710071
  2.北京电子科技学院，北京 100070
- 作者简介：
  
  [ "赵耿男，1964年2月出生于四川省苍溪市.博士，教授，主要研究领域为混沌密码理论及应用.中国电子学会会员编号：E190005205S.E-mail: zg@besti.edu.cn" ]
  [ "吴锐男，1997年10月出生于安徽省桐城市.硕士，主要研究领域为混沌保密通信.E-mail: ruiwu@stu.xidian.edu.cn" ]
  [ "马英杰女，1979年6月出生于吉林省通化市.博士，副教授，主要研究领域为混沌保密通信.E-mail: dmzm12@163.com" ]
  [ "董有恒男，1995年5月出生于山东省济宁市.博士，主要研究领域为混沌密码学.E-mail: Dyh_231@bupt.edu.cn" ]
  黄思婕女，1998年5月出生于山西省抚州市.硕士，主要研究领域为混沌扩频通信. E-mail: 20011210147@stu.xidian.edu.cn
- 基金信息：
  
  北京高校“高精尖”学科建设项目(3201017);国家自然科学基金(61772047)
- DOI：10.12263/DZXB.20230134
  中图分类号： TN918
- 收稿：2023-02-15，
  
  修回：2023-08-10，
  
  纸质出版：2024-09-25
- 稿件说明：
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赵耿, 吴锐, 马英杰, 等. 基于多层元胞自动机的动态随机耦合映像格系统性能分析[J]. 电子学报, 2024, 52(09): 3111-3122.

ZHAO Geng, WU Rui, MA Ying-jie, et al. Performance Analysis of Dynamic Random Coupled Map Lattices System Based on Multilayer Elementary Cellular Automata[J]. Acta Electronica Sinica, 2024, 52(09): 3111-3122.
赵耿, 吴锐, 马英杰, 等. 基于多层元胞自动机的动态随机耦合映像格系统性能分析[J]. 电子学报, 2024, 52(09): 3111-3122. DOI：10.12263/DZXB.20230134

ZHAO Geng, WU Rui, MA Ying-jie, et al. Performance Analysis of Dynamic Random Coupled Map Lattices System Based on Multilayer Elementary Cellular Automata[J]. Acta Electronica Sinica, 2024, 52(09): 3111-3122. DOI：10.12263/DZXB.20230134

摘要

基于多层元胞自动机的时空混沌系统设计了一款用于图像加密的伪随机数发生器.针对现有的基于耦合映像格系统仍存在参数空间有限、局部混沌行为等问题，本文提出一种基于多层元胞自动机的伪随机耦合映像格系统.在初等元胞自动机基础上设计出多层元胞自动机，将耦合系统与多层元胞自动机同时进行迭代，通过自动机的迭代输出得到耦合系统中每个格子的动态耦合方案以及伪随机扰动方法.本文通过分岔图、Kolmogorov Sinai熵和输出序列均匀性对耦合映像格系统进行对比分析，并分析了系统生成序列的随机性和任意两个格之间的相关性.理论分析和实验结果表明，与其它耦合映射格系统相比，该系统具有更好的混沌特性和更大的参数空间，系统生成的序列具有较好的遍历性、均匀性和随机性.研究结果表明该系统在密码学领域具有广阔的应用前景.

Abstract

A pseudo-random number generator for image encryption has been developed

utilizing a spatiotemporal chaotic system with multilayer elementary cellular automata. To solve the existing problems of limited parameter space and local chaotic behavior based on coupled image lattice system

a dynamic random coupled map lattices (DRCML) system based on a multilayer elementary cellular automaton (MECA) is proposed. The MECA is designed on the basis of the elementary cellular automaton (ECA)

and DRCML system is iterating with the MECA simultaneously

and the DRCML system of each lattice in the coupled system and the pseudo-random perturbation method are obtained through the iterative output of the MECA. The DRCML system is compared and analyzed by bifurcation diagram

Kolmogorov Sinai entropy and output sequence uniformity

and the correlation between the randomness of the generated sequence of the system and any two lattices is analyzed. The theoretical analysis and experimental results show that the DRCML system has better chaotic properties and wider parameter space than other coupled map lattices systems

and the generated sequences have better ergodicity

uniformity and randomness. The results show that the DRCML system has a promising application in the field of cryptography.

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references

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