基于分区初等元胞自动机的二维伪随机耦合映像格系统及其动态特性

董有恒; 赵耿; 马英杰

doi:10.11959/j.issn.1000-436x.2022001

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基于分区初等元胞自动机的二维伪随机耦合映像格系统及其动态特性

学术论文 | 更新时间：2024-06-05

- 基于分区初等元胞自动机的二维伪随机耦合映像格系统及其动态特性
- Two-dimensional pseudo-random coupled map lattices system based on partitioned elementary cellular automata and its dynamic properties
- 通信学报 2022年43卷第1期页码：71-82
- 作者机构：
  
  1. 北京邮电大学网络空间安全学院，北京 100089
  2. 北京电子科技学院网络空间安全系，北京 100071
- 作者简介：
  
  [ "董有恒（1995- ），男，山东济宁人，北京邮电大学博士生，主要研究方向为混沌密码理论及应用等" ]
  [ "赵耿（1964- ），男，四川苍溪人，博士，北京邮电大学教授、博士生导师，主要研究方向为混沌密码理论及应用、信息安全等" ]
  [ "马英杰（1979- ），女，吉林通化人，博士，北京电子科技学院副教授、硕士生导师，主要研究方向为通信系统、混沌保密通信等" ]
- 基金信息：
  
  北京高校“高精尖”学科建设基金资助项目(3201017);国家自然科学基金资助项目(61772047)
- DOI：10.11959/j.issn.1000-436x.2022001
  中图分类号： TN918
- 网络出版日期：2022-01，
  
  纸质出版日期：2022-01-25
- 稿件说明：
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董有恒, 赵耿, 马英杰. 基于分区初等元胞自动机的二维伪随机耦合映像格系统及其动态特性[J]. 通信学报, 2022,43(1):71-82.

Youheng DONG, Geng ZHAO, Yingjie MA. 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.
董有恒, 赵耿, 马英杰. 基于分区初等元胞自动机的二维伪随机耦合映像格系统及其动态特性[J]. 通信学报, 2022,43(1):71-82. DOI： 10.11959/j.issn.1000-436x.2022001.

Youheng DONG, Geng ZHAO, Yingjie MA. 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. DOI： 10.11959/j.issn.1000-436x.2022001.

摘要

针对基于耦合映像格的时空混沌系统中，某些控制参数会导致弱混沌的现象，以及系统生成序列频率分布不均的情况，提出了一种基于分区初等元胞自动机的二维伪随机耦合映像格系统。首先，基于初等元胞自动机，设计了高维的分区初等元胞自动机。然后，根据该高维自动机的输出，实现了伪随机的耦合方案，同时将自动机的输出作为扰动添加至时空混沌系统中。利用K熵、分岔图等对二维伪随机耦合映像格系统的动态特性进行了对比分析，同时对系统生成序列的分布特性、相关性以及随机性进行了研究。结果表明，该系统建立了更强更广泛的混沌特性，拥有良好的复杂性、遍历性和非周期性。此外，该系统生成的序列具有更均匀的分布和序列之间更低的相关性，并拥有良好的伪随机性。因此，二维伪随机耦合映像格系统在密码系统和混沌保密通信中具有广阔的应用前景。

Abstract

To solve the weak chaos in the spatiotemporal chaotic system based on coupled map lattices under some control parameters and the un-uniformity of sequences generated by the coupled map lattices

a two-dimensional pseudo-random coupled map lattices (2D-PRCML) system was proposed.Firstly

the two-dimensional partitioned elementary cellular automata (2D-PECA) was designed to establish pseudo-random coupling.Secondly

iterative results of 2D-PECA were utilized to perturb the 2D-PRCML system.The chaotic behaviors of the proposed system

such as the bifurcation diagram

Kolmogorov-Sinai entropy

were investigated.Moreover

the uniformity of sequences generated by the 2D-PRCML system was discussed

and the correlation coefficients between any two sequences generated by different lattices were acquired.The analyses and tests indicate that the 2D-PRCML system exhibits stronger chaotic behavior.Furthermore

the sequence generated by the proposed system possesses better uniformity

randomness

and unpredictability.The outstanding properties of the 2D-PRCML system prove that it is more suitable for applying in cryptography and chaotic secure communication.

关键词

Keywords

references

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