基于二维动态元胞自动机的伪随机耦合映像格系统及其动态特性

Pseudo random coupled image lattice system based on two dimensional dynamic cellular automata and its dynamic characteristics

针对时空混沌系统中遇到的混沌强度不足等问题,提出了一种基于二维动态元胞自动机的伪随机耦合映射格系统方案。基于初等元胞自动机,设计了二维动态元胞自动机,通过变换其迭代次数,动态选取迭代规则和方向,实现状态的多样性更新,从而增强了元胞的伪随机特性。在每次元胞状态更新时,根据格子所对应元胞的行和列位置动态生成耦合索引值,并利用索引值对混沌序列施加扰动提升序列的随机性,降低了格子之间的相关性。对系统动力学特性进行分析,发现其有较强的混沌特性和随机性,能够有效延长系统的周期,增强遍历性。最后,利用SHA-256运算生成混沌系统初始化参数,结合系统的输出序列和DNA编码设计出一种图像加密算法,并对该算法进行信息熵等性能分析。实验结果表明,该算法加密结果拥有较好的统计特性和安全性,在图像加密领域有较好的应用前景。

This paper proposed a pseudorandom coupled mapping lattice system scheme based on two-dimensional dynamic cellular automata to address the issue of insufficient chaos intensity in spatiotemporal chaotic systems.It designed the two-dimensional dynamic cellular automata based on elementary cellular automata,which achieved state diversity update through varying iteration counts and dynamically selecting iteration rules and directions,thereby enhancing the pseudorandom properties of the cells.During each cell state update.It dynamically generated coupling index values based on the row and column positions of the corresponding cells,and used these index values to perturb the chaotic sequences,improving their randomness and reducing correlations between cells.Analysis of the system’s dynamic characteristics revealed strong chaos and randomness,effectively extending the system’s period and enhancing ergodicity.Finally,this paper designed an image encryption algorithm using SHA-256 operations to generate initialization parameters for the chaotic system,combined with the system’s output sequence and DNA encoding.Performance analysis of the algorithm,including information entropy,show that it possesses good statistical properties and security,promising good application potential in the field of image encryption.