Research On Reversibility Of Cellular Automata And Its Application In Image Encryption

With the booming development of information technology,the application of digital images in daily life is gradually expanding,and the security risks faced by digital images are becoming more and more serious.When the traditional encryption algorithm is applied to the field of image encryption,the digital image has the characteristics of large amount of data,strong correlation between image pixels,which makes the encryption effect is not ideal,so it is necessary to study the new image encryption algorithm.Reversible cellular automata is a kind of spatiotemporal discrete dynamic system,with simple composition structure,local interaction,high parallelism,reversibility and other characteristics,which make reversible cellular automata have better security and reliability in the field of cryptography,so the study of reversible cellular automata has important research significance and application prospects.Based on the analysis of existing research results on the reversibility of cellular automata,this thesis conducts relevant research and exploration on the reversibility of one-dimensional and two-dimensional cellular automata,as well as the methods for constructing reversible cellular automata.The main research achievements and innovative points achieved are as follows:(1)Research on the reversibility of the existing one-dimensional cellular automata is limited to deducing the conditions required for its reversibility without giving the state transition function of its corresponding reversible cellular automata,and research on the invertibility of two-dimensional cellular automata is limited to the Moore type neighborhood.In this thesis,the matrix analysis method is used to study whether the matrix form of onedimensional reversible cellular automata state transition function has generality and the reversible condition of three common two-dimensional neighborhood models.The results show that only the state transition matrix of the reversible cellular automata under one-dimensional zero boundary conditions can be represented by matrices with general forms.The linear rules of the three two-dimensional neighborhood models can be divided into four categories:necessarily reversible,necessarily irreversible,partially reversible and irregularly reversible.(2)A method to construct a two-dimension second-order coupled reversible cellular automata is proposed,and based on the constructed reversible cellular automata,an image encryption algorithm which can encrypt grayscale images is proposed.The proposed reversible cellular automata has complex cellular evolution and large rule space,so it is safe enough to be used in image encryption.The proposed encryption algorithm is divided into three steps.Firstly,a proposed XZigzag transform is used to scramble the image,then a proposed pseudo-random sequence generation method based on cellular automata is used to generate a pseudo-random sequence matrix to scramble the image again,and finally,the reversible cellular automata constructed is used to diffuse the image.The results of simulation experiment and security analysis show that the image encryption algorithm proposed in this thesis has better encryption effect and security.(3)A prototype system for the judgment of reversibility of cellular automata and its application in image encryption is designed and implemented.The system has three main functions,firstly,it can display spatiotemporal evolution diagram of any rule of the cellular automata used and constructed in this thesis,secondly,it can judge the reversibility of onedimensional and two-dimensional linear cellular automata,and finally,it can implement encryption and decryption operations on grayscale images and display the related security analysis results.