The Research Of Image Encryption Algorithms Based On Combinatorial Design Theory And Related Problems

In recent years,accompanying with the fast development of the multimedia and net-work technology,prodigious amounts of image information is transmitted via Internet.How to ensure the safety of the image information has become an important problem in the Internet world.Image encryption is the primary solution.Due to the specific charac-teristics of image data,such as large data volume,two-dimensional spatial distribution,and a lot of redundancy in the original images,the traditional encryption algorithms are generally not suitable for image encryption.Then a lot of encryption algorithms specific to images have been proposed.The image encryption algorithms based on combinatorial design theory are highly representative among all the algorithms.The application of combinatorial design theory in cryptology is long-standing.There also have been some remarkable accomplishments in image encryption,such as the image encryption algorithms based on Latin squares,the image encryption algorithms based oil magic squares.This paper mainly uses self-orthogonal Latin squares,Latin cubes and orthogonal arrays to construct several image encryption algorithms.Moreover,we cryptanalyze an existing image encryption algorithm and give the improvement method.This thesis is organized as follows:In the introduction,we introduce the background and the essential concepts in cryp-tology,summarize the basic technologies and evaluation criteria in image encryption,and then analyze the advantages and disadvantages of chaos theory in image encryption.On this basis,we discuss the research significance of combinatorial design theory in image encryption.In chapter 1,we propose an image encryption algorithm based on self-orthogonal Latin squares.Ordinary Latin squares can only generate 1D mappings.To use these 1D mappings for image confusion,we need to permute the image row by row and column by column.It will affect the efficiency of encryption.In the proposed image encryption algorithm,we use one self-orthogonal Latin square to generate a 2D mapping,and then use this 2D mapping to permute the image directly.The efficiency is improved greatly.In chapter 2,we propose an image encryption algorithm based on one Latin cube.In the traditional image encryption algorithms,the permutation process is only related to secret key,while it is always irrelevant to the plaintext images.Besides,the traditional algorithms always need to convert the 2D image into 1D data stream before substitution.It overlooks the 2D attribute of the image,and then influences the encryption effect.In the proposed algorithm,firstly we use one Latin cube to construct a highly plaintext-related permutation scheme,and then we use this Latin cube to construct a substitution scheme specific to 2D image.Finally,the proposed algorithm has strong diffusivity,and it can resist differential attack effectively.In chapter 3,we propose an image encryption algorithm based on orthogonal Latin cubes and bit matrices.The bit matrix of an image is a three-dimensional array.The permutations on bit matrix can not only change the locations of all the pixels,but also change the values of all the pixels.A set of orthogonal Latin cubes can generate several 3D mappings.Using these 3D mappings to permute the bit matrix,the security of the proposed algorithm can be greatly improved.In chapter 4,we propose an image encryption algorithm based on an orthogonal array with t=2.In an orthogonal array with t=2,any four columns correspond to a couple of orthogonal Latin squares,and any couple of orthogonal Latin squares can generate a 2D mapping.Therefore,an orthogonal array with t=2 can generate multiple 2D mappings for image permutation.Besides,each column of an orthogonal array can be used for image substitution.When the network environment is not very safe,we can choose different columns for different plaintext images to perform permutation and substitution.It will lead to a completely different encryption process,while the computation load remains unchanged.Then the proposed algorithm can realize the balance between security and efficiency satisfactorily.In chapter 5,we analyze an existing image encryption algorithm based on DNA se-quence and hyperchaotic system.On this basis,we give chosen plaintext attack scheme and known plaintext attack scheme,and then research the improvement method.Crypt-analysis and cryptography are two aspects which are both opposite and unitary.Only after the examination of all the cryptanalysis can the encryption algorithm be ensured secure.Therefore,cryptanalysis has guiding significance for the design of secure image encryption algorithms.In the end,we conclude the paper and list some further research problems.