Studies On Image Encryption And Some Estimations Of Security

With the rapidly development of internet communication and multimedia technology, information security, including image security, comes to be an increasingly important problem. At the same time, popular application of multimedia technology and increasingly transmission ability of network gradually leads us to be inclined to acquire information directly and clearly through images. Hence, image data security and transmission have become a critical and imperative issue.In part one of this thesis, we briefly discuss about scrambling and encryption of digital images. After introducing several novel scrambling algorithms[2][3], we define the concept of ergodic matrix, which can be used to scramble the positions of the pixels of an image. Subsequently we analyze the isomorphism relationship between ergodic matrices and the corresponding permutation group. By defining the permutation symbol operation system of ergodic matrices, we constructed a union form to express all existed permutation algorithms. Finally, we proposed a novel improved self-adaptive algorithms and testified its combining encryption effect with its position and energy information.In part two of this thesis, we analyze the dynamic states of an image caused by image iteration, as a result we point out that the holographicity exists with chaotic characters simultaneously during image scrambling. Then, restoration of data loss resulting from transmission after scrambling is also progressed.In the end of this thesis, the decryption algorithm of the pure position permutation algorithms is proved. Based on probability theory, it can be proved that the image encrypted by pure position permutation algorithm can be decrypted if we obtain some information of original image and its encrypted one as the reference. Therefore, we proposed an conception of fuzzy ergodic matrices, which is used for the decryption algorithm. Some Estimations of Security is also shown.