Research On Secondary Arnold Transformation And Centro-invertible Matrices

Digital image processing is a method and technique about image enhancement, division, noise elimination, restore, and feature extraction, which is a strong comprehensive interdisciplinary. With the development of science and technology, the technology of digital image processing is investigated and developed quickly, which is widely used in aviation and aerospace, scientific research, medical diagnosis, biomedical engineering, industrial and agricultural production, weather, military, transportation, media, communications, and greatly benefits economic and social. With the development of the Internet, image and video frequently transports on the network, which raises the image information security problems. Image encryption is a primary method to treat these problems. At present, as one of the important problems in the field of information security, image encryption is widely concerned. Image scrambling is one of the methods to realize image encryption, which achieves the goal of image encryption through change each image pixel position by algorithm. Classical algorithm includes Arnold transform, Tangram, Fibonacci transformation and fractal Hilbert curve, Affine transformation, etc. And most of them don’t change the pixel values. In this thesis, Arnold transformation is investigated and improved. We segment and transform images twice by Arnold transformation in order to improve the image scrambling effect. The experimental results show that, the algorithm reduces the correlation of adjacent pixels inside the image, thus can obtain better encryption effect.This thesis mainly consists of three parts:In the first part, widely applications of digital image processing and the importance of the image encryption are introduced firstly. Then the research status and development trend of digital image processing and several kinds of common image scrambling algorithm are described. In the end, the traditional Arnold transformation image scrambling encryption algorithms are introduced, and the periodic of the algorithms are investigated.In the second part, the secondary Arnold transformation algorithms for image scrambling encryption are given, including the basic idea, the principle of the algorithm and implementation approach. Additionally, the basic steps and the flow chart of the algorithm and decryption process are proposed. In the end, we conclude encrypted security by comparing the experimental result of traditional Arnold transform image scrambling encryption algorithm and the algorithm raised in this thesis.Due to the significant applications of invertible matrices in the secondary Arnold transform algorithms, it is necessary to construct these matrices and investigate their properties. In the third part, properties of the some special invertible matrices over ring such as involutory matrices,centro-invertible matrices,generalized centro-invertible matrices are investigated.