The Design On Chaotic Image Encryption Algorithm Using Mathematical Model

At present, the research of cloud computing and big data like a raging fire, with the deepening and rapid development of the mobile internet, the safety and privacy protection of image have been paid more and more attention. In response to these realities of demands, it is necessary to strength the research on image encryption. As a new science, chaos has extensive and deep contact with cryptography. The chaos-based encryption has been widely studied, especially in terms of the image encryption. As the author known, many encryption algorithms are directly based on the matrix transformation or their own definition of strict rules, some have defects or flaws in the design. In addition, some encryption algorithms simply use pseudo random sequences generated by chaotic system to deal with the sequences of image directly. Aiming at these problems, we try to propose some novel chaos-based image encryption algorithms by using several mathematical models, such as Brown motion, genetic operator and cellular automaton.(1) A new image encryption algorithm using chaos and based on the Brown motion has been proposed. The algorithm take each pixel of the image as a "Brown particle", and the entire image as a "container". To simulate the Brown motion on these "particles" by means of Monte Carlo method, thus, the purpose of the image confusion has been achieved.(2) Based on the design of genetic operators, a new type of chaos-based image encryption scheme has been researched. Each pixel has been regarded as an "individual", and every bit of the "individual" as a "gene". The new structure of "select-crossover-mutation" building on the modern cryptography system has been put forwarded. The encryption can be completed by selecting some of the "individuals", making crossover and mutation on them.(3) A new chaos-based image encryption scheme which fulfilled the theory of cellular automaton has been given. Corresponding to the idea of Langton’ Ant cellular automaton, the scheme imagine the 2-dimensional structure of the entire image as a "checkerboard", each grid stored one pixel. According to the rules given by Langton, the ants climb different grids and change their states. The algorithm gradually collected the pixels which have been "climbed", and finally get the result of image scrambling.(4) By using the KD tree to partition the space, a new image encryption algorithm has been presented. The algorithm put the confusion of the image as a problem of spatial segmentation, which randomly divide the image according to the sample of random data points and make multi-level partition recursively. The scrambling result can be got by using Knuth permutation algorithm to randomly recombine the divided blocks.