Chaos-Based Image Encryption Algorithms In Fractional Transform Domain

With the development of Internet and computer and the popularization of images and digital devices in the world,the importance of information security is increasingly prominent.The secure and efficient image encryption algorithm becomes the goal pursued by scholars.The image encryption technologies in fractional transform domains have been paid much attention due to its strong robustness and high key space.On the basis of the analysis of existing image encryption schemes,two chaos-based image encryption algorithms in fractional transform domain are designed in this dissertation.The specific research contents are as follows.An image encryption algorithm is proposed based on phase-truncated short-time fractional Fourier transform and hyper-chaotic system.The original image is divided into four non-overlapping sub-images which are encoded with the encryption unit consisting of phase-truncated short-time fractional Fourier transform,wave-based permutation and fractional Fourier transform.The encoded sub-images compose an interim image,while the amplitude matrix and the phase matrix for recovering the original image can be extracted from the interim image with phase truncation and phase reservation.The positions and the values of the amplitude matrix elements are modified with the wave-based permutation method and the bitwise XOR operation controlled by Chen's hyper-chaotic system,which increases the anti-interference ability.The generation of initial values of Chen's hyper-chaotic system is subject to four control parameters and the pixel mean value of the original image.The simulation results indicate that the image encryption algorithm has high robustness against the common attacks.An image encryption algorithm based on multiple-order fractional discrete Tchebichef transform with chaotic system is derived.The fractional orders and the generating sequence of multiple-order fractional discrete Tchebichef transform generated by 2D Logistic-adjusted-Sine map are used to transform the original image to obtain the real-valued image.The multi-round diffusion method consisting of the bitwise XOR operation controlled by 2D Sine Logistic modulation map,multidirectional scanning and multidirectional inverse scanning is exploited to change the positions and the values of the real-valued image,which makes the one-pixel change in the original image spread to the all over encryption image.The statistical information of the original image is converted into two binary sequences using SHA-256 function and MD5 function,and then the keys of the image encryption algorithm are deduced with two binary sequences and the control parameters.Simulation results and security analyses demonstrate the feasibility and the robustness of the image encryption algorithm.