Image Encryption Hybrid Algorithm Based On The Co-sparse Model

The signal sparse representation aims to represent the signal with few atoms which are selected from a dictionary.The sparse representation of the image could be realized with a fixed dictionary or a learning dictionary to represent the essential features of the image and has been used in a wide range of the fields of image processing,such as: image denoising,blind source separation,image encryption and etc.There are two models for the signal sparse representation: synthesis sparse model and cosparse model.On the basis of the cosparse model,two image encryption algorithms are proposed.The main contributions are summarized as below:1.An iterative double random phase image encryption algorithm based on the learning dictionary is proposed.The cosparse representation of the plaintext image is obtained by using a learned dictionary and the dictionary can be adopted as the key.Then the cosparse representation is scrambled by the random pixel exchange technology;and the double random phase encryption technology is adopted to encrypt the scrambled cosparse representation.The security of the algorithm is enhanced further by binding the discriminant matrices in random pixel exchange technology with the random matrices in double random phase encryption technology.2.A novel image compression–encryption hybrid algorithm based on the cosparse representation is proposed.The sparse representation of an image could obtained with an overcomplete fixed dictionary,and the order of the atoms in the fixed dictionary is scrambled by the Logistic map.And then the compressive sensing(CS)is introduced to re-encrypt the sparse representation and reduce its dimension simultaneously,where the measurement matrix of the CS is adopted as a circulant matrix and its first row is generated by Logistic map.To enhance the security,a pixel-scrambling method controlled by the Logistic map is employed.The proposed image compression-encryption algorithm could provide a considerable compression performance with a good security.