| As an information carrier,image carries a large amount of important information.Therefore,it is important to ensure the security of image information during the transmission process.Usually,the traditional image encryption algorithms have small key space and are easy to disturb by the channel noise.To ensure the secure transmission of private images,two image encryption algorithms based on fractional Hermite transform and chaotic system were proposed in this dissertation.The specific work of this dissertation is as follows:A gray image encryption algorithm based on the fractional Hermite transform was proposed.The encryption matrix utilized in the algorithm is related to plaintext and relatively controllable.After Zigzag scanning and Arnold transform,the original image was encrypted by the encryption matrix,which was generated by the linear feedback shift register combined with the hyper-chaotic system.The initial input of the linear feedback shift register contains the pixel values of the original image,which improves the security and the plaintext correlation of the encryption matrix.The fractional Hermite transform was performed on the encrypted result of the linear feedback shift register,which was a process of fractional convolution between the input image signal and the image analysis filter with the Hermite transform property.Then,the image after the fractional Hermite transform was subjected to cyclic shift operation and XOR operation to obtain the ciphertext image.In the whole encryption process,the pixels were scrambled and diffused before and after the fractional Hermite transform,which improved the randomness of the pixel values of the ciphertext image.Compared with other typical image encryption algorithms,this algorithm significantly enhances the efficiency of image encryption on the premise of ensuring security.It is shown that the gray image encryption algorithm based on the fractional Hermite transform has good security and effectiveness,and can resist various common attacks effectively.By combining fractional Hermite transform with multiple chaotic systems,a chaotic color image encryption algorithm was designed.The three color components of the original image were encrypted with three different chaotic systems.The initial values of each chaotic system were obtained from the pixel values of the original image with the Hash function SHA-512.After Zigzag scanning of the original image,the positions of pixels were scrambled preliminarily.Then,the resulting image was equidistantly sampled by the fractional Hermite transform to protect the effective image information from interfering with noises.The pixel values were diffused by cyclic shift operation and three chaotic systems.The pixel positions of the image were scrambled by the cyclic shift operation and the pixel values were XORed at the same time,so that the pixel values of the component image can be diffused.Three corresponding encryption matrices generated with three chaotic systems were XORed with three color component images,respectively.Each row and each column of the component image were XORed in different ways,which reduced the correlation between the pixels of the component image.Histogram,correlation,information entropy,differential attack,key sensitivity,key space,cutting attack,noise attack,chosen plaintext attack,algorithm complexity and algorithm comparison were analyzed.It is demonstrated that the proposed color image encryption algorithm based on fractional Hermite transform and multiple chaotic systems has high robustness and efficiency. |
