Image Encryption Algorithms Based On Fractional Sumudu Transform And Fractional Mellin Transform

In recent years, fractional integral transforms have been widely concerned in the field of information processing. Various kinds of new fractional transforms as important mathematical tools are employed in the fields of optical information processing, digital signal processing and so on. This thesis introduces the basic principles of fractional Sumudu transformation, fractional Fourier transform and fractional Mellin transform. Two new image encryption algorithms are designed by using the fractional Sumudu transform and fractional Mellin transform, respectively. A multiple-image encryption scheme is designed by using the log-polar transform. The main research work is as follows:A double random phase encoding algorithm based on fractional Sumudu transform and fractional Fourier transform is proposed. By introducing fractional Sumudu transform defined by Mittag-Leffler function and modified fractional Riemann-Liouville derivative to the double random phase encoding algorithm based on fractional Fourier transform, the proposed algorithm can take full advantage of smooth feature of fractional Sumudu transform to confuse and diffuse gray values of image. The introduction of fractional Sumudu transform improves the sensitivity of order of the fractional Fourier transform and enhances the security of the encryption system.An image encryption scheme based on fractional Mellin transform and phase retrieval algorithm is designed. Arbitrary image can be chosen as the ciphertext in this encryption scheme, then the selected annular domain of ciphertext transformed by fractional Mellin transform. By processing the amplitude of the transformed result and the image to be encrypted with phase retrieval algorithm, phase-key can be obtained. The computer simulation results demonstrate that the algorithm is reliable, and the algorithm can also be extended to the field of multiple-image encryption.An image encryption algorithm based on log-polar transform and double random phase encoding is proposed. The images to be encrypted are transformed into annular domains respectively by using data compression feature of log-polar transform. Then the annular domains are superimposed into one image. The composite image is encoded by double random phase encoding. The computer simulation results verify the security and robustness of this method.