Optical Image Encryption Algorithms Based On Fractional Mellin Transform

With the rapid development of the network multimedia, communication and propagation techniques, information security is of serious concern. As an information carrier, image is widely used in many fields for its vivid expression. Consequently, image security is a significant topic in information security. Image encryption is one of the effective approaches to ensure the security of the private image information. Various optical as well as digital techniques have been proposed for image encryption, including the well known image encryption scheme based on fractional Fourier transform which is a hot research point in recent years. But most of the image encryption systems based on mathematical transform are linear systems which are relatively weak in comparison to the nonlinear encryption systems. The reason is that the functional relationship among plaintext, ciphertext and key is comparatively simple in a linear encryption system, which makes the encryption system potentially insecure against some common attacks such as chosen- and known-plaintext attacks. To solve this problem, fractional Mellin transform (FrMT) is introduced to image encryption in the dissertation. As a nonlinear transform, fractional Mellin transform can effectively intensify the security of the image encryption system, and it can also provide fractional orders to be the keys of the encryption system. The research work is summarized as follows.An image encryption algorithm based on fractional Mellin transform is proposed and corresponding optical setup is provided. In the nonlinear encryption system, different annular domains of the original image are transformed by FrMTs of different orders, and then the outputs are further encrypted by comprehensively using fractional Fourier transform, amplitude encoding and phase encoding. The encryption system has ability against known-plaintext, chosen-plaintext, chosen-ciphertext and ciphertext-only attacks for the nonlinear property of FrMT. Besides, fractional orders of FrMT, the radii of annular domains, phase masks produced in iteration, and etc. are the keys of the encryption system, which enlarge the key space.The multi-order discrete fractional Mellin transform (MODFrMT) is constructed and the corresponding image encryption scheme is proposed. MODFrMT is derived by transforming the image with multi-order discrete fractional Fourier transform (MODFrFT) in log-polar coordinates, where MODFrFT is generalized from the closed-form expression of the discrete fractional Fourier transform. MODFrMT overcomes the deficiency of comparatively low sensitivity of the fractional orders, and it provides more parameters to be the keys. Meanwhile, MODFrMT can be realized by fast Fourier transform to reduce the computation burden. Simulation results demonstrate that the encryption algorithm is against to common attacks, sensitive to keys and has good robustness.Reality preserving fractional Mellin transform (RPFrMT) is constructed and corresponding image encryption algorithm is proposed. The output of the FrMT is always complex-valued, and the phase information of the complex-valued image should be recorded by holography which makes the encryption system complicated. To solve this problem, reality preserving fractional Mellin transform is constructed. The output of the RPFrMT is real-valued for the real-valued input, which ensures that ciphertext is real-valued and convenient for display, storage and transmission. In the encryption process, the original color image is first transformed from RGB color space to R'G'B'color space by rotating the color cube. The three components of the output are then transformed by RPFrMT of different fractional orders. To further enhance the security of the encryption system, the result of the former step is scrambled by three dimensional scrambling to obtain the final encrypted data. The fractional orders of RPFrMT, the rotation angles and the four seeds involved in three dimensional scrambling are keys. Simulation results demonstrate the feasibility, effectiveness and security of the encryption algorithm. By transforming the gray images into three color components of a specially constructed color image, the color image encryption can be used to encrypt three gray images.