A novel image encryption method based on fractional discrete Meixner moments

In order to improve the performance of the Meixner moments, we suggest in this article a new set of Fractional Discrete Meixner Polynomials (FrDMPs), a sort of a generalization of the traditional whole order. Firstly, we introduce the necessary algebraic derivatives of FrDMPs using the spectral decomposition of Discrete Meixner Polynomials (DMPs) for any order without numerical fluctuation and always preserving the property of orthogonality thanks to the algorithm of the Gram-Schmidt process. Then, we determine the eigenvalues and the corresponding multiplicity of the Meixner transform matrix. An image encryption and decryption method was proposed based on jigsaw transform and generation of Fractional Discrete Meixner Moments (FrDMMs), in which the image is broken up into bit planes. Each bit plane undergoes a jigsaw transform is divided into blocks and encrypted. The transformed bit planes are combined together and then encrypted using random phase masks and fractional discrete Meixner moments. In addition, we introduce a new encryption and decryption scheme based on the proposed FrDMMs. This scheme has a good encryption effect because the fractional parameters used as key to the encrypted data. Experimental results show that the encryption scheme is sensitive to keys, it is resist a variety of attacks, and decrypted images are almost non-distored, which indicate excellent encryption effect, sufficient security and robustness of the method.