Novel Scheme for Image Encryption and Decryption Based on a Hermite-Gaussian Matrix

Abstract

Media security is an issue of great concern over the internet and during wireless transmissions. In this paper, a novel scheme for image encryption and decryption is proposed based on a Hermite-Gaussian matrix and an array of subkeys. The proposed scheme includes a secret key that is processed to extract an array of subkeys, which are employed with the extracted phase part of the inverse Fourier transform of a Hermite-Gaussian matrix to encrypt and decrypt a grayscale image. After key generation and the production of two columns of subkeys, the Hermite-Gaussian matrix is multiplied by the first group of subkeys and subjected to a modulus operation (the remainder) with the second group, and the resulting matrix is verified for singularity. If the singularity test is passed, then the resulting image is multiplied by the original image and the output is subjected to a modulus operation and is used for the following subkeys. However, if the singularity test fails, then a new subkey is chosen and the process is repeated until all subkeys are tested and used to produce the encrypted image. For subsequent decryption, the reverse process is implemented to recover the original image from the encrypted one. Statistical analysis shows that the proposed scheme is robust and is strong against attacks. The correlation factor, among other tests, shows that reshuffling the image pixels reduces the correlation between neighboring pixels to very low values (i.e., <1%).