Image encryption scheme based on a Gaussian apertured reality-preserving fractional Mellin transform

An image encryption scheme based on a Gaussian apertured reality-preserving fractional Mellin transform (GARPFrMT) is proposed. The GARPFrMT was realized in the diffraction domain. The Gaussian aperture, like a soft aperture, improved the amount of light that passed through the lens compared to a hard aperture and reduced the light leakage at the edge of the lens, assisting to some extent in resisting direct attacks. In the proposed scheme, the reality-preserving transform was constructed in the diffraction domain to ensure that the cipher-text is real. The GARPFrMT is a nonlinear transformation used for eliminating potential insecurity existing in the linear image encryption system. In order to further enhance the security of the encryption system, an Arnold transform, and a bitwise XOR operation were employed for permutation and scrambling in the encryption process. Simulation results and theoretical analysis show that the proposed algorithm is feasible and capable of withstanding several common attacks.