A watermarking-based asymmetric cryptosystem using gyrator transform, QZ modulation, and fractional vortex toroidal phase mask

A watermarking scheme has been proposed, using gyrator transform (GT), a random phase mask (RPM) in the input plane, and a phase mask named fractional vortex toroidal phase mask (FVTPM) in the frequency plane. The use of FVTPM provides additional encryption parameters, besides overcoming the problem of axis-alignment associated with an optical set-up. To make the system asymmetric, use is made of phase-truncation (PT) and phase-reservation (PR). The complex images are further processed with Quasi-Zernike (QZ) decomposition resulting in two upper quasi-triangular matrices, two unitary matrices, and encryption keys. The encrypted image resulting from the application of the GT is attenuated by a factor and combined with a host image to provide a watermarked image. The decryption process is the reverse of the encryption. Digital implementation of the proposed scheme has been performed using MATLAB 2023. The validity of the proposed scheme has been established by comparing the results of decryption with the input images. The sensitivity to encryption keys such as rotation angle of GT has been studied. In addition, the performance of the scheme has also been evaluated in terms of mean-squared-error (MSE), peak signal-to-noise ratio (PSNR), structural similarity index measure (SSIM), entropy, histograms analysis, correlation analysis, occlusion-, and noise attacks. The proposed technique provides enhanced security due to various parameters used.