A symmetric optical cryptosystem based on QZ decomposition and Hermite Gaussian beam speckles

In this paper, we propose a new asymmetric optical cryptosystem for phase image encoding with the utilization of speckles generated by scattering the Hermite Gaussian beams (HGBs) through a rough surface. These speckle patterns are unique and almost impossible to clone as one cannot mimic the physical process. The generalized Schur decomposition, named as, QZ decomposition, approach is used to generate unique private keys for decrypting the encoded data. The plaintext image is first phase-encoded and then modulated with the pattern obtained by the convolution of HGBs and random phase masks. The modulated image is then Fresnel propagated for a distance of z1, and the QZ decomposition operation is performed on the complex wavefront to generate the private keys. Afterward, the gyrator transforms with a rotational angle (α), and the phase truncation is used to further process the information. The phase truncation and phase reservation (PT/PR) will result in another phase private key, which will be utilized for decryption. A non-linear power function is introduced to modify the amplitude part after PT/PR operation and the resultant is modulated using an HGB amplitude mask to get an intermediate wavefront. Finally, the encrypted image is obtained by Fresnel propagating the intermediate wavefront with a distance of z2. The effectiveness and validity of the proposed method are tested and verified through numerical simulations. A series of potential attacks such as contamination and plaintext attacks have been tried and tested to further check the robustness of the proposed method. The results confirm the efficacy of the proposed method.