Nonlinear double image encryption using 2D non-separable linear canonical transform and phase retrieval algorithm

In this paper, we propose a new asymmetric method for double image encryption using the two-dimensional non-separable linear canonical transform (2D NS-LCT) and an iterative phase retrieval algorithm (PRA). First an encryption security key is generated using the PRA. Then two images (2D intensities) are combined to form a complex image. The 2D NS-LCT of this complex valued image is then obtained. A nonlinear phase truncation operation is applied to the transformed image and the amplitude is retained and used as the private key. The phase term is multiplied by the security PRA generated key and the inverse 2D NS-LCT is applied to the result giving the output encrypted image. The robustness of the proposed technique is tested against noise, occlusion and chosen-plaintext attacks. Numerical results are presented demonstrating the security of the proposed technique.