Fault tolerance properties of a double phase encoding encryption technique

Abstract

We investigate the robustness of an image encryption technique that uses random phase encoding in both the input plane and the Fourier plane when the encrypted image has been distorted. The distortions include different types of noise, loss of encrypted data, and the binarization of the encrypted image. It is shown that decryption transforms the noise added to the encrypted image to a wide-sense stationary additive white noise. Consequently, regardless of the type of the noise added to the encrypted image, the quality of the recovered image can be improved by processing techniques designed for filtering out additive white noise. The double-phase encryption technique distributes the input image over the entire output plane, which provides robustness to the distortions due to loss of encrypted data. Regarding the binarization, it enables easy implementation and data compression while recovering images of good quality may be possible.