Method of attack on schemes of optical encryption with spatially incoherent illumination

Abstract

Optical encryption with spatially incoherent illumination does not suffer from speckle noise and does not require holographic registration setup like coherent techniques do. However, as only light intensity distribution is considered, mean value of image to be encrypted is always above zero which leads to intensive zero spatial frequency peak in image spectrum. Consequently, in case of spatially incoherent illumination, image spectrum, as well as an encryption key spectrum, cannot be white. This can be used to crack encryption system. If encryption key is very sparse, encrypted image might contain parts or even whole unhidden original image. In case of denser keys, original image boundaries still might be partially visible. This will not provide correct decryption key, but will allow to significantly narrow the search for one. Therefore, in this paper new attack method on schemes of optical encryption with spatially incoherent illumination is presented. Method is based on detection of original image boundaries in the encrypted image. Because encryption is accomplished via optical convolution of original image with encryption key, encryption key can be found if original image is known. In proposed method, in place of original image (which is unknown to the attacker) we use random matrices. Reconstructed in this way keys are extremely noisy even in case of simplest keys, but after binarization they provide areas of encryption key points possible locations. In case of simplest keys proposed method allows to acquire correct key. In case of complex keys it allows to narrow the search for one. Results of numerical experiments on breaking the system of optical encryption with spatially incoherent illumination are presented.