Photon-counting double-random-phase encoding for secure image verification and retrieval

The integration of photon-counting imaging techniques and optical encryption systems can improve information authentication robustness against intruder attacks. Photon-counting imaging generates distributions with far fewer photons than conventional imaging and provides substantial bandwidth reduction by generating sparse encrypted data. We show that photon-limited encrypted distributions have sufficient information for successful decryption, authentication and signal retrieval. Additional compression of the encrypted distribution is applied by limiting the number of phase values used to reproduce the phase information of the complex-valued encrypted data. The validity of this technique-with and without phase compression-is probed through simulated experiments for two types of input images: alphanumerical signs and dithered natural scenes.