Optical cryptanalysis: Metrics of robustness and cost functions

The robustness of optical encryption systems is often quantified by plotting the normalised root mean square (NRMS) error against a particular error in the decryption process, i.e., misalignment of, or pixel errors in the decryption key. In addition, the NRMS appears as a cost function in heuristic iterative attacking techniques, employed to crack optical encryption systems. In fact several other potential measures can be used to quantify the error of a decryption process, for example the lambda parameter, entropy and different auto-focus (image sharpness) based values, i.e., the sum modulus difference and the focus value. Based on detailed numerical simulations, it is shown that in comparison to these other metrics the NRMS provides the best results when attacking an optical encryption system. (C) 2011 Elsevier Ltd. All rights reserved.