An Information Theoretic Measure for Secrecy Loss in Stochastic Discrete Event Systems

While cryptography is used to protect the content of secret information (message) by making it undecipherable, behaviors (as opposed to information) may not be encrypted, and may only be protected by partially or fully hiding through creation of ambiguity by providing covers that generate indistinguishable observations from secrets. Having a cover together with partial observability does cause ambiguity about the system behaviors to be kept secret, yet some information about secrets may still be leaked due to statistical difference between the occurrence probabilities of the secrets and their covers. One possible quantification of statistical difference between two distributions is based on their Jenson-Shannon divergence (JSD). We propose a computation of JSD for systems modeled as partially-observed Markov chains (POMC). Since an adversary is likely to discriminate more if he/she observes for a longer period, our goal is to evaluate the worst-case loss of secrecy as obtained in limit over longer and longer observations. Illustrative example is provided to demonstrate the proposed computation approach.