Quantification of distributed secrecy loss in stochastic discrete event systems under bounded-delay communications

Unlike information, behaviors cannot be encrypted and may instead be protected by providing covers that generate indistinguishable observations from behaviors needed to be kept secret. Such a scheme may still leak information about secrets due to statistical difference between the occurrence probabilities of the secrets and their covers. Jensen-Shannon Divergence (JSD) is a possible means of quantifying statistical difference between two distributions and was used to measure such information leak as in our earlier work [1]. This paper studies secrecy quantification in stochastic partially-observed discrete event systems in the presence of distributed collusive attackers/observers, each with its own local partial observability, generalizing the setting of single observer in [1]. The local observers collude and exchange their observations over communication channels that introduce bounded delays. We propose a method to compute the JSD-based secrecy measure in this distributed setting by introducing bounded-delay channel models to extend the system model to capture the effect of exchange of observations, and to measure the distributed secrecy loss.