Quantification of Centralized/Distributed Secrecy in Stochastic Discrete Event Systems

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 can be used to measure such information leak as is presented in this chapter. Using JSD, we quantify loss of secrecy in stochastic partially-observed discrete event systems in two settings: (i) the centralized setting, corresponding to a single attacker/observer, and (ii) the distributed collusive setting, corresponding to multiple attackers/observers, exchanging their observed information. In the centralized case, an observer structure is formed and used to aide the computation of JSD, in the limit, as the length of observations approach infinity to quantify the worst case loss of secrecy. In the distributed collusive case, channel models are introduced to extend the system model to capture the effect of exchange of observations, that allows the JSD computation of the centralized case to be applied over the extended model to measure the distributed secrecy loss.