Current-state opacity verification in discrete event systems using an observer net

Due to the proliferation of contemporary computer-integrated systems and communication networks, there is more concern than ever regarding privacy, given the potential for sensitive data exploitation. A recent cyber-security research trend is to focus on security principles and develop the foundations for designing safety-critical systems. In this work, we investigated the problem of verifying current-state opacity in discrete event systems using labeled Petri nets. A system is current-state opaque provided that the current-state estimate cannot be revealed as a subset of secret states. We introduced a new sub-model of the system, named an observer net. The observer net have the same structure as the plant, but it is distinguished by the use of colored markers as well as simultaneous and recursive transition enabling and firing, which offer an efficient state estimation. We considered two settings of the proposed approach: an on-line setting, in which a current-state opacity algorithm is proposed. The algorithm waits for the occurrence of an observable event and determines if the current observation of a plant reveals the secret behaviour, as well as, an off-line setting, where the verification problem is solved based on a state estimator called a colored estimator. In this context, necessary and sufficient conditions for verifying opacity are developed with illustrative examples to demonstrate the presented approach.