On-line verification of current-state opacity by Petri nets and integer linear programming

Abstract

Opacity is a security and privacy property that evaluates whether an external observer (intruder) can infer a secret of a system by observing its behavior. This paper proposes an on-line approach to address the problem of current-state opacity in discrete event systems (DESs) modeled in a labeled Petri Net (PN) framework and by observing its evolution. An observation of the system is said to be current-state opaque if the intruder is unable to determine whether the current state of the system is within a set of secret states, otherwise it is said to be not current-state opaque. The proposed approach to verify the current-state opacity works on-line: the verification algorithm waits for the occurrence of an observable event and uses Integer Linear Programming problem solutions to verify if the behavior of the system is current-state opaque to the intruder under the given observation. Moreover, the proposed method is applied in two different settings: (i) a centralized approach where the intruder has full knowledge of the system model but can partially observe the system behavior; (ii) a decentralized approach where a set of intruders can observe different event sets and collaborate with a coordinator to disclose the same secret. Finally, experimental results are presented to demonstrate the efficiency of the proposed method.