Revelation Time for Initial-State Opacity Measurement in Timed Discrete Event Systems

The reliance of many emerging applications on shared cyber-infrastructures has prompted the study of various notions for security and privacy, including notions for deterministic, non-deterministic, and probabilistic systems. The main contribution of this work is to extend these ideas to timed stochastic systems, by introducing and analyzing timing aspects of initial-state opacity, as measures of vulnerability to security violations. More specifically, we consider partially observed stochastic Petri net (POSPN) models that behave according to Markovian dynamics. We assume that certain events are observable to an outside observer (intruder) and we are interested in initial-state opacity, i.e., determining whether an intruder can infer that the initial marking of the system necessarily lies within a given secret set of initial states. In case initial-state opacity is violated for some behavior in the system, we are also interested in knowing how much time the system remains safe before this violation occurs.