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Opacity, as an important property in information-flow security, characterizesthe ability of a system to keep some secret information from an intruder. Indiscrete-event systems, based on a standard setting in which an intruder hasthe complete knowledge of the system's structure, the standard versions ofcurrent-state opacity and initial-state opacity cannot perfectly characterizehigh-level privacy requirements. To overcome such a limitation, in this paperwe propose two stronger versions of opacity in partially-observeddiscrete-event systems, called \emph{strong current-state opacity} and\emph{strong initial-state opacity}. Strong current-state opacity describesthat an intruder never makes for sure whether a system is in a secret state atthe current time, that is, if a system satisfies this property, then for eachrun of the system ended by a secret state, there exists a non-secret run whoseobservation is the same as that of the previous run. Strong initial-stateopacity captures that the visit of a secret state at the initial time cannot beinferred by an intruder at any instant. Specifically, a system is said to bestrongly initial-state opaque if for each run starting from a secret state,there exists a non-secret run of the system that has the same observation asthe previous run has. To verify these two properties, we propose twoinformation structures using a novel concurrent-composition technique, whichhas exponential-time complexity$O(|X|^4|\Sigma_o||\Sigma_{uo}||\Sigma|2^{|X|})$, where $|X|$ (resp.,$|\Sigma|$, $|\Sigma_o|$, $|\Sigma_{uo}|$) is the number of states (resp.,events, observable events, unobservable events) of a system.

Strong current-state and initial-state opacity of discrete-event systems