Notions of security and opacity in discrete event systems

Abstract

In this paper, we follow a state-based approach to extend the notion of opacity in computer security to discrete event systems. A system is (S, P )-opaque if the evolution of its true state through a set of secret states S remains opaque to an observer who is observing activity in the system through the projection map P . In other words, based on observations through the mapping P , the observer is never certain that the current state of the system is within the set of secret states S. We also introduce the stronger notion of (S, P, K)-opacity which requires opacity to remain true for K observations following the departure of the system's state from the set S. We show that the state-based definition of opacity enables the use of observer constructions for verification purposes. In particular, the verification of (S, P, K)-opacity is accomplished via an observer with K-delay which is constructed to capture state estimates with K-delay. These are the estimates of the state of the system K observations ago and are consistent with all observations (including the last K observations). We also analyze the properties and complexity of the observer with Kdelay.

Opaque superlanguages and sublanguages in discrete event systems

“…The natural projection P : Σ * −→ Σ * o used in [2], [9] and most other papers, where Σ o ⊆ Σ is a subset of observable events, is a special case of observation mapping. In general, however, θ can be any observation mapping, not restricted to the natural projection.…”

“…Motivated by security applications where the information flow in the system needs to be kept secret (that is, opaque) to outside observers or intruders, opacity has recently been investigated in the framework of discrete event systems [9]- [13]. The objective of opacity is to investigate security and privacy of a system; and therefore opacity requires that the system's secret behavior is opaque to an external observer who is able to observe some events that occur in the system.…”

“…The objective of opacity is to investigate security and privacy of a system; and therefore opacity requires that the system's secret behavior is opaque to an external observer who is able to observe some events that occur in the system. The notion of opacity in computer security has been extended in [9] to DES. It follows a state-based approach in [9] where opacity requires that the intruder can never be certain that the current state of the system is in a set of secret states.…”

“…The notion of opacity in computer security has been extended in [9] to DES. It follows a state-based approach in [9] where opacity requires that the intruder can never be certain that the current state of the system is in a set of secret states. A language-based approach [13] requires that none of the multiple observers with different observation capabilities is able to determine whether the actual behavior of the system belongs to a secret language.…”

Opacity of discrete event systems and its applications

“…Secrecy has been studied before, for example, in [1] [5] [2] [6] [22]. In [2], for a finite state system with partial observers and for each observer, a secret is defined as a subset of trajectories.…”