Synthesis of opaque systems with static and dynamic masks

Abstract

Opacity is a security property formalizing the absence of secret information leakage and we address in this paper the problem of synthesizing opaque systems. A secret predicate S over the runs of a system G is opaque to an external user having partial observability over G, if s/he can never infer from the observation of a run of G that the run belongs to S. We choose to control the observability of events by adding a device, called a mask, between the system G and the users. We first investigate the case of static partial observability where the set of events the user can observe is fixed a priori by a static mask. In this context, we show that checking whether a system is opaque is PSPACE-complete, which implies that computing an optimal static mask ensuring opacity is also a PSPACE-complete problem. Next, we introduce dynamic partial observability where the set of events the user can observe changes over time and is chosen by a dynamic mask. We show how to check that a system is opaque w.r.t. to a dynamic mask and also address the corresponding synthesis problem: given a system G and secret states S, compute the set of dynamic masks under which S is opaque. Our main result is that the set of such masks can be finitely represented and can be computed in EXPTIME and this is a lower bound. Finally we also address the problem of computing an optimal mask.

Opacity with powerful attackers

“…Our approach does not only consist of checking whether opacity holds, but also provides the means to control a system in such a way that observed traces are not sufficient to decide whether the current state of the system is a secret one. Another enforcement technique was proposed by Cassez et al (2012). This approach consists of dynamically changing the observation of an attacker using masks that hide a subset of transition labels that would otherwise be seen by the attacker.…”

“…The verification of opacity is then reduced to the question of reachability of F = 2 S in Det A (G). This verification is PSPACE-complete (Cassez et al, 2012) in the standard setting where attackers observe only a subset of the labels attached to transitions (defined as attacker A 1 later in this section). As G is deterministic, Proposition 1 can be rephrased as a property of Det A (G).…”

“…The secret S is not opaque w.r.t. A 1 whenever there exists µ ∈ T r A1 (G) such that ∆ o (X o , µ) ⊆ S and the verification is reduced to a reachability problem as described in Cassez et al (2012).…”

“…For the hardness, one can reuse the results of (Cassez et al, 2012), showing that opacity with observers that simply read projections of runs on Σ o is PSPACEcomplete.…”

Diagnosis and opacity problems for infinite state systems modeled by recursive tile systems

“…The opacity problem consists in determining whether an observer, who knows the system's behavior but who imperfectly observes it, is able to reconstruct critical information (e.g., a password stored in a file, the value of some hidden variables, etc.). More precisely, the setting of state-based opacity (Cassez et al 2012) considers a discrete event system having a subset of unobservable events, and a subset of secret states. Then the problem amounts to determining whether it is possible to infer, from observation of the system, if it has reached a secret state.…”