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Synthesis of opaque systems with static and dynamic masks

Franck Cassez 1 Jérémy Dubreil 2 Hervé Marchand 3 
2 COMETE - Concurrency, Mobility and Transactions
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
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.
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Submitted on : Tuesday, January 24, 2012 - 2:09:26 PM
Last modification on : Wednesday, February 2, 2022 - 3:58:48 PM
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Franck Cassez, Jérémy Dubreil, Hervé Marchand. Synthesis of opaque systems with static and dynamic masks. Formal Methods in System Design, Springer Verlag, 2012, 40 (1), pp.88-115. ⟨10.1007/s10703-012-0141-9⟩. ⟨hal-00662539⟩



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