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F. Cassez, J. Dubreil, H. Marchand. Synthesis of Opaque Systems with Static and Dynamic Masks. Formal Methods in System Design, 40(1):88-115, 2012.

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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


Jérémy Dubreil
Hervé Marchand http://www.irisa.fr/prive/hmarchan

BibTex Reference

   Author = {Cassez, F. and Dubreil, J. and Marchand, H.},
   Title = {Synthesis of Opaque Systems with Static and Dynamic Masks},
   Journal = {Formal Methods in System Design},
   Volume = {40},
   Number = {1},
   Pages = {88--115},
   Year = {2012}

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