Skip to main content

# Dynamic observers for the synthesis of opaque systems

## Authors

Franck Cassez, Jérémy Dubreil and Hervé Marchand

NICTA

Irisa

## Abstract

In this paper, we address the problem of synthesizing \emph{opaque} systems. A secret predicate $S$ over the runs of a system $G$ is \emph{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 first investigate the case of \emph{static} partial observability where the set of events the user can observe is fixed a priori. In this context, we show that checking whether a system is opaque is PSPACE-complete, which implies that computing an optimal static observer ensuring opacity is also a PSPACE-complete problem.

Next, we introduce \emph{dynamic} partial observability where the set of events the user can observe changes over time.

We show how to check that a system is opaque \wrt to a dynamic observer and also address the corresponding synthesis problem: given a system $G$ and secret states $S$, compute the set of dynamic observers under which $S$ is opaque. Our main result is that the set of such observers can be finitely represented and can be computed in EXPTIME.

## BibTeX Entry

  @techreport{Cassez_DM_09:tr,
author           = {Cassez, Franck and Dubreil, Jérémy and Marchand, Hervé},
number           = {1930},
month            = oct,
year             = {2009},
keywords         = {security, opacity, dynamic observation},
title            = {Dynamic Observers for the Synthesis of Opaque Systems},
type             = {Technical Report},
institution      = {IRISA},
address          = {Rennes, France}
}

## Download

Served by Apache on Linux on seL4.