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Quantifying opacity†

Published online by Cambridge University Press:  12 November 2014

BÉATRICE BÉRARD ,
JOHN MULLINS  and
MATHIEU SASSOLAS
BÉATRICE BÉRARD
Affiliation:
Sorbonne Université, Université P. & M. Curie, LIP6, CNRS UMR 7606, Paris, France Email: beatrice.berard@lip6.fr
JOHN MULLINS
Affiliation:
École Polytechnique de Montréal, Dept. of Comp. & Soft. Eng., Montreal (Quebec), Canada Email: john.mullins@polymtl.ca
MATHIEU SASSOLAS*
Affiliation:
Sorbonne Université, Université P. & M. Curie, LIP6, CNRS UMR 7606, Paris, France Email: beatrice.berard@lip6.fr Université Paris-Est, LACL, Créteil, France Email: mathieu.sassolas@u-pec.fr
*
‡Corresponding author: mathieu.sassolas@u-pec.fr – Université Paris-Est, LACL, 61 avenue du Général de gaulle, F-94010 Créteil Cedex, France.
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Abstract

Opacity is a general language-theoretic framework in which several security properties of a system can be expressed. Its parameters are a predicate, given as a subset of runs of the system, and an observation function, from the set of runs into a set of observables. The predicate describes secret information in the system and, in the possibilistic setting, it is opaque if its membership cannot be inferred from observation.

In this paper, we propose several notions of quantitative opacity for probabilistic systems, where the predicate and the observation function are seen as random variables. Our aim is to measure (i) the probability of opacity leakage relative to these random variables and (ii) the level of uncertainty about membership of the predicate inferred from observation. We show how these measures extend possibilistic opacity, we give algorithms to compute them for regular secrets and observations, and we apply these computations on several classical examples. We finally partially investigate the non-deterministic setting.

Type
Special Issue: Quantitative Information Flow
Information
Mathematical Structures in Computer Science , Volume 25 , Issue 2: Quantitative Information Flow , February 2015 , pp. 361 - 403
Copyright
Copyright © Cambridge University Press 2014 

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Footnotes

†

Part of this work has been published in the proceedings of Qest'10 (Bérard et al. 2010).

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