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DOI: 10.4230/LIPIcs.FSTTCS.2017.13
URN: urn:nbn:de:0030-drops-83844
URL: http://drops.dagstuhl.de/opus/volltexte/2018/8384/
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Bérard, Béatrice ; Haddad, Serge ; Lefaucheux, Engel

Probabilistic Disclosure: Maximisation vs. Minimisation

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LIPIcs-FSTTCS-2017-13.pdf (0.6 MB)


Abstract

We consider opacity questions where an observation function provides to an external attacker a view of the states along executions and secret executions are those visiting some state from a fixed subset. Disclosure occurs when the observer can deduce from a finite observation that the execution is secret, the epsilon-disclosure variant corresponding to the execution being secret with probability greater than 1 - epsilon. In a probabilistic and non deterministic setting, where an internal agent can choose between actions, there are two points of view, depending on the status of this agent: the successive choices can either help the attacker trying to disclose the secret, if the system has been corrupted, or they can prevent disclosure as much as possible if these choices are part of the system design. In the former situation, corresponding to a worst case, the disclosure value is the supremum over the strategies of the probability to disclose the secret (maximisation), whereas in the latter case, the disclosure is the infimum (minimisation). We address quantitative problems (comparing the optimal value with a threshold) and qualitative ones (when the threshold is zero or one) related to both forms of disclosure for a fixed or finite horizon. For all problems, we characterise their decidability status and their complexity. We discover a surprising asymmetry: on the one hand optimal strategies may be chosen among deterministic ones in maximisation problems, while it is not the case for minimisation. On the other hand, for the questions addressed here, more minimisation problems than maximisation ones are decidable.

BibTeX - Entry

@InProceedings{brard_et_al:LIPIcs:2018:8384,
  author =	{B{\'e}atrice B{\'e}rard and Serge Haddad and Engel Lefaucheux},
  title =	{{Probabilistic Disclosure: Maximisation vs. Minimisation}},
  booktitle =	{37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)},
  pages =	{13:1--13:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-055-2},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{93},
  editor =	{Satya Lokam and R. Ramanujam},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8384},
  URN =		{urn:nbn:de:0030-drops-83844},
  doi =		{10.4230/LIPIcs.FSTTCS.2017.13},
  annote =	{Keywords: Partially observed systems, Opacity, Markov chain, Markov decision process}
}

Keywords: Partially observed systems, Opacity, Markov chain, Markov decision process
Seminar: 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017)
Issue Date: 2018
Date of publication: 26.01.2018


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