Document Open Access Logo

Probabilistic Disclosure: Maximisation vs. Minimisation

Authors Béatrice Bérard, Serge Haddad, Engel Lefaucheux



PDF
Thumbnail PDF

File

LIPIcs.FSTTCS.2017.13.pdf
  • Filesize: 0.56 MB
  • 14 pages

Document Identifiers

Author Details

Béatrice Bérard
Serge Haddad
Engel Lefaucheux

Cite AsGet BibTex

Béatrice Bérard, Serge Haddad, and Engel Lefaucheux. Probabilistic Disclosure: Maximisation vs. Minimisation. In 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 93, pp. 13:1-13:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.FSTTCS.2017.13

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.
Keywords
  • Partially observed systems
  • Opacity
  • Markov chain
  • Markov decision process

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads

References

  1. C. Baier and J.-P. Katoen. Principles of model checking. MIT Press, 2008. Google Scholar
  2. Boaz Barak, Oded Goldreich, Russell Impagliazzo, Steven Rudich, Amit Sahai, Salil P. Vadhan, and Ke Yang. On the (im)possibility of obfuscating programs. In Joe Kilian, editor, Advances in Cryptology - CRYPTO 2001, 21st Annual International Cryptology Conference, Santa Barbara, California, USA, August 19-23, 2001, Proceedings, volume 2139 of Lecture Notes in Computer Science, pages 1-18. Springer, 2001. URL: http://dx.doi.org/10.1007/3-540-44647-8_1.
  3. Béatrice Bérard, Krishnendu Chatterjee, and Nathalie Sznajder. Probabilistic opacity for markov decision processes. Inf. Process. Lett., 115(1):52-59, 2015. URL: http://dx.doi.org/10.1016/j.ipl.2014.09.001.
  4. Béatrice Bérard, Olga Kouchnarenko, John Mullins, and Mathieu Sassolas. Preserving opacity on interval markov chains under simulation. In Christos G. Cassandras, Alessandro Giua, and Zhiwu Li, editors, 13th International Workshop on Discrete Event Systems, WODES 2016, Xi'an, China, May 30 - June 1, 2016, pages 319-324. IEEE, 2016. URL: http://dx.doi.org/10.1109/WODES.2016.7497866.
  5. Béatrice Bérard, John Mullins, and Mathieu Sassolas. Quantifying opacity. Mathematical Structures in Computer Science, 25(2):361-403, 2015. URL: http://dx.doi.org/10.1017/S0960129513000637.
  6. Dietmar Berwanger and Laurent Doyen. On the power of imperfect information. In Ramesh Hariharan, Madhavan Mukund, and V. Vinay, editors, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2008, December 9-11, 2008, Bangalore, India, volume 2 of LIPIcs, pages 73-82. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2008. URL: http://dx.doi.org/10.4230/LIPIcs.FSTTCS.2008.1742.
  7. Jeremy Bryans, Maciej Koutny, Laurent Mazaré, and Peter Y. A. Ryan. Opacity generalised to transition systems. Int. J. Inf. Sec., 7(6):421-435, 2008. URL: http://dx.doi.org/10.1007/s10207-008-0058-x.
  8. Krishnendu Chatterjee, Laurent Doyen, Hugo Gimbert, and Thomas A. Henzinger. Randomness for free. In Petr Hlinený and Antonín Kucera, editors, Mathematical Foundations of Computer Science 2010, 35th International Symposium, MFCS 2010, Brno, Czech Republic, August 23-27, 2010. Proceedings, volume 6281 of Lecture Notes in Computer Science, pages 246-257. Springer, 2010. URL: http://dx.doi.org/10.1007/978-3-642-15155-2_23.
  9. Krishnendu Chatterjee, Laurent Doyen, and Thomas A. Henzinger. Qualitative analysis of partially-observable markov decision processes. In Petr Hlinený and Antonín Kucera, editors, Mathematical Foundations of Computer Science 2010, 35th International Symposium, MFCS 2010, Brno, Czech Republic, August 23-27, 2010. Proceedings, volume 6281 of Lecture Notes in Computer Science, pages 258-269. Springer, 2010. URL: http://dx.doi.org/10.1007/978-3-642-15155-2_24.
  10. Krishnendu Chatterjee, Koushik Sen, and Thomas A. Henzinger. Model-checking omega-regular properties of interval markov chains. In Roberto M. Amadio, editor, Foundations of Software Science and Computational Structures, 11th International Conference, FOSSACS 2008, Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2008, Budapest, Hungary, March 29 - April 6, 2008. Proceedings, volume 4962 of Lecture Notes in Computer Science, pages 302-317. Springer, 2008. URL: http://dx.doi.org/10.1007/978-3-540-78499-9_22.
  11. Hugo Gimbert and Youssouf Oualhadj. Probabilistic automata on finite words: Decidable and undecidable problems. In Samson Abramsky, Cyril Gavoille, Claude Kirchner, Friedhelm Meyer auf der Heide, and Paul G. Spirakis, editors, Automata, Languages and Programming, 37th International Colloquium, ICALP 2010, Bordeaux, France, July 6-10, 2010, Proceedings, Part II, volume 6199 of Lecture Notes in Computer Science, pages 527-538. Springer, 2010. URL: http://dx.doi.org/10.1007/978-3-642-14162-1_44.
  12. Jean Goubault-Larrecq and Roberto Segala. Random measurable selections. In Franck van Breugel, Elham Kashefi, Catuscia Palamidessi, and Jan Rutten, editors, Horizons of the Mind. A Tribute to Prakash Panangaden - Essays Dedicated to Prakash Panangaden on the Occasion of His 60th Birthday, volume 8464 of Lecture Notes in Computer Science, pages 343-362. Springer, 2014. URL: http://dx.doi.org/10.1007/978-3-319-06880-0_18.
  13. D. J. D. Hughes and V. Shmatikov. Information Hiding, Anonymity and Privacy: a Modular Approach. Journal of Computer Security, 12(1):3-36, 2004. Google Scholar
  14. Laurent Mazaré. Decidability of opacity with non-atomic keys. In Theodosis Dimitrakos and Fabio Martinelli, editors, Formal Aspects in Security and Trust: Second IFIP TC1 WG1.7 Workshop on Formal Aspects in Security and Trust (FAST), an event of the 18th IFIP World Computer Congress, August 22-27, 2004, Toulouse, France, volume 173 of IFIP, pages 71-84. Springer, 2004. URL: http://dx.doi.org/10.1007/0-387-24098-5_6.
  15. Christos H. Papadimitriou and John N. Tsitsiklis. The complexity of markov decision processes. Math. Oper. Res., 12(3):441-450, 1987. URL: http://dx.doi.org/10.1287/moor.12.3.441.
  16. A. Paz. Introduction to Probabilistic Automata. Academic Press, 1971. Google Scholar
  17. Anooshiravan Saboori and Christoforos N. Hadjicostis. Current-state opacity formulations in probabilistic finite automata. IEEE Trans. Automat. Contr., 59(1):120-133, 2014. URL: http://dx.doi.org/10.1109/TAC.2013.2279914.
  18. Koushik Sen, Mahesh Viswanathan, and Gul Agha. Model-checking markov chains in the presence of uncertainties. In Holger Hermanns and Jens Palsberg, editors, Tools and Algorithms for the Construction and Analysis of Systems, 12th International Conference, TACAS 2006 Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2006, Vienna, Austria, March 25 - April 2, 2006, Proceedings, volume 3920 of Lecture Notes in Computer Science, pages 394-410. Springer, 2006. URL: http://dx.doi.org/10.1007/11691372_26.
  19. M. Sipser. Introduction to the theory of computation. Thomson Course Technology, 2006. Google Scholar
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail