Opacity for linear constraint Markov chains

On a partially observed system, a secret φ is opaque if an observer cannot ascertain that its trace belongs to φ. We consider specifications given as Constraint Markov Chains (CMC), which are underspecified Markov chains where probabilities on edges are required to belong to some set. The nondeterminism is resolved by a scheduler, and opacity on this model is defined as a worst case measure over all implementations obtained by scheduling. This measures the information obtained by a passive observer when the system is controlled by the smartest scheduler in coalition with the observer. When restricting to the subclass of Linear CMC, we compute (or approximate) this measure and prove that refinement of a specification can only improve opacity.

[1]  Axel Legay,et al.  Maximizing entropy over Markov processes , 2013, J. Log. Algebraic Methods Program..

[2]  Kim Guldstrand Larsen,et al.  Specification and refinement of probabilistic processes , 1991, [1991] Proceedings Sixth Annual IEEE Symposium on Logic in Computer Science.

[3]  Krishnendu Chatterjee,et al.  Probabilistic opacity for Markov decision processes , 2014, Inf. Process. Lett..

[4]  Olga Kouchnarenko,et al.  Preserving opacity on Interval Markov Chains under simulation , 2016, 2016 13th International Workshop on Discrete Event Systems (WODES).

[5]  Pavol Cerný,et al.  Preserving Secrecy Under Refinement , 2006, ICALP.

[6]  Roberto Segala,et al.  Modeling and verification of randomized distributed real-time systems , 1996 .

[7]  Jean-Philippe Vial,et al.  Theory and algorithms for linear optimization - an interior point approach , 1998, Wiley-Interscience series in discrete mathematics and optimization.

[8]  Maciej Koutny,et al.  Opacity generalised to transition systems , 2005, International Journal of Information Security.

[9]  James Worrell,et al.  LTL Model Checking of Interval Markov Chains , 2013, TACAS.

[10]  Krishnendu Chatterjee,et al.  Model-Checking omega-Regular Properties of Interval Markov Chains , 2008, FoSSaCS.

[11]  J. Norris.  Appendix: probability and measure , 1997 .

[12]  Mathieu Sassolas,et al.  Quantifying Opacity , 2010, QEST.

[13]  Mahesh Viswanathan,et al.  Model-Checking Markov Chains in the Presence of Uncertainties , 2006, TACAS.

[14]  Nir Piterman,et al.  From Nondeterministic Buchi and Streett Automata to Deterministic Parity Automata , 2006, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06).

[15]  Christel Baier,et al.  Comparative branching-time semantics for Markov chains , 2005, Inf. Comput..

[16]  David Chaum,et al.  The dining cryptographers problem: Unconditional sender and recipient untraceability , 1988, Journal of Cryptology.

[17]  Michael R. Clarkson,et al.  Hyperproperties , 2008, 2008 21st IEEE Computer Security Foundations Symposium.

[18]  Christoforos N. Hadjicostis,et al.  Current-State Opacity Formulations in Probabilistic Finite Automata , 2014, IEEE Transactions on Automatic Control.

[19]  Sachin Lodha,et al.  Probabilistic Anonymity , 2007, PinKDD.

[20]  Christel Baier,et al.  Principles of Model Checking (Representation and Mind Series) , 2008 .

[21]  Kim G. Larsen,et al.  Constraint Markov Chains , 2011, Theor. Comput. Sci..

[22]  Laurent Mazaré,et al.  Decidability of Opacity with Non-Atomic Keys , 2004, Formal Aspects in Security and Trust.

[23]  Benoît Delahaye,et al.  Consistency for Parametric Interval Markov Chains , 2015, SynCoP.

[24]  Moshe Y. Vardi.  Automatic verification of probabilistic concurrent finite state programs , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).