Abstract
Opacity is an information flow property that captures the notion of plausible deniability in dynamic systems, that is whether an intruder can deduce that “secret” behavior has occurred. In this paper we provide a general framework of opacity to unify the many existing notions of opacity that exist for discrete event systems. We use this framework to discuss language-based and state-based notions of opacity over automata. We present several methods for language-based opacity verification, and a general approach to transform state-based notions into language-based ones. We demonstrate this approach for current-state and initial-state opacity, unifying existing results. We then investigate the notions of K-step opacity. We provide a language-based view of K-step opacity encompassing two existing notions and two new ones. We then analyze the corresponding language-based verification methods both formally and with numerical examples. In each case, the proposed methods offer significant reductions in runtime and space complexity.
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Notes
While Hep,2 could be designed to be deterministic, our nondeterministic Hep,2 offers reduced complexity.
The library is available at https://gitlab.eecs.umich.edu/M-DES-tools/desops/.
References
Bérard B, Mullins J, Sassolas M (2015) Quantifying Opacity. Math Struct Comput Sci 25 (2):361–403. https://doi.org/10.1017/S0960129513000637, arXiv:1301.6799
Bérard B, Haar S, Schmitz S, Schwoon S (2017) The Complexity of Diagnosability and Opacity Verification for Petri Nets. In Application and Theory of Petri Nets and Concurrency (pp. 200–220). Springer International Publishing. https://doi.org/10.1007/978-3-319-57861-3_13
Bryans J, Koutny M, Ryan P (2005) Modelling Opacity Using Petri Nets. Electr Notes Theor Comput Sci 121:101–115. https://doi.org/10.1016/j.entcs.2004.10.010
Bryans J W, Koutny M, Mazaré L, Ryan P Y A (2008) Opacity generalised to transition systems. Int J Inf Secur 7(6):421–435. https://doi.org/10.1007/s10207-008-0058-x
Cassandras C G, Lafortune S (2008) Introduction to discrete event systems, 2nd edn. Springer, New York
Cassez F (2009) The Dark Side of Timed Opacity. In: Park J H, Chen H-H, Atiquzzaman M, Lee C, Kim T-, Yeo S-S (eds) Advances in Information Security and Assurance, Lecture Notes in Computer Science. Springer, Berlin, pp 21–30
Cassez F, Dubreil J, Marchand H (2009) Dynamic Observers for the Synthesis of Opaque Systems. In: Liu Z, Ravn A P (eds) Automated Technology for Verification and Analysis, Lecture Notes in Computer Science. Springer, Berlin, pp 352–367
Clarkson M R, Finkbeiner B, Koleini M, Micinski K K, Rabe M N, Sãnchez C (2014) Temporal Logics for Hyperproperties. In: Abadi M, Kremer S (eds) Principles of Security and Trust, Lecture Notes in Computer Science. Springer, Berlin, pp 265–284
Doyen L, Raskin J-F (2009) Antichains for the Automata-Based Approach to Model-Checking. Log Methods Comput Sci 5(1):5. https://doi.org/10.2168/LMCS-5(1:5)2009, arXiv:0902.3958
Dubreil J, Darondeau P, Marchand H (2010) Supervisory Control for Opacity. IEEE Trans Autom Control 55(5):1089–1100. https://doi.org/10.1109/TAC.2010.2042008, IEEE Transactions on Automatic Control
Falcone Y, Marchand H (2013) Runtime Enforcement of K-step Opacity, pp 7271–7278. https://doi.org/10.1109/CDC.2013.6761043
Falcone Y, Marchand H (2015) Enforcement and validation (at runtime) of various notions of opacity. Discret Event Dyn Syst 25(4):531–570. https://doi.org/10.1007/s10626-014-0196-4
Focardi R, Gorrieri R, Martinelli F (2000) Non Interference for the Analysis of Cryptographic Protocols. In: Montanari U, Rolim J D P, Welzl E (eds) Automata, Languages and Programming, Lecture Notes in Computer Science. Springer, Berlin, pp 354–372
Hadjicostis C N (2020) Introduction to Estimation and Inference in Discrete Event Systems. In: Hadjicostis C N (ed) Estimation and Inference in Discrete Event Systems: A Model-Based Approach with Finite Automata, Communications and Control Engineering. Springer International Publishing, Cham, pp 1–14. https://doi.org/10.1007/978-3-030-30821-6_1
Jacob R, Lesage J-J, Faure J-M (2016) Overview of discrete event systems opacity: Models, validation, and quantification. Annu Rev Control 41:135–146. https://doi.org/10.1016/j.arcontrol.2016.04.015, https://www.sciencedirect.com/science/article/pii/S1367578816300189
Lan H, Tong Y, Guo J, Giua A (2020) Comments on “A new approach for the verification of infinite-step and K-step opacity using two-way observers”? [Automatica 80 (2017) 162–171]. Automatica 122:109290. https://doi.org/10.1016/j.automatica.2020.109290, https://www.sciencedirect.com/science/article/pii/S0005109820304891
Lin F (2011) Opacity of discrete event systems and its applications. Automatica 47(3):496–503. https://doi.org/10.1016/j.automatica.2011.01.002, http://www.sciencedirect.com/science/article/pii/S0005109811000173
Masopust T, Yin X (2019) Complexity of detectability, opacity and A-diagnosability for modular discrete event systems. Automatica 101:290–295. https://doi.org/10.1016/j.automatica.2018.12.019, https://linkinghub.elsevier.com/retrieve/pii/S0005109818306253
Mazaré L (2004) Using unification for opacity properties. In: Proceedings of the Workshop on Issues in the Theory of Security (wits’04), pp 165–176
Reiter M K, Rubin A D (1998) Crowds: anonymity for Web transactions. ACM Trans Inf Syst Secur 1(1):66–92. https://doi.org/10.1145/290163.290168
Saboori A, Hadjicostis C N (2009a) Verification of K-step opacity and analysis of its complexity. In: Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, pp 205–210. ISSN: 0191-2216
Saboori A, Hadjicostis C N (2009b) Verification of infinite-step opacity and analysis of its complexity*. IFAC Proc Vol 42(5):46–51. https://doi.org/10.3182/20090610-3-IT-4004.00013, https://www.sciencedirect.com/science/article/pii/S1474667015355944
Saboori A, Hadjicostis C N (2007) Notions of security and opacity in discrete event systems. In: 2007 46th IEEE Conference on Decision and Control, pp 5056–5061. ISSN: 0191-2216
Saboori A, Hadjicostis C N (2008) Verification of initial-state opacity in security applications of DES. In: 2008 9th International Workshop on Discrete Event Systems, pp 328–333
Stockmeyer L J, Meyer A R (1973) Word problems requiring exponential time(Preliminary Report). In: Proceedings of the fifth annual ACM symposium on Theory of computing, STOC ’73. https://doi.org/10.1145/800125.804029. Association for Computing Machinery, New York, pp 1–9
Tong Y, Li Z, Seatzu C, Giua A (2017) Verification of State-Based Opacity Using Petri Nets. IEEE Trans Autom Control 62(6):2823–2837. https://doi.org/10.1109/TAC.2016.2620429. IEEE Transactions on Automatic Control
Willems J C (2007) The Behavioral Approach to Open and Interconnected Systems. IEEE Control Syst Mag 27(6):46–99. https://doi.org/10.1109/MCS.2007.906923. IEEE Control Systems Magazine
Wintenberg A, Blischke M, Lafortune S, Ozay N (2021) A General Language-Based Framework for Specifying and Verifying Notions of Opacity. arXiv:2103.10501
Wu Y-C, Lafortune S (2013) Comparative analysis of related notions of opacity in centralized and coordinated architectures. Discret Event Dyn Syst 23 (3):307–339. https://doi.org/10.1007/s10626-012-0145-z
Wu Y-C, Lafortune S (2014) Synthesis of insertion functions for enforcement of opacity security properties. Automatica 50(5):1336–1348. https://doi.org/10.1016/j.automatica.2014.02.038, https://www.sciencedirect.com/science/article/pii/S0005109814000764
Wu Y-C, Raman V, Rawlings B C, Lafortune S, Seshia S A (2018) Synthesis of Obfuscation Policies to Ensure Privacy and Utility. J Autom Reason 60(1):107–131. https://doi.org/10.1007/s10817-017-9420-x
Wu Y-C, Sankararaman K A, Lafortune S (2014) Ensuring Privacy in Location-Based Services: An Approach Based on Opacity Enforcement. IFAC Proc Vol 47 (2):33–38. https://doi.org/10.3182/20140514-3-FR-4046.00008, https://linkinghub.elsevier.com/retrieve/pii/S1474667015373778
Yin X, Lafortune S (2017) A new approach for the verification of infinite-step and K-step opacity using two-way observers. Automatica 80:162–171. https://doi.org/10.1016/j.automatica.2017.02.037, http://www.sciencedirect.com/science/article/pii/S0005109817301115
Yin X, Li Z, Wang W, Li S (2017) Infinite-step opacity of stochastic discrete-event systems. In: 2017 11th Asian Control Conference (ASCC), pp 102–107
Yin X, Zamani M, Liu S (2020) On Approximate Opacity of Cyber-Physical Systems. IEEE Trans Autom Control:1–1. https://doi.org/10.1109/TAC.2020.2998733, IEEE Transactions on Automatic Control
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The authors would like to thank the reviewers for their useful and very detailed comments. They were most helpful in improving the paper for clarity and precision.
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Guest Editors: Rong Su and Carlos Basilio
Research supported in part by US NSF under grants CNS-1738103, CNS-1801342, and ECCS-1553873.
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Wintenberg, A., Blischke, M., Lafortune, S. et al. A general language-based framework for specifying and verifying notions of opacity. Discrete Event Dyn Syst 32, 253–289 (2022). https://doi.org/10.1007/s10626-021-00357-x
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DOI: https://doi.org/10.1007/s10626-021-00357-x