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Statistical Model Checking for Probabilistic Hyperproperties of Real-Valued Signals

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Model Checking Software (SPIN 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13255))

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Abstract

Many security-related properties—such as non-interference—cannot be captured by traditional trace-based specification formalisms such as LTL. The reason is that they relate the events of two (or more) traces of the system, and LTL can only reason on one execution at a time. A number of hyper-property extensions of LTL have been proposed in the past few years, and case studies showing their ability to express interesting properties have also been shown. However, there has been less attention to hyper-properties for quantitative (timed) systems as well as very little work on developing a practically useful tool. Instead existing work focused on using ad-hoc implementations.

In this paper we present a probabilistic hyper-property logic HPSTL for stochastic hybrid and timed systems and we show how to integrate the logic into existing statistical model checking tools. To show the feasibility of our approach we integrate the technique into a prototype implementation inside Uppaal  SMC and apply it to the analysis of three side-channel attack examples. To our knowledge this is the first full implementation of a hyper logic inside a fully-fledged modelling environment.

Work partially sponsored by the ERC Advanced Grant LASSO, the Villum Investigator Grant S4OS, Danish National Research Center DIREC as well as the FNRS PDR/OL project T.0137.21.

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Notes

  1. 1.

    Here \(s_i\in Z_i\) is a shorthand for \(s_i(z_o)\in \zeta _i^o\) for any \(o=1\ldots l\).

  2. 2.

    For formulas involving multiple path formulas there are multiple monitors as well.

  3. 3.

    The Uppaal models and scripts for reproducing the results in the paper is available from https://github.com/dannybpoulsen/HyperPropertiesModels.

  4. 4.

    Note that to highlight the differences, we have elided the graph for the “worst case” running time (which always has probability = 1, since both branches take the same amount of time).

References

  1. Ábrahám, E., Bartocci, E., Bonakdarpour, B., Dobe, O.: Probabilistic hyperproperties with nondeterminism. In: Hung, D.V., Sokolsky, O. (eds.) ATVA 2020. LNCS, vol. 12302, pp. 518–534. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59152-6_29

    Chapter  Google Scholar 

  2. Ábrahám, E., Bonakdarpour, B.: HyperPCTL: a temporal logic for probabilistic hyperproperties. In: McIver, A., Horvath, A. (eds.) QEST 2018. LNCS, vol. 11024, pp. 20–35. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99154-2_2

    Chapter  Google Scholar 

  3. Agat, J.: Transforming out timing leaks. In: Proceedings of the Annual ACM Symposium on Principles of Programming Languages (POPL 2000), pp. 40–53 (2000)

    Google Scholar 

  4. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994). https://doi.org/10.1016/0304-3975(94)90010-8

    Article  MathSciNet  MATH  Google Scholar 

  5. Bonakdarpour, B., Sanchez, C., Schneider, G.: Monitoring hyperproperties by combining static analysis and runtime verification. In: Margaria, T., Steffen, B. (eds.) ISoLA 2018. LNCS, vol. 11245, pp. 8–27. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03421-4_2

    Chapter  Google Scholar 

  6. Bulychev, P., David, A., Larsen, K.G., Legay, A., Li, G., Poulsen, D.B.: Rewrite-based statistical model checking of WMTL. In: Qadeer, S., Tasiran, S. (eds.) RV 2012. LNCS, vol. 7687, pp. 260–275. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-35632-2_25

    Chapter  Google Scholar 

  7. Chaum, D.: The dining cryptographers problem: Unconditional sender and recipient untraceability. J. Cryptology 1, 65–75 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Clarkson, M.R., Finkbeiner, B., Koleini, M., Micinski, K.K., Rabe, M.N., Sánchez, C.: Temporal logics for hyperproperties. In: Abadi, M., Kremer, S. (eds.) POST 2014. LNCS, vol. 8414, pp. 265–284. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-642-54792-8_15

    Chapter  Google Scholar 

  9. Clarkson, M.R., Schneider, F.B.: Hyperproperties. J. Comput. Secur. 18(6), 1157–1210 (2010)

    Article  Google Scholar 

  10. Clopper, C.J., Pearson, E.S.: The use of confidence or fiducial limits illustrated in the case of the binomial. Biometrika 26(4), 404–413 (1934). http://www.jstor.org/stable/2331986

  11. David, A., Larsen, K.G., Legay, A., Mikucionis, M., Poulsen, D.B.: Uppaal SMC tutorial. Int. J. Softw. Tools Technol. Transf. 17(4), 397–415 (2015), https://doi.org/10.1007/s10009-014-0361-y

  12. David, A., Larsen, K.G., Legay, A., Mikučionis, M., Poulsen, D.B., van Vliet, J., Wang, Z.: Statistical model checking for networks of priced timed automata. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 80–96. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24310-3_7

    Chapter  MATH  Google Scholar 

  13. Dimitrova, R., Finkbeiner, B., Torfah, H.: Probabilistic hyperproperties of markov decision processes. In: Hung, D.V., Sokolsky, O. (eds.) ATVA 2020. LNCS, vol. 12302, pp. 484–500. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59152-6_27

    Chapter  Google Scholar 

  14. Dobe, O., Ábrahám, E., Bartocci, E., Bonakdarpour, B.: HyperProb: a model checker for probabilistic hyperproperties. In: Huisman, M., Păsăreanu, C., Zhan, N. (eds.) FM 2021. LNCS, vol. 13047, pp. 657–666. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-90870-6_35

    Chapter  Google Scholar 

  15. Finkbeiner, B., Hahn, C., Stenger, M., Tentrup, L.: Monitoring hyperproperties. In: Lahiri, S., Reger, G. (eds.) RV 2017. LNCS, vol. 10548, pp. 190–207. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-67531-2_12

    Chapter  Google Scholar 

  16. Finkbeiner, B., Hahn, C., Stenger, M., Tentrup, L.: Rvhyper: A runtime verification tool for temporal hyperproperties. CoRR abs/1906.00798 (2019). http://arxiv.org/abs/1906.00798

  17. Finkbeiner, B., Hahn, C., Torfah, H.: Model checking quantitative hyperproperties. In: Chockler, H., Weissenbacher, G. (eds.) CAV 2018. LNCS, vol. 10981, pp. 144–163. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-96145-3_8

    Chapter  Google Scholar 

  18. Finkbeiner, B., Rabe, M.N., Sánchez, C.: Algorithms for model checking HyperLTL and HyperCTL\(^*\). In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9206, pp. 30–48. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21690-4_3

    Chapter  Google Scholar 

  19. Hsu, T.H., Bonakdarpour, B., Sánchez, C.: Hyperqube: A qbf-based bounded model checker for hyperproperties (2021). https://arxiv.org/abs/2109.12989

  20. Jaeger, M., Larsen, K.G., Tibo, A.: From statistical model checking to run-time monitoring using a bayesian network approach. In: Deshmukh, J., Ničković, D. (eds.) RV 2020. LNCS, vol. 12399, pp. 517–535. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-60508-7_30

    Chapter  Google Scholar 

  21. Koymans, R.: Specifying real-time properties with metric temporal logic. Real Time Syst. 2(4), 255–299 (1990). https://doi.org/10.1007/BF01995674

  22. Legay, A., Lukina, A., Traonouez, L.M., Yang, J., Smolka, S.A., Grosu, R.: Statistical model checking. In: Steffen, B., Woeginger, G. (eds.) Computing and Software Science. LNCS, vol. 10000, pp. 478–504. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-91908-9_23

    Chapter  Google Scholar 

  23. Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30206-3_12

    Chapter  MATH  Google Scholar 

  24. Nguyen, L.V., Kapinski, J., Jin, X., Deshmukh, J.V., Johnson, T.T.: Hyperproperties of real-valued signals. In: Proceedings of the 15th ACM-IEEE International Conference on Formal Methods and Models for System Design, pp. 104–113 (2017)

    Google Scholar 

  25. Wang, Y., Nalluri, S., Bonakdarpour, B., Pajic, M.: Statistical model checking for hyperproperties. In: 2021 IEEE 34th Computer Security Foundations Symposium (CSF), pp. 1–16. IEEE (2021)

    Google Scholar 

  26. Wang, Y., Zarei, M., Bonakdarpour, B., Pajic, M.: Statistical verification of hyperproperties for cyber-physical systems. ACM Trans. Embed. Comput. Syst. 18(5s), 92:1–92:23 (2019). https://doi.org/10.1145/3358232

  27. Younes, H.L.S., Simmons, R.G.: Probabilistic verification of discrete event systems using acceptance sampling. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 223–235. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45657-0_17

    Chapter  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Aalborg University, Aalborg, Denmark

    Shiraj Arora, René Rydhof Hansen, Kim Guldstrand Larsen & Danny Bøgsted Poulsen

  2. Department of Computer Science, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Axel Legay

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  1. Shiraj Arora
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Correspondence to Danny Bøgsted Poulsen .

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Editors and Affiliations

  1. Cornell University, Ithaca, NY, USA

    Owolabi Legunsen

  2. University of Illinois Urbana-Champaign, Urbana, IL, USA

    Grigore Rosu

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Arora, S., Hansen, R.R., Larsen, K.G., Legay, A., Poulsen, D.B. (2022). Statistical Model Checking for Probabilistic Hyperproperties of Real-Valued Signals. In: Legunsen, O., Rosu, G. (eds) Model Checking Software. SPIN 2022. Lecture Notes in Computer Science, vol 13255. Springer, Cham. https://doi.org/10.1007/978-3-031-15077-7_4

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