Skip to main content
SpringerLink
Log in

Formalizing Probabilistic Noninterference

  • Conference paper
Certified Programs and Proofs (CPP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8307))

Included in the following conference series:

Abstract

We present an Isabelle formalization of probabilistic noninterference for a multi-threaded language with uniform scheduling. Unlike in previous settings from the literature, here probabilistic behavior comes from both the scheduler and the individual threads, making the language more realistic and the mathematics more challenging. We study resumption-based and trace-based notions of probabilistic noninterference and their relationship, and also discuss compositionality w.r.t. the language constructs and type-system-like syntactic criteria. The formalization uses recent development in the Isabelle probability theory library.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. The POPLmark challenge (2009), http://www.seas.upenn.edu/~plclub/poplmark/

  2. Audebaud, P., Paulin-Mohring, C.: Proofs of randomized algorithms in Coq. S. of Comp. Prog. 74(8), 568–589 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Barthe, G., D’Argenio, P.R., Rezk, T.: Secure information flow by self-composition. In: CSFW, pp. 100–114 (2004)

    Google Scholar 

  4. Barthe, G., Daubignard, M., Kapron, B.M., Lakhnech, Y.: Computational indistinguishability logic. In: CCS, pp. 375–386 (2010)

    Google Scholar 

  5. Barthe, G., Grégoire, B., Béguelin, S.Z.: Formal certification of code-based cryptographic proofs. In: POPL, pp. 90–101 (2009)

    Google Scholar 

  6. Barthe, G., Nieto, L.P.: Formally verifying information flow type systems for concurrent and thread systems. In: FMSE, pp. 13–22 (2004)

    Google Scholar 

  7. Boudol, G.: On typing information flow. In: Van Hung, D., Wirsing, M. (eds.) ICTAC 2005. LNCS, vol. 3722, pp. 366–380. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Boudol, G., Castellani, I.: Noninterference for concurrent programs and thread systems. Theoretical Computer Science 281(1-2), 109–130 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Cock, D.: Verifying probabilistic correctness in Isabelle with pGCL. In: SSV, pp. 167–178 (2012)

    Google Scholar 

  10. Cock, D.: Practical probability: Applying pGCL to lattice scheduling. In: Blazy, S., Paulin-Mohring, C., Pichardie, D. (eds.) ITP 2013. LNCS, vol. 7998, pp. 311–327. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  11. Hölzl, J.: Analyzing discrete-time Markov chains with countable state space in Isabelle/HOL. Draft, http://home.in.tum.de/~hoelzl/classifying

  12. Hölzl, J., Nipkow, T.: Verifying pCTL model checking. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 347–361. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  13. Hurd, J., McIver, A., Morgan, C.: Probabilistic guarded commands mechanized in HOL. Theor. Comput. Sci. 346(1) (2005)

    Google Scholar 

  14. Kammüller, F., Wenzel, M., Paulson, L.C.: Locales - a sectioning concept for Isabelle. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 149–166. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  15. Kemeny, J.G., Snell, J.L., Knapp, A.W.: Denumerable Markov chains, 2nd edn. Springer (1976)

    Google Scholar 

  16. Larsen, K.G., Skou, A.: Bisimulation through probabilistic testing. Information and Computation 94(1), 1–28 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  17. Mantel, H.: A uniform framework for the specification and verification of security properties. Ph.D. thesis, Univ. of Saarbrücken (2003)

    Google Scholar 

  18. Mantel, H., Sudbrock, H.: Flexible scheduler-independent security. In: Gritzalis, D., Preneel, B., Theoharidou, M. (eds.) ESORICS 2010. LNCS, vol. 6345, pp. 116–133. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. McIver, A., Morgan, C.: Abstraction, Refinement and Proof for Probabilistic Systems. Springer (2005)

    Google Scholar 

  20. Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL: A Proof Assistant for Higher-order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)

    Google Scholar 

  21. Paulson, L.C., Blanchette, J.C.: Three years of experience with Sledgehammer, a practical link between automatic and interactive theorem provers. In: IWIL (2010)

    Google Scholar 

  22. Popescu, A., Hölzl, J.: Formal development associated with this paper, http://www21.in.tum.de/~popescua/prob.zip (to appear in the Archive of Formal Proofs, 2013)

  23. Popescu, A., Hölzl, J., Nipkow, T.: Proving concurrent noninterference. In: Hawblitzel, C., Miller, D. (eds.) CPP 2012. LNCS, vol. 7679, pp. 109–125. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  24. Popescu, A., Hölzl, J., Nipkow, T.: Noninterfering schedulers - when possibilistic noninterference implies probabilistic noninterference. In: CALCO, pp. 236–252 (2013)

    Google Scholar 

  25. Sabelfeld, A.: Confidentiality for multithreaded programs via bisimulation. In: Broy, M., Zamulin, A.V. (eds.) PSI 2003. LNCS, vol. 2890, pp. 260–274. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  26. Sabelfeld, A., Myers, A.C.: Language-based information-flow security. IEEE Journal on Selected Areas in Communications 21(1), 5–19 (2003)

    Article  Google Scholar 

  27. Sabelfeld, A., Sands, D.: Probabilistic noninterference for multi-threaded programs. In: CSFW, pp. 200–214 (2000)

    Google Scholar 

  28. Smith, G.: A new type system for secure information flow. In: CSFW, pp. 115–125 (2001)

    Google Scholar 

  29. Smith, G.: Probabilistic noninterference through weak probabilistic bisimulation. In: CSFW, pp. 3–13 (2003)

    Google Scholar 

  30. Smith, G.: Improved typings for probabilistic noninterference in a multi-threaded language. Journal of Computer Security 14(6), 591–623 (2006)

    Google Scholar 

  31. Smith, G., Volpano, D.: Secure information flow in a multi-threaded imperative language. In: POPL, pp. 355–364 (1998)

    Google Scholar 

  32. Volpano, D., Smith, G.: Probabilistic noninterference in a concurrent language. Journal of Computer Security 7(2,3), 231–253 (1999)

    Google Scholar 

  33. Volpano, D., Smith, G., Irvine, C.: A sound type system for secure flow analysis. Journal of Computer Security 4(2,3), 167–187 (1996)

    Google Scholar 

  34. Zdancewic, S., Myers, A.C.: Observational determinism for concurrent program security. In: CSFW, pp. 29–43 (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität München, Germany

    Andrei Popescu, Johannes Hölzl & Tobias Nipkow

  2. Institute of Mathematics Simion Stoilow of the Romanian Academy, Romania

    Andrei Popescu

Authors
  1. Andrei Popescu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johannes Hölzl
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tobias Nipkow
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Microsoft Research Cambridge, 21 Station Road, CB1 2FB, Cambridge, UK

    Georges Gonthier

  2. Canberra Research Lab., NICTA, PO Box 8001, 2601, Canberra, ACT, Australia

    Michael Norrish

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

Popescu, A., Hölzl, J., Nipkow, T. (2013). Formalizing Probabilistic Noninterference. In: Gonthier, G., Norrish, M. (eds) Certified Programs and Proofs. CPP 2013. Lecture Notes in Computer Science, vol 8307. Springer, Cham. https://doi.org/10.1007/978-3-319-03545-1_17

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03545-1_17

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03544-4

  • Online ISBN: 978-3-319-03545-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation