Advertisement

A Probabilistic Applied Pi–Calculus

  • Jean Goubault-Larrecq
  • Catuscia Palamidessi
  • Angelo Troina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4807)

Abstract

We propose an extension of the Applied Pi–calculus by introducing nondeterministic and probabilistic choice operators. The semantics of the resulting model, in which probability and nondeterminism are combined, is given by Segala’s Probabilistic Automata driven by schedulers which resolve the nondeterministic choice among the probability distributions over target states. Notions of static and observational equivalence are given for the enriched calculus. In order to model the possible interaction of a process with its surrounding environment a labeled semantics is given together with a notion of weak bisimulation which is shown to coincide with the observational equivalence. Finally, we prove that results in the probabilistic framework are preserved in a purely nondeterministic setting.

Keywords

Equational Theory Security Protocol Probabilistic Apply Extended Process Oblivious Transfer 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abadi, M., Fournet, C.: Mobile Values, New Names, and Secure Communication. In: POPL 2001, pp. 104–115. ACM Press, New York (2001)CrossRefGoogle Scholar
  2. 2.
    Abadi, M., Gordon, A.D.: A Calculus for Cryptographic Protocols: The Spi Calculus. Information and Computation 148(1), 1–70 (1999)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Aldini, A., Bravetti, M., Gorrieri, R.: A Process-algebraic Approach for the Analysis of Probabilistic Non Interference. Journal of Computer Security 12, 191–245 (2004)Google Scholar
  4. 4.
    Barrett, C.L., Eidenbenz, S.J., Kroc, L., Marathe, M., Smith, J.P.: Parametric Probabilistic Sensor Network Routing. In: WSNA 2003, pp. 122–131. ACM Press, New York (2003)CrossRefGoogle Scholar
  5. 5.
    Buscemi, M.G., Montanari, U.: CC–pi: A Constraint–based Language for Specifying Service Level Agreements. In: ESOP 2007. LNCS, vol. 4421, pp. 19–32. Springer, Heidelberg (2007)Google Scholar
  6. 6.
    Cao, Q., Abdelzaher, T., He, T., Stankovic, J.: Towards Optimal Sleep Scheduling in Sensor Networks for Rare-event Detection. In: IPSN 2005, pp. 20–27. IEEE Computer Society Press, Los Alamitos (2005)Google Scholar
  7. 7.
    Cleaveland, R., Parrow, J., Steffen, B.: The concurrency workbench: a semantics-based tool for the verification of concurrent systems. ACM Trans. Program. Lang. Syst. 15(1), 36–72 (1993)CrossRefGoogle Scholar
  8. 8.
    Cortier, V., Abadi, M.: Deciding Knowledge in Security Protocols under Equational Theories. Theoretical Computer Science 367(1–2), 2–32 (2006)zbMATHMathSciNetGoogle Scholar
  9. 9.
    Dershowitz, N., Jouannaud, J.-P.: Rewrite Systems. Handbook of Theoretical Computer Science. Formal Models and Sematics (B) B, 243–320 (1990)MathSciNetGoogle Scholar
  10. 10.
    Di Pierro, A., Hankin, C., Wiklicky, H.: Approximate Non-Interference. Journal of Computer Security 12, 37–82 (2004)Google Scholar
  11. 11.
    Dolev, D., Yao, A.C.: On the Security of Public Key Protocols. IEEE Transactions on Information Theory 29(12), 198–208 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Even, S., Goldreich, O., Lempel, A.: A Randomized protocol for Signing Contracts. Communications of the ACM 28(6), 637–647 (1985)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Goguen, J.A., Thatcher, J.W., Wagner, E.G., Wright, J.B.: Initial Algebra Semantics and Continuous Algebras. Journal of the ACM 24(1), 68–95 (1977)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Jung, A., Tix, R.: The Troublesome Probabilistic Powerdomain. In: Proc. of Workshop on Computation and Approximation. ENTCS, vol. 13, Elsevier, Amsterdam (1998)Google Scholar
  15. 15.
    Lowe, G.: Casper: A compiler for the analysis of security protocols. Journal of Computer Security 6, 53–84 (1998)Google Scholar
  16. 16.
    Mislove, M.W., Ouakine, J., Worrell, J.: Axioms for Probability and Nondeterminism. In: EXPRESS 2003, 96th edn. ENTCS, pp. 7–28. Elsevier, Amsterdam (2004)Google Scholar
  17. 17.
    Milner, R.: Communication and Concurrency. Prentice Hall, Englewood Cliffs (1989)zbMATHGoogle Scholar
  18. 18.
    Milner, R.: Communicating and Mobile Systems: the π–Calculus. Cambridge University Press, Cambridge (1999)Google Scholar
  19. 19.
    Mitchell, J.C.: Foundations for Programming Languages. MIT Press, Cambridge (1996)Google Scholar
  20. 20.
    Mitchell, J.C., Ramanathan, A., Scedrov, A., Teague, V.: Polynomial-time Process Calculus for the Analysis of Cryptographic Protocols. Theoretical Computer Science 353(1–3), 118–164 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Niehren, J., Mueller, M.: Constraints for Free in Concurrent Computation. In: Kanchanasut, K., Levy, J.-J. (eds.) ACSC. LNCS, vol. 1023, pp. 171–186. Springer, Heidelberg (1995)Google Scholar
  22. 22.
    Rabin, M.O.: How to Exchange Secrets by Oblivious Transfer. Unpublished manuscript (1981)Google Scholar
  23. 23.
    Rivest, R., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public-Key Cryptosystems. Communications of the ACM 21(2), 120–126 (1978) Previously released as an MIT “Technical Memo” in April 1977zbMATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Saraswat, V.A., Rinard, M.C., Panangaden, P.: Semantic Foundations of Concurrent Constraint Programming. In: POPL 1991, pp. 333–352. ACM Press, New York (1991)CrossRefGoogle Scholar
  25. 25.
    Schneider, S.: Security properties and CSP. In: Proc. of the IEEE Symposium on Security and Privacy (1996)Google Scholar
  26. 26.
    Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, MIT, Laboratory for Computer Science (1995)Google Scholar
  27. 27.
    Segala, R., Lynch, N.: Probabilistic Simulations for Probabilistic Processes. Nordic Journal of Computing 2(2), 250–273 (1995)zbMATHMathSciNetGoogle Scholar
  28. 28.
    Victor, B., Moller, F.: The Mobility Workbench - A Tool for the pi-Calculus. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 428–440. Springer, Heidelberg (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jean Goubault-Larrecq
    • 1
  • Catuscia Palamidessi
    • 2
  • Angelo Troina
    • 1
    • 2
  1. 1.LSV - ENS Cachan, 61 Avenue du Président Wilson, 94235 CachanFrance
  2. 2.LIX - École Polytechnique, Rue de Saclay, 91128 PalaiseauFrance

Personalised recommendations