Skip to main content
Log in

Modal tableaux for verifying stream authentication protocols

  • Published:
Autonomous Agents and Multi-Agent Systems Aims and scope Submit manuscript

Abstract

To develop theories to specify and reason about various aspects of multi-agent systems, many researchers have proposed the use of modal logics such as belief logics, logics of knowledge, and logics of norms. As multi-agent systems operate in dynamic environments, there is also a need to model the evolution of multi-agent systems through time. In order to introduce a temporal dimension to a belief logic, we combine it with a linear-time temporal logic using a powerful technique called fibring for combining logics. We describe a labelled modal tableaux system for the resulting fibred belief logic (FL) which can be used to automatically verify correctness of inter-agent stream authentication protocols. With the resulting fibred belief logic and its associated modal tableaux, one is able to build theories of trust for the description of, and reasoning about, multi-agent systems operating in dynamic environments.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Archer, M. (2002). Proving correctness of the basic TESLA multicast stream authentication protocol with TAME. In Workshop on issues in the theory of security. Unpaginated proceedings available from http://www.dsi.unive.it/IFIPWG1_7/WITS2002/prog/annotated_program.html.

  2. Artosi, A., Benassi, P., Governatori, G., & Rotolo, A. (1998). Shakespearian modal logic: A labelled treatment of modal identity. Advances in modal logic, 1, 1–21. CSLI.

  3. Bennett B., Dixon Cl., Fisher M., Hustadt U., Franconi E., Horrocks I., de Rijke M. (2002). Combinations of modal logics. Artificial Intelligence Review 17(1): 1—20

    Article  MATH  Google Scholar 

  4. Broadfoot P., & Lowe, G. (2002). Analysing a stream authentication protocol using model checking. In Proc 7th ESORICS.

  5. Burrows M., Abadi M., Needham R.M. (1990). A logic of authentication. ACM Transactions on Computer Systems 8(1): 18–36

    Article  Google Scholar 

  6. Clarke, E., Jha, S., & Marrero, W. (1998). A machine checkable logic of knowledge for specifying security properties of electronic commerce protocols. In Proceedings of the Workshop on Formal Methods and Security Protocols.

  7. Costa-Leite, A. (2004). Towards a general theory of the combination of logics. In Aspects of universal logic, Travaux de Logique [Works on logic] (Vol. 17, pp.219–230). Université de Neuchatel.

  8. Dixon, C., Carmen Fernández Gago, M., Fisher, M., van der Hoek, W. (2004). Using temporal logics of knowledge in the formal verification of security protocols. In Proceedings of the 11th International Symposium on Temporal Representation and Reasoning (TIME 2004) (pp. 148–151). Tatihou Island, Normandie: IEEE Computer Society.

  9. Durgin N., Mitchell J., Pavlovic D. (2003). A compositional logic for proving security properties of protocols. Journal of Computer Security 11, 677–721

    Google Scholar 

  10. Elofson, G. (1998). Developing trust with intelligent agent: An exploratory study. In Proceedings of the first International Workshop on Trust (pp. 125–139).

  11. Finger M., Gabbay D.M. (1997). Adding a temporal dimension to a logic system. Journal of Logic, Language and Information 1, 221–237

    MathSciNet  Google Scholar 

  12. Fisher M. (2004). Temporal development methods for agent-based systems. Autonomous Agents and Multi-Agent Systems 10(1): 41–66

    Article  Google Scholar 

  13. Fitting, M. (1983). Proof methods for modal and intuitionistic logics. Reidel.

  14. Gabbay, D. M. (1999). Fibring logics. OUP.

  15. Gabbay, D. M., & Governatori, G. (2000). Fibred modal tableaux. In Labelled deduction (pp. 163–194). Kluwer.

  16. Governatori, G. (1995). Labelled tableaux for multi-modal logics. In Proc. Tableaux’95, LNAI 918 (pp. 79–94). Springer.

  17. Governatori, G. (1997). Un modello formale per il ragionamento giuridico. PhD thesis, University of Bologna.

  18. Governatori, G., Padmanabhan, V. and Sattar, A. (2002). On fibring semantics for BDI logics. In Proc JELIA 2002, LNCS 2424 (pp. 198–209). Springer.

  19. Halpern J. Y., & Moses, Y. (1992). A guide to completeness and complexity for modal logics of knowledge and belief. In Artificial intelligence (Vol. 54, pp. 319–379).

  20. Hughes, G. E., & Cresswell, M. J. (1996). A new introduction to modal logic. Routledge.

  21. Kripke S. (1963). Semantical considerations on modal logic. Acta Philosophica Fennica 16, 83–94

    MATH  MathSciNet  Google Scholar 

  22. Liu, C. (2001). Logical foundations for reasoning about trust in secure digital communication. In Proceedings of the 14th Australian Joint Conference on Artificial Intelligence, Lecture notes in computer science 2256 (pp. 333–344). Adelaide: Springer.

  23. Liu C., Orgun M.A. (1996). Dealing with multiple granularity of time in temporal logic programming. Journal of Symbolic Computation 22, 699–720

    Article  MATH  MathSciNet  Google Scholar 

  24. Liu C., Orgun M.A. (1999). Verification of reactive systems using temporal logic with clocks. Theoretical Computer Science 220(2): 377–408

    Article  MATH  MathSciNet  Google Scholar 

  25. Liu, C., Ozols, M., & Orgun, M. A. (2004). A temporalised belief logic for specifying the dynamics of trust for multi-agent systems. In Proceedings of the Ninth Asian Computer Science Conference, Lecture notes in computer science (Vol. 3321, pp. 142–156). Springer-Verlag.

  26. Lomuscio, A., & Wozna, B. (2006). A complete and decidable security-specialised logic and its application to the TESLA protocol. In Proceedings of the 5th International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2006) (pp. 145–152). Hakodate: ACM Press.

  27. Ma, J. & Orgun, M. A. (2006). Trust management and trust theory revision. In IEEE transactions on systems, man and cybernetics, part A (Vol. 36, pp. 451–460).

  28. Orgun, M. A., Ma, J., Liu, C., & Governatori, G. (2006). Analysing stream authentication protocols in autonomous agent-based systems. In Proceedings of the Second International Symposium on Dependable Autonomic and Secure Computing (DASC 2006) (pp. 325–332). Indianapolis: IEEE Computer Society.

  29. Paulson, L. C. (1994). Isabelle—a generic theorem prover (with a contribution by T. Nipkow). Springer-Verlag.

  30. Perrig, A. Canetti, R. Tygar, J. D., & Song, D. (2000). Efficient authentication and signing of multicast streams over lossy channels. In IEEE symposium on security and privacy (pp. 56–73).

  31. Yahalom, R., Klein, B., Beth, T. (1993). Trust relationships in secure systems—a distributed authentication perspective. In Proceedings of the 1993 IEEE Symposium on Security and Privacy (p.150).

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Guido Governatori.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Orgun, M.A., Governatori, G. & Liu, C. Modal tableaux for verifying stream authentication protocols. Auton Agent Multi-Agent Syst 19, 53–75 (2009). https://doi.org/10.1007/s10458-007-9027-4

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10458-007-9027-4

Keywords

Navigation