Skip to main content
SpringerLink
Log in

Notions of Knowledge in Combinations of Theories Sharing Constructors

  • Conference paper
  • First Online:
Automated Deduction – CADE 26 (CADE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10395))

Included in the following conference series:

Abstract

One of the most effective methods developed for the analysis of security protocols is an approach based on equational reasoning and unification. In this approach, it is important to have the capability to reason about the knowledge of an intruder. Two important measures of this knowledge, defined modulo equational theories, are deducibility and static equivalence. We present new combination techniques for the study of deducibility and static equivalence in unions of equational theories sharing constructors. Thanks to these techniques, we obtain new modularity results for the decidability of deducibility and static equivalence. In turn, this should allow for the analysis of protocols involving combined equational theories which previous disjoint combination methods could not address due to their non-disjoint axiomatization.

C. Ringeissen—This work has received funding from the European Research Council (ERC) under the H2020 research and innovation program (grant agreement No. 645865-SPOOC).

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 69.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 89.99
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

References

  1. Abadi, M., Cortier, V.: Deciding knowledge in security protocols under equational theories. Theoret. Comput. Sci. 367(1–2), 2–32 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  2. Abadi, M., Fournet, C.: Mobile values, new names, and secure communication. In: Proceedings of the 28th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2001, pp. 104–115. ACM, New York (2001)

    Google Scholar 

  3. Armando, A., et al.: The AVISPA tool for the automated validation of internet security protocols and applications. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 281–285. Springer, Heidelberg (2005). doi:10.1007/11513988_27

    Chapter  Google Scholar 

  4. Baader, F., Nipkow, T.: Term Rewriting and All That. Cambridge University Press, New York (1998)

    Book  MATH  Google Scholar 

  5. Baader, F., Schulz, K.U.: Unification in the union of disjoint equational theories: combining decision procedures. J. Symb. Comput. 21(2), 211–243 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  6. Baader, F., Tinelli, C.: Deciding the word problem in the union of equational theories. Inf. Comput. 178(2), 346–390 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  7. Baudet, M., Cortier, V., Delaune, S.: YAPA: a generic tool for computing intruder knowledge. ACM Trans. Comput. Log. 14(1), 4 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  8. Blanchet, B.: An efficient cryptographic protocol verifier based on prolog rules. In: 14th IEEE Computer Security Foundations Workshop (CSFW-14 2001), 11–13 June 2001, Cape Breton, Nova Scotia, Canada, pp. 82–96. IEEE Computer Society (2001)

    Google Scholar 

  9. Chadha, R., Cheval, V., Ciobâcă, Ş., Kremer, S.: Automated verification of equivalence properties of cryptographic protocols. ACM Trans. Comput. Log. 17(4), 23:1–23:32 (2016). https://hal.inria.fr

    Article  MathSciNet  Google Scholar 

  10. Chevalier, Y., Rusinowitch, M.: Hierarchical combination of intruder theories. Inf. Comput. 206(2–4), 352–377 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Comon-Lundh, H., Treinen, R.: Easy intruder deductions. In: Dershowitz, N. (ed.) Verification: Theory and Practice. LNCS, vol. 2772, pp. 225–242. Springer, Heidelberg (2003). doi:10.1007/978-3-540-39910-0_10

    Chapter  Google Scholar 

  12. Conchinha, B., Basin, D.A., Caleiro, C.: FAST: an efficient decision procedure for deduction and static equivalence. In: Schmidt-Schauß, M. (ed.) Proceedings of RTA 2011, Novi Sad, Serbia. LIPIcs, vol. 10, pp. 11–20. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2011)

    Google Scholar 

  13. Cortier, V., Delaune, S.: Decidability and combination results for two notions of knowledge in security protocols. J. Autom. Reason. 48(4), 441–487 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Cremers, C.J.F.: The scyther tool: verification, falsification, and analysis of security protocols. In: Gupta, A., Malik, S. (eds.) CAV 2008. LNCS, vol. 5123, pp. 414–418. Springer, Heidelberg (2008). doi:10.1007/978-3-540-70545-1_38

    Chapter  Google Scholar 

  15. Ciobâcă, Ş., Delaune, S., Kremer, S.: Computing knowledge in security protocols under convergent equational theories. J. Autom. Reason. 48(2), 219–262 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  16. Dolev, D., Yao, A.C.: On the security of public key protocols (extended abstract). In: 22nd Annual Symposium on Foundations of Computer Science, 28–30 October 1981, Nashville, Tennessee, USA, pp. 350–357. IEEE Computer Society (1981)

    Google Scholar 

  17. Domenjoud, E., Klay, F., Ringeissen, C.: Combination techniques for non-disjoint equational theories. In: Bundy, A. (ed.) CADE 1994. LNCS, vol. 814, pp. 267–281. Springer, Heidelberg (1994). doi:10.1007/3-540-58156-1_19

    Chapter  Google Scholar 

  18. Erbatur, S., Kapur, D., Marshall, A.M., Narendran, P., Ringeissen, C.: Hierarchical combination. In: Bonacina, M.P. (ed.) CADE 2013. LNCS (LNAI), vol. 7898, pp. 249–266. Springer, Heidelberg (2013). doi:10.1007/978-3-642-38574-2_17

    Chapter  Google Scholar 

  19. Escobar, S., Meadows, C., Meseguer, J.: Maude-NPA: cryptographic protocol analysis modulo equational properties. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007–2009. LNCS, vol. 5705, pp. 1–50. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03829-7_1

    Chapter  Google Scholar 

  20. Millen, J., Shmatikov, V.: Constraint solving for bounded-process cryptographic protocol analysis. In: Proceedings of the 8th ACM Conference on Computer and Communications Security, CCS 2001, pp. 166–175. ACM, New York (2001)

    Google Scholar 

  21. Mödersheim, S., Viganò, L.: The open-source fixed-point model checker for symbolic analysis of security protocols. In: Aldini, A., Barthe, G., Gorrieri, R. (eds.) FOSAD 2007–2009. LNCS, vol. 5705, pp. 166–194. Springer, Heidelberg (2009). doi:10.1007/978-3-642-03829-7_6

    Chapter  Google Scholar 

  22. Paulson, L.C.: The inductive approach to verifying cryptographic protocols. Comput. Secur. 6, 85–128 (1998)

    Article  Google Scholar 

  23. Schmidt, B., Meier, S., Cremers, C.J.F., Basin, D.A.: Automated analysis of Diffie-Hellman protocols and advanced security properties. In: Chong, S. (ed.) 25th IEEE Computer Security Foundations Symposium, CSF 2012, 25–27 June 2012, Cambridge, MA, USA, pp. 78–94. IEEE Computer Society (2012)

    Google Scholar 

  24. Schmidt-Schauß, M.: Unification in a combination of arbitrary disjoint equational theories. J. Symb. Comput. 8, 51–99 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  25. Tiu, A., Goré, R., Dawson, J.E.: A proof theoretic analysis of intruder theories. Log. Methods Comput. Sci. 6(3:12), 1–37 (2010)

    MathSciNet  MATH  Google Scholar 

  26. Turuani, M.: The CL-Atse protocol analyser. In: Pfenning, F. (ed.) RTA 2006. LNCS, vol. 4098, pp. 277–286. Springer, Heidelberg (2006). doi:10.1007/11805618_21

    Chapter  Google Scholar 

Download references

Acknowledgements

We would like to thank Véronique Cortier and Steve Kremer for the thoughtful comments and discussions.

Author information

Authors and Affiliations

  1. Ludwig-Maximilians-Universität, München, Germany

    Serdar Erbatur

  2. University of Mary Washington, Fredericksburg, USA

    Andrew M. Marshall

  3. LORIA – INRIA Nancy-Grand Est, Villers-lès-Nancy, France

    Christophe Ringeissen

Authors
  1. Serdar Erbatur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrew M. Marshall
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christophe Ringeissen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Christophe Ringeissen .

Editor information

Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Leonardo de Moura

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Erbatur, S., Marshall, A.M., Ringeissen, C. (2017). Notions of Knowledge in Combinations of Theories Sharing Constructors. In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-63046-5_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-63045-8

  • Online ISBN: 978-3-319-63046-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation