Journal of Automated Reasoning

, Volume 48, Issue 2, pp 197–217 | Cite as

Reducing Equational Theories for the Decision of Static Equivalence



Static equivalence is a well established notion of indistinguishability of sequences of terms which is useful in the symbolic analysis of cryptographic protocols. Static equivalence modulo equational theories allows for a more accurate representation of cryptographic primitives by modelling properties of operators by equational axioms. We develop a method that allows us in some cases to simplify the task of deciding static equivalence in a multi-sorted setting, by removing a symbol from the term signature and reducing the problem to several simpler equational theories. We illustrate our technique at hand of bilinear pairings.


Computer security Formal methods Static equivalence 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abadi, M., Cortier, V.: Deciding knowledge in security protocols under equational theories. Theor. Comp. Sci. 367(1), 2–32 (2006)MathSciNetMATHCrossRefGoogle Scholar
  2. 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’01), pp. 104–115. ACM Press (2001)Google Scholar
  3. 3.
    Arnaud, M., Cortier, V., Delaune, S.: Combining algorithms for deciding knowledge in security protocols. In: Proceedings of the 6th International Symposium on Frontiers of Combining Systems (FroCoS’07). Lecture Notes in Computer Science, vol. 4720, pp. 103–117. Springer (2007)Google Scholar
  4. 4.
    Baudet, M.: Deciding security of protocols against off-line guessing attacks. In: Proceedings of the 12th ACM Conference on Computer and Communications Security (CCS’05), pp. 16–25. ACM Press (2005)Google Scholar
  5. 5.
    Baudet, M., Cortier, V., Delaune, S.: YAPA: a generic tool for computing intruder knowledge. In: Treinen, R. (ed.) Proceedings of the 20th International Conference on Rewriting Techniques and Applications (RTA’09). Lecture Notes in Computer Science, Brasília, Brazil, vol. 5595, pp. 148–163. Springer (2009)Google Scholar
  6. 6.
    Baudet, M., Cortier, V., Kremer, S.: Computationally sound implementations of equational theories against passive adversaries. Inf. Comput. 207(4), 496–520 (2009)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    Blanchet, B., Abadi, M., Fournet, C.: Automated verification of selected equivalences for security protocols. Journal of Logic and Algebraic Programming 75(1), 3–51 (2008)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Boneh, D., Franklin, M.K.: Identity-based encryption from the weil pairing. In: Proceedings of the 21st Annual International Cryptology Conference on Advances in Cryptology (CRYPTO’01). Lecture Notes in Computer Science, vol. 2139, pp. 213–229. Springer (2001)Google Scholar
  9. 9.
    Chevalier, Y., Rusinowitch, M.: Hierarchical combination of intruder theories. Inf. Comput. 206(2–4), 352–377 (2008)MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    Ciobâcă, Ş., Delaune, S., Kremer, S.: Computing knowledge in security protocols under convergent equational theories. In: Schmidt, R. (ed.) Proceedings of the 22nd International Conference on Automated Deduction (CADE’09). Lecture Notes in Computer Science, Montreal, Canada, pp. 355–370. Springer (2009)Google Scholar
  11. 11.
    Comon, H.: Inductionless induction. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, vol. I, pp. 913–962. Elsevier (2001)Google Scholar
  12. 12.
    Corin, R., Doumen, J., Etalle, S.: Analysing password protocol security against off-line dictionary attacks. In: Proceedings of the 2nd International Workshop on Security Issues with Petri Nets and other Computational Models (WISP 2004). ENTCS, vol. 121, pp. 47–63. Elsevier (2004)Google Scholar
  13. 13.
    Cortier, V., Delaune, S., Lafourcade, P.: A survey of algebraic properties used in cryptographic protocols. J. Comput. Secur. 14(1), 1–43 (2006)Google Scholar
  14. 14.
    Dolev, D., Yao, A.C.: On the security of public key protocols. IEEE Trans. Inf. Theory 29(2), 198–208 (1983)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Joux, A.: A one round protocol for tripartite Diffie-Hellman. In: Proceedings of the 4th International Symposium on Algorithmic Number Theory (ANTS-IV). Lecture Notes in Computer Science, vol. 1838, pp. 385–394. Springer (2000)Google Scholar
  16. 16.
    Kremer, S., Mazaré, L.: Adaptive soundness of static equivalence. In: Proceedings of the 12th European Symposium on Research in Computer Security (ESORICS’07). Lecture Notes in Computer Science, vol. 4734, pp. 610–625. Springer (2007)Google Scholar
  17. 17.
    Kremer, S., Mazaré, L.: Computationally sound analysis of protocols using bilinear pairings. J. Comput. Secur. (2010, to appear)Google Scholar
  18. 18.
    Kremer, S., Mercier, A., Treinen, R.: Reducing equational theories for the decision of static equivalence. In: Datta, A. (ed.) Proceedings of the 13th Asian Computing Science Conference (ASIAN’09). Lecture Notes in Computer Science, Seoul, Korea, vol. 5913, pp. 94–108. Springer (2009)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.LSV, ENS Cachan, CNRS, INRIACachanFrance
  2. 2.PPSUniversité Paris Diderot - Paris 7ParisFrance

Personalised recommendations