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Abstract

Many recent results are concerned with interpreting proofs of security done in symbolic models in the more detailed models of computational cryptography. In the case of symmetric encryption, these results stringently demand that no key cycle (e.g. {k} k ) can be produced during the execution of protocols. While security properties like secrecy or authentication have been proved decidable for many interesting classes of protocols, the automatic detection of key cycles has not been studied so far.

In this paper, we prove that deciding the existence of key-cycles is NP-complete for a bounded number of sessions. Next, we observe that the techniques that we use are of more general interest and apply them to reprove the decidability of a significant existing fragment of protocols with timestamps.

Keywords

Security Protocol Deduction System Constraint System Security Property Cryptographic Protocol 
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.

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References

  1. 1.
    Abadi, M., Rogaway, P.: Reconciling two views of cryptography (the computational soundness of formal encryption). Journal of Cryptology 2, 103–127 (2002)MathSciNetGoogle Scholar
  2. 2.
    Adão, P., Bana, G., Herzog, J., Scedrov, A.: Soundness of formal encryption in the presence of key-cycles. In: di Vimercati, S.d.C., Syverson, P.F., Gollmann, D. (eds.) ESORICS 2005. LNCS, vol. 3679, pp. 374–396. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  3. 3.
    Armando, A., Basin, D., Boichut, Y., Chevalier, Y., Compagna, L., Cuellar, J., Hankes Drielsma, P., Heám, P.C., Kouchnarenko, O., Mantovani, J., Mödersheim, S., von Oheimb, D., Rusinowitch, M., Santiago, J., Turuani, M., Viganò, L., Vigneron, L.: 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)CrossRefGoogle Scholar
  4. 4.
    Backes, M., Pfitzmann, B.: Symmetric encryption in a simulatable Dolev-Yao style cryptographic library. In: Proc. 17th IEEE Computer Science Foundations Workshop (CSFW 2004), pp. 204–218 (2004)Google Scholar
  5. 5.
    Backes, M., Pfitzmann, B., Scedrov, A.: Key-dependent message security under active attacks. Cryptology ePrint Archive, Report 2005/421 (2005)Google Scholar
  6. 6.
    Bellare, M., Rogaway, P.: Entity authentication and key distribution. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 232–249. Springer, Heidelberg (1994)Google Scholar
  7. 7.
    Blanchet, B.: An efficient cryptographic protocol verifier based on Prolog rules. In: Proc. 14th IEEE Computer Security Foundations Workshop (CSFW 2001), pp. 82–96 (2001)Google Scholar
  8. 8.
    Blanchet, B., Podelski, A.: Verification of cryptographic protocols: Tagging enforces termination. In: Gordon, A.D. (ed.) FOSSACS 2003. LNCS, vol. 2620, pp. 136–152. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  9. 9.
    Bozga, L., Ene, C., Lakhnech, Y.: A symbolic decision procedure for cryptographic protocols with time stamps. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 177–192. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  10. 10.
    Clark, J., Jacob, J.: A survey of authentication protocol literature (1997), Available at: http://www.cs.york.ac.uk/~jac/papers/drareviewps.ps
  11. 11.
    Comon-Lundh, H.: Résolution de contraintes et recherche d’attaques pour un nombre borné de sessions. Available at: http://www.lsv.ens-cachan.fr/~comon/CRYPTO/bounded.ps
  12. 12.
    Comon-Lundh, H., Cortier, V.: New decidability results for fragments of first-order logic and application to cryptographic protocols. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 148–164. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Comon-Lundh, H., Shmatikov, V.: Intruder deductions, constraint solving and insecurity decision in presence of exclusive or. In: Proc. of 18th Annual IEEE Symposium on Logic in Computer Science (LICS 2003), pp. 271–280 (2003)Google Scholar
  14. 14.
    Cortier, V., Zălinescu, E.: Deciding key cycles for security protocols, extended version, Available at: http://www.loria.fr/~zalinesc/papers/cz_keycycles.ps
  15. 15.
    Durgin, N., Lincoln, P., Mitchell, J., Scedrov, A.: Undecidability of bounded security protocols. In: Proc. of the Workshop on Formal Methods and Security Protocols (1999)Google Scholar
  16. 16.
    Goldwasser, S., Micali, S.: Probabilistic encryption. Journal of Computer and System Sciences 28, 270–299 (1984)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Janvier, R., Lakhnech, Y., Mazare, L.: (De)Compositions of Cryptographic Schemes and their Applications to Protocols. Cryptology ePrint Archive, Report 2005/020 (2005)Google Scholar
  18. 18.
    Laud, P.: Encryption cycles and two views of cryptography. In: Nordic Workshop on Secure IT Systems (NORDSEC 2002) (2002)Google Scholar
  19. 19.
    Lowe, G.: Breaking and fixing the Needham-Schroeder public-key protocol using FDR. In: Margaria, T., Steffen, B. (eds.) TACAS 1996. LNCS, vol. 1055, pp. 147–166. Springer, Heidelberg (1996)Google Scholar
  20. 20.
    Lowe, G.: A hierarchy of authentication specification. In: 10th Computer Security Foundations Workshop (CSFW 1997), pp. 31–44 (1997)Google Scholar
  21. 21.
    Micciancio, D., Warinschi, B.: Soundness of formal encryption in the presence of active adversaries. In: Naor, M. (ed.) TCC 2004. LNCS, vol. 2951, pp. 133–151. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  22. 22.
    Millen, J.K., Shmatikov, V.: Constraint solving for bounded-process cryptographic protocol analysis. In: Proc. 8th ACM Conference on Computer and Communications Security (CCS 2001), pp. 166–175 (2001)Google Scholar
  23. 23.
    Needham, R.M., Schroeder, M.D.: Using encryption for authentication in large networks of computers. Commun. ACM 21(12), 993–999 (1978)MATHCrossRefGoogle Scholar
  24. 24.
    Ramanujam, R., Suresh, S.P.: Tagging makes secrecy decidable for unbounded nonces as well. In: Pandya, P.K., Radhakrishnan, J. (eds.) FSTTCS 2003. LNCS, vol. 2914, pp. 363–374. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  25. 25.
    Rusinowitch, M., Turuani, M.: Protocol insecurity with finite number of sessions and composed keys is NP-complete. Theoretical Computer Science 299, 451–475 (2003)MATHCrossRefMathSciNetGoogle Scholar
  26. 26.
    Schrijver, A.: Theory of Linear and Integer Programming. Wiley, Chichester (1998)MATHGoogle Scholar
  27. 27.
    Verma, K.N., Seidl, H., Schwentick, T.: On the Complexity of Equational Horn Clauses. In: Nieuwenhuis, R. (ed.) CADE 2005. LNCS, vol. 3632, pp. 337–352. Springer, Heidelberg (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Véronique Cortier
    • 1
  • Eugen Zălinescu
    • 1
  1. 1.Loria UMR 7503 & INRIA Lorraine projet Cassis & CNRSFrance

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