Modelling Time for Authenticated Key Exchange Protocols

  • Jörg Schwenk
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8713)


The notion of time plays an important role in many practically deployed cryptographic protocols, ranging from One-Time-Password (OTP) tokens to the Kerberos protocol. However, time is difficult to model in a Turing machine environment.

We propose the first such model, where time is modelled as a global counter \(\cal T\). We argue that this model closely matches several implementations of time in computer environments. The usefulness of the model is shown by giving complexity-theoretic security proofs for OTP protocols and HMQV-like one-round AKE protocols.


Authenticated key agreement timestamps provable security OTP Kerberos 


  1. 1.
    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)CrossRefGoogle Scholar
  2. 2.
    Hopcroft, J.E., Motwani, R., Ullman, J.D.: Introduction to Automata Theory, Languages, and Computation. 3rd edn. Addison-Wesley (2006)Google Scholar
  3. 3.
    Hofheinz, D., Shoup, V.: Gnuc: A new universal composability framework. Cryptology ePrint Archive, Report 2011/303 (2011),
  4. 4.
    Mills, D., Martin, J., Burbank, J., Kasch, W.: Network Time Protocol Version 4: Protocol and Algorithms Specification. RFC 5905 (Proposed Standard) (June 2010)Google Scholar
  5. 5.
    Magkos, E., Burmester, M., Chrissikopoulos, V.: Receipt-freeness in large-scale elections without untappable channels. In: Schmid, B., Stanoevska-Slabeva, K., Tschammer, V. (eds.) Towards the E-Society. IFIP, vol. 202, pp. 683–694. Springer, Boston (2001)Google Scholar
  6. 6.
    M’Raihi, D., Bellare, M., Hoornaert, F., Naccache, D., Ranen, O.: HOTP: An HMAC-Based One-Time Password Algorithm. RFC 4226 (Informational) (December 2005)Google Scholar
  7. 7.
    M’Raihi, D., Machani, S., Pei, M., Rydell, J.: TOTP: Time-Based One-Time Password Algorithm. RFC 6238 (Informational) (May 2011)Google Scholar
  8. 8.
    Cremers, C.J.F.: Session-state reveal is stronger than ephemeral key reveal: Attacking the naxos authenticated key exchange protocol. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 20–33. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  9. 9.
    Schwenk, J.: Modelling time, or a step towards reduction-based security proofs for otp and kerberos. IACR Cryptology ePrint Archive 2013, 604 (2013)Google Scholar
  10. 10.
    Massias, H., Avila, X.S., Quisquater, J.J.: Timestamps: Main issues on their use and implementation. In: WETICE, pp. 178–183. IEEE Computer Society (1999)Google Scholar
  11. 11.
    Haber, S., Massias, H.: Time-stamping. In: van Tilborg, H.C.A., Jajodia, S. (eds.) Encyclopedia of Cryptography and Security, 2nd edn., pp. 1299–1303. Springer (2011)Google Scholar
  12. 12.
    Moran, T., Shaltiel, R., Ta-Shma, A.: Non-interactive timestamping in the bounded-storage model. J. Cryptology 22(2), 189–226 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Buldas, A., Niitsoo, M.: Optimally tight security proofs for hash-then-publish time-stamping. In: [27], pp. 318–335Google Scholar
  14. 14.
    Liu, Z., Lu, M.: Authentication protocols with time stamps: – encryption algorithm dependent. In: Arabnia, H.R. (ed.) International Conference on Internet Computing, pp. 81–86. CSREA Press (2006)Google Scholar
  15. 15.
    Paterson, K.G., Stebila, D.: One-time-password-authenticated key exchange. In: [27], pp. 264–281Google Scholar
  16. 16.
    Bellare, M., Rogaway, P.: Provably secure session key distribution: The three party case, pp. 57–66 (1995)Google Scholar
  17. 17.
    Manulis, M.: Provably secure group key exchange (2007)Google Scholar
  18. 18.
    Canetti, R., Krawczyk, H.: Analysis of key-exchange protocols and their use for building secure channels. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 453–474. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Barbosa, M., Farshim, P.: Security analysis of standard authentication and key agreement protocols utilising timestamps. In: Preneel, B. (ed.) AFRICACRYPT 2009. LNCS, vol. 5580, pp. 235–253. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  20. 20.
    Matsumoto, T., Takashima, Y., Imai, H.: On seeking smart public-key-distribution systems. IEICE Transactions E69-E(2), 99–106 (1986)Google Scholar
  21. 21.
    Menezes, A., Qu, M., Vanstone, S.A.: Some new key agreement protocols providing mutual implicit authentication. In: Second Workshop on Selected Areas in Cryptography, SAC 1995 (1995)Google Scholar
  22. 22.
    Law, L., Menezes, A., Qu, M., Solinas, J.A., Vanstone, S.A.: An efficient protocol for authenticated key agreement. Des. Codes Cryptography 28(2), 119–134 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Bellare, M., Palacio, A.: The knowledge-of-exponent assumptions and 3-round zero-knowledge protocols. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 273–289. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  24. 24.
    Krawczyk, H.: HMQV: A high-performance secure diffie-hellman protocol. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 546–566. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  25. 25.
    Choo, K.K.R., Boyd, C., Hitchcock, Y.: Examining indistinguishability-based proof models for key establishment protocols. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 585–604. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  26. 26.
    Krawczyk, H.: HMQV: A high-performance secure Diffie-Hellman protocol. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 546–566. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Steinfeld, R., Hawkes, P. (eds.): ACISP 2010. LNCS, vol. 6168. Springer, Heidelberg (2010)zbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Jörg Schwenk
    • 1
  1. 1.Horst Görtz Institute for IT-SecurityRuhr-University BochumGermany

Personalised recommendations