Skip to main content
SpringerLink
Log in
Book cover

International Conference on Financial Cryptography and Data Security

FC 2008: Financial Cryptography and Data Security pp 53–68Cite as

Revisiting Pairing Based Group Key Exchange

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5143))

Abstract

Secure communication within a large group of users such as participants in a phone or video conference relies on the availability of secure data and efficient data transmission. Group key exchange protocols allow a (large) group of n users to establish a joint secret key which can be used in symmetric systems to efficiently en- and decrypt messages to and from the group. To deal with varying constellations of the groups and to ensure key freshness it is essential that the group key exchange protocol is efficient.

Most protocols are generalizations of two-party protocols like Diffie-Hellman key exchange. The Burmester and Desmedt I protocol establishes a key in a constant number of rounds independent of the size of the group of users and in O(n) complexity of computation per user.

After Joux’s proposal to use pairings to enable a one-round tripartite key exchange (KE) several extensions of existing group KE and authenticated key exchange (AKE) protocols were published. However, quite a few turned out to be flawed and the complexity is often worse than for the original scheme. In this paper we propose a new constant round pairing based group AKE protocol which requires a lower computational complexity per user compared to previous proposals. Furthermore, the scheme is particularly interesting for groups in which some members enjoy more computational power than others. The protocol is most efficient if these members constitute roughly half of the group.

We also provide a pairing-based version of the Burmester-Desmedt II group key exchange which runs in 3 rounds and requires only O(logn) computation and communication.

Both protocols are faster than any published pairing-based key exchange protocols. If the parameters are chosen appropriately so that the pairing computations are fast the protocols can outperform the respective DL-based Burmester-Desmedt key exchange protocols.

This is a preview of subscription content, 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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barua, R., Dutta, R., Sarkar, P.: Extending Joux’s protocol to multi party key agreement. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 205–217. Springer, Heidelberg (2003)

    Google Scholar 

  2. Barua, R., Dutta, R., Sarkar, P.: Provably secure authenticated tree based group key agreement protocol using pairing. In: López, J., Qing, S., Okamoto, E. (eds.) ICICS 2004. LNCS, vol. 3269, pp. 92–104. Springer, Heidelberg (2004); (see also: ePrint archive, 2004/090)

    Google Scholar 

  3. Boneh, D., Franklin, M.: Identity based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 213–229. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. Boneh, D., Franklin, M.: Identity based encryption from the Weil pairing. SIAM J. Comput. 32(3), 586–615 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  5. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 514–532. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Boneh, D., Lynn, B., Shacham, H.: Short signatures from the Weil pairing. J. Cryptology 17, 297–319 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  7. Bresson, E., Chevassut, O., Pointcheval, D., Quisquater, J.-J.: Provably authenticated group Diffie-Hellman key exchange. In: Proc. 8th Annual ACM Conference on Computer and Communications Security, pp. 255–264 (2001)

    Google Scholar 

  8. Burmester, M., Desmedt, Y.: A secure and efficient conference key distribution system. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 275–286. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  9. Burmester, M., Desmedt, Y.: Efficient and secure conference key distribution. In: Lomas, M. (ed.) Security Protocols 1996. LNCS, vol. 1189, pp. 119–130. Springer, Heidelberg (1997)

    Google Scholar 

  10. Burmester, M., Desmedt, Y.: A secure and scalable group key exchange system. Information Processing Letters 94(3), 137–143 (2005)

    Article  MathSciNet  Google Scholar 

  11. Burmester, M., Desmedt, Y.: Identity-based Key Infrastructures (IKI). In: Security and Protection in Information Processing Systems – SEC 2004, pp. 167–176. Kluwer, Dordrecht (2004)

    Google Scholar 

  12. Choi, K.Y., Hwang, J.Y., Lee, D.H.: Efficient ID-based group key agreement with bilinear maps. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 130–144. Springer, Heidelberg (2004)

    Google Scholar 

  13. Desmedt, Y., Lange, T., Burmester, M.: Scalable Authenticated Tree Based Group Key Exchange for Ad-Hoc Groups. In: Financial Crypto 2007. LNCS, vol. 4886, pp. 104–118. Springer, Heidelberg (2007)

    Google Scholar 

  14. Du, X., Wang, Y., Ge, J., Wang, Y.: An improved ID-based authenticated group key agreement scheme. ePrint archive, 2003/260 (2003)

    Google Scholar 

  15. Frey, G., Müller, M., Rück, H.G.: The Tate pairing and the discrete logarithm applied to elliptic curve cryptosystems. IEEE Trans. Inform. Theory 45(5), 1717–1719 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ingemarsson, I., Tang, D.T., Wong, C.W.: A conference key distribution system. IEEE Trans. Inform. Theory 28, 714–720 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  17. Joux, A.: A one round protocol for tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 385–394. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  18. Just, M., Vaudenay, S.: Authenticated multi-party key agreement. In: Kim, K.-c., Matsumoto, T. (eds.) ASIACRYPT 1996. LNCS, vol. 1163, pp. 36–49. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  19. Katz, J., Yung, M.: Scalable protocols for authenticated group key exchange. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 110–125. Springer, Heidelberg (2003), http://www.cs.umd.edu/~jkatz/research.html

    Google Scholar 

  20. Miyaji, A., Nakabayashi, M., Takano, S.: New Explicit Conditions of Elliptic Curve Traces for FR-Reduction. IEICE Trans. Fundamentals E84-A(5), 1234–1243 (2001)

    Google Scholar 

  21. Onete, C.: Elliptic Curves and Pairing Based Cryptosystems. Internship report, Technische Universiteit Eindhoven (2008)

    Google Scholar 

  22. Verheul, E.: Evidence that XTR Is More Secure than Supersingular Elliptic Curves Cryptosystems. J. Cryptology 17, 277–296 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. BT Chair of Information Security, Department of Computer Science, University College London, UK

    Yvo Desmedt

  2. Department of Mathematics and Computer Science, Technische Universiteit Eindhoven, Netherlands

    Tanja Lange

Authors
  1. Yvo Desmedt
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tanja Lange
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Gene Tsudik

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Desmedt, Y., Lange, T. (2008). Revisiting Pairing Based Group Key Exchange. In: Tsudik, G. (eds) Financial Cryptography and Data Security. FC 2008. Lecture Notes in Computer Science, vol 5143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85230-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85230-8_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85229-2

  • Online ISBN: 978-3-540-85230-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation