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Strongly Secure One-Round Group Authenticated Key Exchange in the Standard Model

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Cryptology and Network Security (CANS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 8257))

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Abstract

One-round group authenticated key exchange (GAKE) protocols typically provide implicit authentication and appealing bandwidth efficiency. As a special case of GAKE – the pairing-based one-round tripartite authenticated key exchange (3AKE), recently gains much attention of research community due to its strong security. Several pairing-based one-round 3AKE protocols have recently been proposed to achieve provable security in the g-eCK model. In contrast to earlier GAKE models, the g-eCK model particularly formulates the security properties regarding resilience to the leakage of various combinations of long-term key and ephemeral session state, and provision of weak perfect forward secrecy in a single model. However, the g-eCK security proofs of previous protocols are only given under the random oracle model. In this work, we give a new construction for pairing-based one-round 3AKE protocol which is provably secure in the g-eCK model without random oracles. Security of proposed protocol is reduced to the hardness of Cube Bilinear Decisional Diffie-Hellman (CBDDH) problem for symmetric pairing. We also extend the proposed 3AKE scheme to a GAKE scheme with more than three group members, based on multilinear maps. We prove g-eCK security of our GAKE scheme in the standard model under the natural multilinear generalization of the CBDDH assumption.

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References

  1. Al-Riyami, S.S., Paterson, K.G.: Tripartite authenticated key agreement protocols from pairings. In: Paterson, K.G. (ed.) Cryptography and Coding 2003. LNCS, vol. 2898, pp. 332–359. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  2. Baek, J., Safavi-Naini, R., Susilo, W.: Efficient multi-receiver identity-based encryption and its application to broadcast encryption. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 380–397. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Bellare, M., Boldyreva, A., Palacio, A.: An uninstantiable random-oracle-model scheme for a hybrid-encryption problem. In: Cachin, C., Camenisch, J. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 171–188. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  4. Bellare, M., Rogaway, P.: Random oracles are practical: A paradigm for designing efficient protocols. In: Ashby, V. (ed.) ACM CCS 1993: 1st Conference on Computer and Communications Security, pp. 62–73. ACM Press (November 1993)

    Google Scholar 

  5. 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)

    Chapter  Google Scholar 

  6. Boneh, D., Silverberg, A.: Applications of multilinear forms to cryptography. IACR Cryptology ePrint Archive, Report 2002/80 (2002), http://eprint.iacr.org/

  7. Bresson, E., Chevassut, O., Pointcheval, D.: Dynamic group Diffie-Hellman key exchange under standard assumptions. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 321–336. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

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

    Google Scholar 

  9. Canetti, R., Goldreich, O., Halevi, S.: The random oracle methodology, revisited (preliminary version). In: 30th Annual ACM Symposium on Theory of Computing, pp. 209–218. ACM Press (May 1998)

    Google Scholar 

  10. Fujioka, A., Manulis, M., Suzuki, K., Ustaoğlu, B.: Sufficient condition for ephemeral key-leakage resilient tripartite key exchange. In: Susilo, W., Mu, Y., Seberry, J. (eds.) ACISP 2012. LNCS, vol. 7372, pp. 15–28. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. Garg, S., Gentry, C., Halevi, S.: Candidate multilinear maps from ideal lattices. In: Johansson, T., Nguyen, P.Q. (eds.) EUROCRYPT 2013. LNCS, vol. 7881, pp. 1–17. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  12. Gorantla, M.C., Boyd, C., González Nieto, J.M.: Modeling key compromise impersonation attacks on group key exchange protocols. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 105–123. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  13. Hofheinz, D., Jager, T., Kiltz, E.: Short signatures from weaker assumptions. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 647–666. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  15. LaMacchia, B.A., Lauter, K., Mityagin, A.: Stronger security of authenticated key exchange. In: Susilo, W., Liu, J.K., Mu, Y. (eds.) ProvSec 2007. LNCS, vol. 4784, pp. 1–16. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  16. Li, Y., Yang, Z.: Strongly secure one-round group authenticated key exchange in the standard model. In: Abdalla, M., Nita-Rotaru, C., Dahab, R. (eds.) CANS 2013. LNCS, vol. 8257, pp. 123–142. Springer, Heidelberg (2013)

    Google Scholar 

  17. Lim, M.-H., Lee, S., Park, Y., Lee, H.: An enhanced one-round pairing-based tripartite authenticated key agreement protocol. In: Gervasi, O., Gavrilova, M.L. (eds.) ICCSA 2007, Part II. LNCS, vol. 4706, pp. 503–513. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Manulis, M., Suzuki, K., Ustaoglu, B.: Modeling leakage of ephemeral secrets in tripartite/group key exchange. In: Lee, D., Hong, S. (eds.) ICISC 2009. LNCS, vol. 5984, pp. 16–33. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Shoup, V.: Lower bounds for discrete logarithms and related problems. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 256–266. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  20. Shoup, V.: Sequences of games: a tool for taming complexity in security proofs. Cryptology ePrint Archive, Report 2004/332 (2004), http://eprint.iacr.org/

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Authors and Affiliations

  1. Horst Göortz Institute for IT Security, Ruhr-University Bochum, Germany

    Yong Li & Zheng Yang

Authors
  1. Yong Li
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  2. Zheng Yang
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Editor information

Editors and Affiliations

  1. École Normale Supérieure and CNRS,, 45 rue d’Ulm, 75005, Paris, France

    Michel Abdalla

  2. Department of Computer Science, Purdue University, LWSN 2142J, 305 N. University Street,, 47907, West Lafayette, IN, USA

    Cristina Nita-Rotaru

  3. Institute of Computing, University of Campinas, Avenida Albert Einstein 1251, 13083-852, Campinas, SP, Brazil

    Ricardo Dahab

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Li, Y., Yang, Z. (2013). Strongly Secure One-Round Group Authenticated Key Exchange in the Standard Model. In: Abdalla, M., Nita-Rotaru, C., Dahab, R. (eds) Cryptology and Network Security. CANS 2013. Lecture Notes in Computer Science, vol 8257. Springer, Cham. https://doi.org/10.1007/978-3-319-02937-5_7

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  • DOI: https://doi.org/10.1007/978-3-319-02937-5_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-02936-8

  • Online ISBN: 978-3-319-02937-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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