Two More Efficient Variants of the J-PAKE Protocol

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9696)

Abstract

Recently, the password-authenticated key exchange protocol J-PAKE of Hao and Ryan (Workshop on Security Protocols 2008) was formally proven secure in the algebraic adversary model by Abdalla et al. (IEEE S&P 2015). In this paper, we propose and examine two variants of J-PAKE - which we call RO-J-PAKE and CRS-J-PAKE - that each makes the use of two less zero-knowledge proofs than the original protocol. We show that they are provably secure following a similar strategy to that of Abdalla et al. We also study their efficiency as compared to J-PAKE’s, also taking into account how the groups are chosen. Namely, we treat the cases of subgroups of finite fields and elliptic curves. Our work reveals that, for subgroups of finite fields, CRS-J-PAKE is indeed more efficient than J-PAKE, while RO-J-PAKE is much less efficient. On the other hand, when instantiated with elliptic curves, both RO-J-PAKE and CRS-J-PAKE are more efficient than J-PAKE, with CRS-J-PAKE being the best of the three. Regardless of implementation, we note that RO-J-PAKE enjoys a looser security reduction than both J-PAKE and CRS-J-PAKE. CRS-J-PAKE has the tightest security proof, but relies on an additional trust assumption at setup time.

Keywords

Password-authenticated key exchange J-PAKE Efficiency Random oracle Common reference string Zero-knowledge proof 

References

  1. 1.
  2. 2.
  3. 3.
    OpenSSL (2015). https://www.openssl.org/
  4. 4.
    Thread Protocol (2015). http://threadgroup.org/
  5. 5.
    Abdalla, M., Benhamouda, F., MacKenzie, P.: Security of the J-PAKE password-authenticated key exchange protocol. In: 2015 IEEE Symposium on Security and Privacy, SP 2015, pp. 571–587. IEEE Computer Society (2015)Google Scholar
  6. 6.
    Abdalla, M., Benhamouda, F., Pointcheval, D.: Public-Key encryption indistinguishable under plaintext-checkable attacks. In: Katz, J. (ed.) PKC 2015. LNCS, vol. 9020, pp. 332–352. Springer, Heidelberg (2015)Google Scholar
  7. 7.
    Abdalla, M., Fouque, P.-A., Pointcheval, D.: Password-Based authenticated key exchange in the three-party setting. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 65–84. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Bellare, M., Pointcheval, D., Rogaway, P.: Authenticated key exchange secure against dictionary attacks. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 139–155. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Bellare, M., Rogaway, P.: Random oracles are practical: a paradigm for designing efficient protocols. In: ACM Conference on Computer and Communications Security, pp. 62–73. ACM Press (1993)Google Scholar
  10. 10.
    Bellovin, S.M., Merritt, M.: Encrypted key exchange: password-based protocols secure against dictionary attacks. In: 1992 IEEE Symposium on Research in Security and Privacy, SP 1992, pp. 72–84 (1992)Google Scholar
  11. 11.
    Boneh, D.: The decision diffie-hellman problem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 48–63. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  12. 12.
    Boyko, V., MacKenzie, P.D., Patel, S.: Provably secure password-authenticated key exchange using diffie-hellman. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 156–171. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  13. 13.
    Brier, E., Coron, J.-S., Icart, T., Madore, D., Randriam, H., Tibouchi, M.: Efficient indifferentiable hashing into ordinary elliptic curves. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 237–254. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Canetti, R., Halevi, S., Katz, J., Lindell, Y., MacKenzie, P.: Universally composable password-based key exchange. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 404–421. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. 15.
    Goldreich, O., Lindell, Y.: Session-Key generation using human passwords only. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 408–432. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  16. 16.
    Groth, J.: Simulation-Sound NIZK proofs for a practical language and constant size group signatures. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 444–459. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  17. 17.
    Groth, J., Ostrovsky, R.: Cryptography in the multi-string model. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 323–341. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  18. 18.
    Hao, F., Ryan, P.: J-PAKE: authenticated key exchange without PKI. Trans. Comput. Sci. 11, 192–206 (2010)MathSciNetGoogle Scholar
  19. 19.
    Jablon, D.P.: Strong password-only authenticated key exchange. ACM SIGCOMM Comput. Commun. Rev. 26(5), 5–26 (1996)CrossRefGoogle Scholar
  20. 20.
    Jiang, S., Gong, G.: Password based key exchange with mutual authentication. In: Handschuh, H., Hasan, M.A. (eds.) SAC 2004. LNCS, vol. 3357, pp. 267–279. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  21. 21.
    Katz, J., Ostrovsky, R., Yung, M.: Efficient password-authenticated key exchange using human-memorable passwords. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 475–494. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  22. 22.
    Katz, J., Vaikuntanathan, V.: Round-Optimal password-based authenticated key exchange. In: Ishai, Y. (ed.) TCC 2011. LNCS, vol. 6597, pp. 293–310. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  23. 23.
    Krawczyk, H.: Cryptographic extraction and key derivation: the HKDF scheme. In: Rabin, T. (ed.) CRYPTO 2010. LNCS, vol. 6223, pp. 631–648. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  24. 24.
    MacKenzie, P.: The PAK Suite: Protocols for Password-Authenticated Key Exchange. DIMACS Technical report 2002-46 (2002)Google Scholar
  25. 25.
    MacKenzie, P.D.: More efficient password-authenticated key exchange. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 361–377. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  26. 26.
    MacKenzie, P.D., Patel, S.: Hard bits of the discrete log with applications to password authentication. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 209–226. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Pointcheval, D.: Password-Based authenticated key exchange. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 390–397. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  28. 28.
    Schnorr, C.-P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1990)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.SnT, University of LuxembourgLuxembourgLuxembourg

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