Computationally-Efficient Password Authenticated Key Exchange Based on Quadratic Residues

  • Muxiang Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4859)


In this paper, we present a computationally efficient password authenticated key exchange protocol based on quadratic residues. The protocol, called QR-CEKE, is derived from the protocol QR-EKE, a previously published password authenticated key exchange protocol based on quadratic residues. The computational time for the client, however, is significant reduced in the protocol QR-CEKE. In comparison with QR-EKE, the protocol QR-CEKE is more suitable to an imbalanced computing environment where a low-end client device communicates with a powerful server over a broadband network. Based on number-theoretic techniques, we show that the computationally efficient password authenticated key exchange protocol is secure against residue attacks, a special type of off-line dictionary attack against password-authenticated key exchange protocols based on factorization. We also provide a formal security analysis of QR-CEKE under the factoring assumption and the random oracle model.


Primitive Root Quadratic Residue Random Oracle Model Dictionary Attack Power Residue 
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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  1. 1.
    Bao, F.: Security analysis of a password authenticated key exchange protocol. In: Boyd, C., Mao, W. (eds.) ISC 2003. LNCS, vol. 2851, pp. 208–217. Springer, Heidelberg (2003)Google Scholar
  2. 2.
    Bellare, M., Pointcheval, D., Rogaway, P.: Authenticated key exchange secure against dictionary attack. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 139–155. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  3. 3.
    Bellovin, S.M., Merritt, M.: Encrypted key exchange: Password-based protocols secure against dictionary attacks. In: Bellovin, S.M., Merritt, M. (eds.) Proc. of the IEEE Symposium on Research in Security and Privacy, Oakland, pp. 72–84 (May 1992)Google Scholar
  4. 4.
    Catalano, D., Pointcheval, D., Pornin, T.: IPAKE: Isomorphisms for Password-based Authenticated Key Exchange. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, Springer, Heidelberg (to appear, 2004)Google Scholar
  5. 5.
    Gennaro, R., Lindell, Y.: A framework for password-based authenticated key exchange. In: Biham, E. (ed.) EUROCRPYT 2003. LNCS, vol. 2656, pp. 524–542. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
  7. 7.
    Lucks, S.: Open key exchange: How to defeat dictionary attacks without encrypting public keys. In: Christianson, B., Lomas, M. (eds.) Proc. Security Protocol Workshop. LNCS, vol. 1361, pp. 79–90. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  8. 8.
    MacKenzie, P., Patel, S., Swaminathan, R.: Password-authenticated key exchange based on RSA. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 599–613. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  9. 9.
    Menezes, A., van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)zbMATHGoogle Scholar
  10. 10.
    Patel, S.: Number theoretic attacks on secure password schemes. In: IEEE Symposium on Security and Privacy, Oakland, California (May 5-7, 1997)Google Scholar
  11. 11.
    Zhu, F., Wong, D., Chan, A., Ye, R.: RSA-based password authenticated key exchange for imbalanced wireless networks. In: Chan, A.H., Gligor, V.D. (eds.) ISC 2002. LNCS, vol. 2433, pp. 150–161. Springer, Heidelberg (2002)Google Scholar
  12. 12.
    Zhang, M.: New approaches to password authenticated key exchange based on RSA. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 230–244. Springer, Heidelberg (2004)Google Scholar
  13. 13.
    Zhang, M.: Password Authenticated Key exchange using quadratic residues. In: Jakobsson, M., Yung, M., Zhou, J. (eds.) ACNS 2004. LNCS, vol. 3089, pp. 248–262. Springer, Heidelberg (2004)Google Scholar
  14. 14.
    Zhang, M.: Further analysis of password authenticated key exchange protocol based on RSA for imbalanced wireless networks. In: Zhang, K., Zheng, Y. (eds.) ISC 2004. LNCS, vol. 3225, pp. 12–24. Springer, Heidelberg (2004)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Muxiang Zhang
    • 1
  1. 1.Verizon Communications Inc., 40 Sylvan Road, Waltham, MA 02451USA

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