Efficient Password-Authenticated Key Exchange Based on RSA

  • Sangjoon Park
  • Junghyun Nam
  • Seungjoo Kim
  • Dongho Won
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4377)

Abstract

In this paper, we propose an efficient password-authenticated key exchange (PAKE) based on RSA, called RSA-EPAKE. Unlike SNAPI using a prime pubic key e greater than an RSA modulus n, RSA-EPAKE uses the public key e of a 96-bit prime, where e = 2H(n, s) + 1 for some s. By the Prime Number Theorem, it is easy to find such an s. But the probability that an adversary finds n and s with \(\gcd(e, \phi(n)) \neq 1\) is less than 2− 80. Hence, in the same as SNAPI, RSA-EPAKE is also secure against e-residue attacks. The computational load on Alice (or Server) and Bob (or Client) in RSA-EPAKE is less than in the previous RSA-based PAKEs such as SNAPI, PEKEP ,CEKEP, and QR-EKE. In addition, the computational load on Bob in RSA-EPAKE is less than in PAKEs based on Diffie-Hellman key exchange (DHKE) with a 160-bit exponent. If we exclude perfect forward secrecy from consideration, the computational load on Alice is a little more than that in PAKEs based on DHKE with a 160-bit exponent. In this paper, we compare RSA-EPAKE with SNAPI, PEKEP, and CEKEP in computation and the number of rounds, and provide a formal security analysis of RSA-EPAKE under the RSA assumption in the random oracle model.

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References

  1. 1.
    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
  2. 2.
    Bellare, M., Rogaway, P.: Entity authentication and key distribution. In: De Santis, A. (ed.) EUROCRYPT 1994. LNCS, vol. 950, pp. 92–111. Springer, Heidelberg (1995)CrossRefGoogle Scholar
  3. 3.
    Bellovin, S., Merritt, M.: Encrypted key exchange: Password-based protocols secure against dictionary attacks. In: Proc. of the IEEE Symposium on Research in Security and Privacy, pp. 72–84 (May 1992)Google Scholar
  4. 4.
    Bellovin, S., Merritt, M.: Augmented encrypted key exchange: A password-based protocol secure against dictionary attacks and password file compromise. In: Proc. of the 1st ACM Conference on Computer and Communications Security, pp. 244–250. ACM, New York (1993)CrossRefGoogle Scholar
  5. 5.
    Boyko, V., MacKenzie, P., 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
  6. 6.
    Catalano, D., Pointcheval, D., Pornin, T.: IPAKE: Isomorphism for password-based authenticated key exchange. In: Franklin, M. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 477–493. Springer, Heidelberg (2004)Google Scholar
  7. 7.
    Gennaro, R., Lindell, Y.: A framework for password-based authenticated key exchange. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 524–542. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  8. 8.
    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
  9. 9.
    Jablon, D.: Strong password-only authenticated key exchange. Computer Communication Review, ACM SIGCOMM 26(5), 5–26 (1996)CrossRefGoogle Scholar
  10. 10.
    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
  11. 11.
    Kwon, T.: Authentication and key agreement via memorable passwords. In: Proc. of Network and Distributed System Security Symposium (February 2001)Google Scholar
  12. 12.
    Lucks, S.: Open key exchange: How to defeat dictionary attacks without encrypting public keys. In: Christianson, B., Lomas, M. (eds.) Security Protocols 1997. LNCS, vol. 1361, pp. 79–90. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. 13.
    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
  14. 14.
    Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)CrossRefGoogle Scholar
  15. 15.
    Patel, S.: Number theoretic attacks on secure password schemes. In: Proc. of IEEE Symposium on Security and Privacy (May 1997)Google Scholar
  16. 16.
    Shoup, V.: A Computational Introduction to Number Theory and Algebra. Cambridge University Press, Cambridge (2005)MATHGoogle Scholar
  17. 17.
    Wong, D., Chan, A., Zhu, F.: More efficient password authenticated key exchange based on RSA. In: Johansson, T., Maitra, S. (eds.) INDOCRYPT 2003. LNCS, vol. 2904, pp. 375–387. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  18. 18.
    Wu, T.: The secure remote password protocol. In: Proc. of Network and Distributed System Security Symposium, Sandiego, pp. 97–111 (March 1998)Google Scholar
  19. 19.
    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)CrossRefGoogle Scholar
  20. 20.
    Zhang, M.: New approaches to password authenticated key exchange based on RSA. Cryptology ePrint Archive, Report 2004/033, http://eprint.iacr.org
  21. 21.
    Zhang, M.: Password authenticated key exchange using quadratic residues. In: Jakobsson, M., Yung, M., Zhou, J. (eds.) ACNS 2004. LNCS, vol. 3089, pp. 233–247. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  22. 22.
    Zhu, F., Wong, D., Chan, A., Ye, R.: RSA-based password authenticated key exchange for imbalance wireless networks. In: Chan, A.H., Gligor, V.D. (eds.) ISC 2002. LNCS, vol. 2433, pp. 150–161. Springer, Heidelberg (2002)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Sangjoon Park
    • 1
  • Junghyun Nam
    • 1
  • Seungjoo Kim
    • 1
  • Dongho Won
    • 1
  1. 1.Information Security Group, School of Information and Communication EngineeringSungkyunkwan UniversityGyeonggi-doKorea

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