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.
This work was supported by the Korean Ministry of Information and Communication under the ITRC (Information Technology Research Center) support program supervised by the IITA (Institute of Information Technology Assessment).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
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)
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)
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)
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)
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)
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)
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)
Jablon, D.: Strong password-only authenticated key exchange. Computer Communication Review, ACM SIGCOMM 26(5), 5–26 (1996)
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)
Kwon, T.: Authentication and key agreement via memorable passwords. In: Proc. of Network and Distributed System Security Symposium (February 2001)
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)
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)
Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1996)
Patel, S.: Number theoretic attacks on secure password schemes. In: Proc. of IEEE Symposium on Security and Privacy (May 1997)
Shoup, V.: A Computational Introduction to Number Theory and Algebra. Cambridge University Press, Cambridge (2005)
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)
Wu, T.: The secure remote password protocol. In: Proc. of Network and Distributed System Security Symposium, Sandiego, pp. 97–111 (March 1998)
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)
Zhang, M.: New approaches to password authenticated key exchange based on RSA. Cryptology ePrint Archive, Report 2004/033, http://eprint.iacr.org
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)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Park, S., Nam, J., Kim, S., Won, D. (2006). Efficient Password-Authenticated Key Exchange Based on RSA. In: Abe, M. (eds) Topics in Cryptology – CT-RSA 2007. CT-RSA 2007. Lecture Notes in Computer Science, vol 4377. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11967668_20
Download citation
DOI: https://doi.org/10.1007/11967668_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69327-7
Online ISBN: 978-3-540-69328-4
eBook Packages: Computer ScienceComputer Science (R0)