Abstract
Three-party key exchange, where two clients aim to agree a session key with the help of a trusted server, is prevalent in present-day systems. In this paper, we present a practical and secure three-party password-based authenticated key exchange protocol over ideal lattices. Aside from hash functions our protocol does not rely on external primitives in the construction and the security of our protocol is directly relied on the Ring Learning with Errors (RLWE) assumption. Our protocol attains provable security. A proof-of-concept implementation shows our protocol is indeed practical.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
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). https://doi.org/10.1007/978-3-540-30580-4_6
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). https://doi.org/10.1007/3-540-45539-6_11
Bellare, M., Rogaway, P.: Provably secure session key distribution: the three party case. In: Proceedings of the Twenty-Seventh Annual ACM Symposium on Theory of Computing, Las Vegas, Nevada, USA, 29 May–1 June 1995, pp. 57–66 (1995)
Boneh, D., Dagdelen, Ö., Fischlin, M., Lehmann, A., Schaffner, C., Zhandry, M.: Random oracles in a quantum world. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 41–69. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_3
Bos, J.W., Costello, C., Naehrig, M., Stebila, D.: Post-quantum key exchange for the TLS protocol from the ring learning with errors problem. In: 2015 IEEE Symposium on Security and Privacy, SP 2015, San Jose, CA, USA, 17–21 May 2015, pp. 553–570 (2015)
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). https://doi.org/10.1007/3-540-45539-6_12
Chang, T.Y., Hwang, M., Yang, W.: A communication-efficient three-party password authenticated key exchange protocol. Inf. Sci. 181(1), 217–226 (2011)
Ding, J.: A simple provably secure key exchange scheme based on the learning with errors problem. IACR Cryptology ePrint Archive 2012, 688 (2012). http://eprint.iacr.org/2012/688
Ding, J., Alsayigh, S., Lancrenon, J., RV, S., Snook, M.: Provably secure password authenticated key exchange based on RLWE for the post-quantum world. In: Handschuh, H. (ed.) CT-RSA 2017. LNCS, vol. 10159, pp. 183–204. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-52153-4_11
Ding, Y., Horster, P.: Undetectable on-line password guessing attacks. Oper. Syst. Rev. 29(4), 77–86 (1995)
Dongna, E., Cheng, Q., Ma, C.: Password authenticated key exchange based on RSA in the three-party settings. In: Pieprzyk, J., Zhang, F. (eds.) ProvSec 2009. LNCS, vol. 5848, pp. 168–182. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04642-1_15
Katz, J., Vaikuntanathan, V.: Smooth projective hashing and password-based authenticated key exchange from lattices. In: Matsui, M. (ed.) ASIACRYPT 2009. LNCS, vol. 5912, pp. 636–652. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-10366-7_37
Kim, H.S., Choi, J.: Enhanced password-based simple three-party key exchange protocol. Comput. Electr. Eng. 35(1), 107–114 (2009)
Krawczyk, H.: HMQV: a high-performance secure Diffie-Hellman protocol. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 546–566. Springer, Heidelberg (2005). https://doi.org/10.1007/11535218_33
Lee, T., Hwang, T., Lin, C.: Enhanced three-party encrypted key exchange without server public keys. Comput. Secur. 23(7), 571–577 (2004)
Lin, C., Sun, H., Hwang, T.: Three-party encrypted key exchange: attacks and a solution. Oper. Syst. Rev. 34(4), 12–20 (2000)
Lin, C., Sun, H., Steiner, M., Hwang, T.: Three-party encrypted key exchange without server public-keys. IEEE Commun. Lett. 5(12), 497–499 (2001)
Lu, R., Cao, Z.: Simple three-party key exchange protocol. Comput. Secur. 26(1), 94–97 (2007)
Lyubashevsky, V.: Lattice signatures without trapdoors. IACR Cryptology ePrint Archive 2011, 537 (2011). http://eprint.iacr.org/2011/537
Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1–23. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-13190-5_1
MacKenzie, P.: The PAK suite: protocols for password-authenticated key exchange. In: DIMACS Technical Report 2002–46, p. 7 (2002)
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). https://doi.org/10.1007/3-540-44448-3_46
Peikert, C.: Lattice cryptography for the internet. In: Mosca, M. (ed.) PQCrypto 2014. LNCS, vol. 8772, pp. 197–219. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-11659-4_12
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM 56(6), 34:1–34:40 (2009)
Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)
Steiner, M., Tsudik, G., Waidner, M.: Refinement and extension of encrypted key exchange. Oper. Syst. Rev. 29(3), 22–30 (1995)
Sun, H., Chen, B., Hwang, T.: Secure key agreement protocols for three-party against guessing attacks. J. Syst. Softw. 75(1–2), 63–68 (2005)
Wang, D., Jian, G., Wang, P.: Zipf’s law in passwords. IACR Cryptology ePrint Archive 2014, 631 (2014). http://eprint.iacr.org/2014/631
Wang, D., Wang, P.: On the implications of Zipf’s law in passwords. In: Askoxylakis, I., Ioannidis, S., Katsikas, S., Meadows, C. (eds.) ESORICS 2016. LNCS, vol. 9878, pp. 111–131. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45744-4_6
Wang, D., Zhang, Z., Wang, P., Yan, J., Huang, X.: Targeted online password guessing: an underestimated threat. In: Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, Vienna, Austria, 24–28 October 2016, pp. 1242–1254 (2016)
Zhang, J., Yu, Y.: Two-round PAKE from approximate SPH and instantiations from lattices. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017. LNCS, vol. 10626, pp. 37–67. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70700-6_2
Zhang, J., Zhang, Z., Ding, J., Snook, M., Dagdelen, Ö.: Authenticated key exchange from ideal lattices. In: Oswald, E., Fischlin, M. (eds.) EUROCRYPT 2015. LNCS, vol. 9057, pp. 719–751. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46803-6_24
Acknowledgments
This article is supported by The National Key Research and Development Program of China (Grant No. 2017YFA0303903), National Cryptography Development Fund (No. MMJJ20170121), and Zhejiang Province Key R&D Project (No. 2017C01062). Authors thank Aijun Ge for discussions and the anonymous ISPEC’19 reviewers for helpful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Liu, C., Zheng, Z., Jia, K., You, Q. (2019). Provably Secure Three-Party Password-Based Authenticated Key Exchange from RLWE. In: Heng, SH., Lopez, J. (eds) Information Security Practice and Experience. ISPEC 2019. Lecture Notes in Computer Science(), vol 11879. Springer, Cham. https://doi.org/10.1007/978-3-030-34339-2_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-34339-2_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-34338-5
Online ISBN: 978-3-030-34339-2
eBook Packages: Computer ScienceComputer Science (R0)