Skip to main content
SpringerLink
Log in

Two-Round PAKE Protocol over Lattices Without NIZK

  • Conference paper
  • First Online:
Information Security and Cryptology (Inscrypt 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11449))

Included in the following conference series:

Abstract

Reducing the number of communication rounds of Password-based Authenticated Key Exchange (\(\textsf {PAKE} \)) protocols is of great practical significance. At PKC’15, Abdalla et al. relaxed the requirements of Gennaro-Lindell’s framework for three-round PAKE protocols, and obtained a two-round PAKE protocol under the traditional DDH-based smooth projective hash function (\(\mathsf {SPHF} \)). At ASIACRYPT’17, Zhang and Yu proposed a lattice-based two-round PAKE protocol via the approximate \(\mathsf {SPHF} \). However, the language of Zhang-Yu’s SPHF depends on simulation-sound non-interactive zero-knowledge (NIZK) proofs, for which there is no concrete construction without random oracle under lattice-based assumptions. To our knowledge, how to design a lattice-based two-round \(\textsf {PAKE} \) protocol via an efficient \(\mathsf {SPHF} \) scheme without NIZK remains a challenge. In this paper, we propose the first two-round \(\textsf {PAKE} \) protocol over lattices without NIZK. Our protocol is in accordance with the framework of Abdalla et al. (PKC’15) while attaining post-quantum security. We overcome the limitations of existing schemes by relaxing previous security assumptions (i.e., both the client and the sever need IND-CCA-secure encryption), and build two new lattice-based \(\mathsf {SPHF} \)s, one for IND-CCA-secure Micciancio-Peikert ciphertext (at the client side) and the other for IND-CPA-secure Regev ciphertext (at the server side). Particularly, our protocol attains provable security.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Note that every \(\text {IND-CCA}2\)-secure scheme is also an \(\text {IND-PCA}\)-secure scheme.

  2. 2.

    The non-adaptive approximate \(\mathsf {SPHF} \) means the adversary can see the projective key \(ph \) before choosing the word \(W \).

  3. 3.

    They improved the Gennaro-Lindell framework to reduce the round number to two.

  4. 4.

    We use big-O notation to asymptotically bound the growth of a running time to within constant factors.

References

  1. Bellovin, S.M., Merritt, M.: Encrypted key exchange: password-based protocols secure against dictionary attacks. In: Proceedings of the IEEE S&P 1992, pp. 72–84 (1992)

    Google Scholar 

  2. 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). https://doi.org/10.1007/3-540-44987-6_29

    Chapter  Google Scholar 

  3. Hao, F., Ryan, P.: J-PAKE: authenticated key exchange without PKI. In: Gavrilova, M.L., Tan, C.J.K., Moreno, E.D. (eds.) Part II. LNCS, vol. 6480, pp. 192–206. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17697-5_10

    Chapter  Google Scholar 

  4. Jarecki, S., Krawczyk, H., Xu, J.: OPAQUE: an asymmetric PAKE protocol secure against pre-computation attacks. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part III. LNCS, vol. 10822, pp. 456–486. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_15

    Chapter  Google Scholar 

  5. Gennaro, R., Lindell, Y.: A framework for password-based authenticated key exchange. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 524–543. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-39200-9_33

    Chapter  Google Scholar 

  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

    Chapter  Google Scholar 

  7. Benhamouda, F., Blazy, O., Chevalier, C., Pointcheval, D., Vergnaud, D.: New techniques for SPHFs and efficient one-round PAKE protocols. In: Canetti, R., Garay, J.A. (eds.) CRYPTO 2013, Part I. LNCS, vol. 8042, pp. 449–475. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-40041-4_25

    Chapter  Google Scholar 

  8. Groce, A., Katz, J.: A new framework for efficient password-based authenticated key exchange. In: Proceedings of the ACM CCS 2010, pp. 516–525 (2010)

    Google Scholar 

  9. 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). https://doi.org/10.1007/978-3-540-30564-4_19

    Chapter  Google Scholar 

  10. 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). https://doi.org/10.1007/978-3-662-46447-2_15

    Chapter  MATH  Google Scholar 

  11. Zhang, J., Yu, Y.: Two-round PAKE from approximate SPH and instantiations from lattices. In: Takagi, T., Peyrin, T. (eds.) ASIACRYPT 2017, Part III. LNCS, vol. 10626, pp. 37–67. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-70700-6_2

    Chapter  Google Scholar 

  12. Micciancio, D., Peikert, C.: Trapdoors for lattices: simpler, tighter, faster, smaller. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol. 7237, pp. 700–718. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-29011-4_41

    Chapter  Google Scholar 

  13. 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

    Chapter  Google Scholar 

  14. Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proceedings of ACM STOC 2005, pp. 84–93 (2005)

    Google Scholar 

  15. 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). https://doi.org/10.1007/978-3-642-19571-6_18

    Chapter  Google Scholar 

  16. Abdalla, M., Benhamouda, F., MacKenzie, P.: Security of the J-PAKE password-authenticated key exchange protocol. In: Proceedings of IEEE S&P 2015, pp. 571–587 (2015)

    Google Scholar 

  17. 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, Part I. LNCS, vol. 9878, pp. 111–131. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45744-4_6

    Chapter  Google Scholar 

  18. Wang, D., Cheng, H., Wang, P., Huang, X., Jian, G.: Zipf’s law in passwords. IEEE Trans. Inform. Foren. Secur. 12(11), 2776–2791 (2017)

    Article  Google Scholar 

  19. Canetti, R., Krawczyk, H.: Universally composable notions of key exchange and secure channels. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 337–351. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_22

    Chapter  Google Scholar 

  20. 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). https://doi.org/10.1007/11426639_24

    Chapter  Google Scholar 

  21. Gentry, C., MacKenzie, P., Ramzan, Z.: A method for making password-based key exchange resilient to server compromise. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 142–159. Springer, Heidelberg (2006). https://doi.org/10.1007/11818175_9

    Chapter  Google Scholar 

  22. Dupont, P.-A., Hesse, J., Pointcheval, D., Reyzin, L., Yakoubov, S.: Fuzzy password-authenticated key exchange. In: Nielsen, J.B., Rijmen, V. (eds.) EUROCRYPT 2018, Part III. LNCS, vol. 10822, pp. 393–424. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-78372-7_13

    Chapter  Google Scholar 

  23. Cramer, R., Shoup, V.: Universal hash proofs and a paradigm for adaptive chosen ciphertext secure public-key encryption. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 45–64. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-46035-7_4

    Chapter  Google Scholar 

  24. Brakerski, Z.: Fully homomorphic encryption without modulus switching from classical GapSVP. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol. 7417, pp. 868–886. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32009-5_50

    Chapter  Google Scholar 

  25. Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem: extended abstract. In: Proceedings of ACM STOC 2009, pp. 333–342 (2009)

    Google Scholar 

  26. Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Proceedings of ACM STOC 2008, pp. 187–196 (2008)

    Google Scholar 

  27. Li, Z., Ma, C., Wang, D.: Leakage resilient leveled FHE on multiple bit message. IEEE Trans. Big Data. https://doi.org/10.1109/TBDATA.2017.2726554

  28. Bellare, M., Rogaway, P.: Entity authentication and key distribution. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 232–249. Springer, Heidelberg (1994). https://doi.org/10.1007/3-540-48329-2_21

    Chapter  Google Scholar 

  29. Bellare, M., Rogaway, P.: Provably secure session key distribution: the three party case. In: Proceedings of ACM STOC 1995, pp. 57–66 (1995)

    Google Scholar 

  30. Katz, J., Ostrovsky, R., Yung, M.: Efficient and secure authenticated key exchange using weak passwords. J. ACM 57(1), 3:1–3:39 (2009)

    Article  MathSciNet  Google Scholar 

  31. Jarecki, S., Krawczyk, H., Shirvanian, M., Saxena, N.: Two-factor authentication with end-to-end password security. In: Abdalla, M., Dahab, R. (eds.) PKC 2018, Part II. LNCS, vol. 10770, pp. 431–461. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_15

    Chapter  Google Scholar 

  32. Huang, K., Manulis, M., Chen, L.: Password authenticated keyword search. In: Proceedings of PAC 2017, pp. 129–140 (2017)

    Google Scholar 

  33. Wang, D., Wang, P.: Two birds with one stone: two-factor authentication with security beyond conventional bound. IEEE Trans. Depend. Secure Comput. 15(4), 708–722 (2018)

    Google Scholar 

  34. Becerra, J., Iovino, V., Ostrev, D., Šala, P., Škrobot, M.: Tightly-secure PAK(E). In: Capkun, S., Chow, S.S.M. (eds.) CANS 2017. LNCS, vol. 11261, pp. 27–48. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-02641-7_2

    Chapter  Google Scholar 

  35. Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: Proceedings of ACM STOC 2008, pp. 197–206 (2008)

    Google Scholar 

  36. Lindner, R., Peikert, C.: Better key sizes (and attacks) for LWE-based encryption. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 319–339. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-19074-2_21

    Chapter  Google Scholar 

  37. Dolev, D., Dwork, C., Naor, M.: Nonmalleable cryptography. SIAM J. Comput. 30(2), 391–437 (2000)

    Article  MathSciNet  Google Scholar 

  38. Boneh, D., Canetti, R., Halevi, S., Katz, J.: Chosen-ciphertext security from identity-based encryption. SIAM J. Comput. 36(5), 1301–1328 (2007)

    Article  MathSciNet  Google Scholar 

  39. Benhamouda, F., Blazy, O., Ducas, L., Quach, W.: Hash proof systems over lattices revisited. In: Abdalla, M., Dahab, R. (eds.) PKC 2018, Part II. LNCS, vol. 10770, pp. 644–674. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-76581-5_22

    Chapter  Google Scholar 

  40. Abdalla, M., Ben Hamouda, F., Pointcheval, D.: Tighter reductions for forward-secure signature schemes. In: Kurosawa, K., Hanaoka, G. (eds.) PKC 2013. LNCS, vol. 7778, pp. 292–311. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-36362-7_19

    Chapter  Google Scholar 

  41. Katz, J., Ostrovsky, R., Yung, M.: Forward secrecy in password-only key exchange protocols. In: Cimato, S., Persiano, G., Galdi, C. (eds.) SCN 2002. LNCS, vol. 2576, pp. 29–44. Springer, Heidelberg (2003). https://doi.org/10.1007/3-540-36413-7_3

    Chapter  MATH  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous reviewers for their helpful advice and comments. This work was supported by the National Natural Science Foundation of China (No. 61802006 and No. 61802214).

Author information

Authors and Affiliations

  1. College of Computer Science and Technology, Qingdao University, Qingdao, China

    Zengpeng Li

  2. School of EECS, Peking University, Beijing, 100871, China

    Ding Wang

Authors
  1. Zengpeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ding Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ding Wang .

Editor information

Editors and Affiliations

  1. University of Wollongong, Wollongong, NSW, Australia

    Fuchun Guo

  2. Fujian Normal University, Fujian, China

    Xinyi Huang

  3. Columbia University, New York, NY, USA

    Moti Yung

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Li, Z., Wang, D. (2019). Two-Round PAKE Protocol over Lattices Without NIZK. In: Guo, F., Huang, X., Yung, M. (eds) Information Security and Cryptology. Inscrypt 2018. Lecture Notes in Computer Science(), vol 11449. Springer, Cham. https://doi.org/10.1007/978-3-030-14234-6_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-14234-6_8

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-14233-9

  • Online ISBN: 978-3-030-14234-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation