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Smooth Projective Hashing and Password-Based Authenticated Key Exchange from Lattices

  • Jonathan Katz
  • Vinod Vaikuntanathan
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5912)

Abstract

We describe a public-key encryption scheme based on lattices — specifically, based on the hardness of the learning with error (LWE) problem — that is secure against chosen-ciphertext attacks while admitting (a variant of) smooth projective hashing. This encryption scheme suffices to construct a protocol for password-based authenticated key exchange (PAKE) that can be proven secure based on the LWE assumption in the standard model. We thus obtain the first PAKE protocol whose security relies on a lattice-based assumption.

Keywords

Encryption Scheme Decryption Algorithm Oblivious Transfer Dictionary Attack Common Reference String 
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.

References

  1. 1.
    Ajtai, M.: Generating hard instances of the short basis problem. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, pp. 1–9. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  2. 2.
    Alwen, J., Peikert, C.: Generating shorter bases for hard random lattices. In: STACS 2009. Dagstuhl Seminar Proceedings, vol. 09001, pp. 75–86. Schloss Dagstuhl (2009), http://drops.dagstuhl.de/portals/STACS09/
  3. 3.
    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)CrossRefGoogle Scholar
  4. 4.
    Bellovin, S.M., Merritt, M.: Encrypted key exchange: Password-based protocols secure against dictionary attacks. In: IEEE Symposium on Security & Privacy, pp. 72–84. IEEE, Los Alamitos (1992)Google Scholar
  5. 5.
    Boyko, V., MacKenzie, P.D., 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.
    Canetti, R., Halevi, S., Katz, J., Lindell, Y., MacKenzie, P.D.: Universally composable password-based key exchange. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 404–421. Springer, Heidelberg (2005)Google Scholar
  7. 7.
    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)CrossRefGoogle Scholar
  8. 8.
    Gennaro, R.: Faster and shorter password-authenticated key exchange. In: Canetti, R. (ed.) TCC 2008. LNCS, vol. 4948, pp. 589–606. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Gennaro, R., Lindell, Y.: A framework for password-based authenticated key exchange. ACM Trans. Information and System Security 9(2), 181–234 (2006)CrossRefGoogle Scholar
  10. 10.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: 40th Annual ACM Symposium on Theory of Computing (STOC), pp. 197–206. ACM Press, New York (2008)Google Scholar
  11. 11.
    Goldreich, O., Lindell, Y.: Session-key generation using human passwords only. Journal of Cryptology 19(3), 241–340 (2006)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Goldwasser, S., Vaikuntanathan, V.: Correlation-secure trapdoor functions and CCA-secure encryption from lattices (manuscript, 2009)Google Scholar
  13. 13.
    Gong, L., Lomas, T.M.A., Needham, R.M., Saltzer, J.H.: Protecting poorly chosen secrets from guessing attacks. IEEE J. Selected Areas in Communications 11(5), 648–656 (1993)CrossRefGoogle Scholar
  14. 14.
    Halevi, S., Krawczyk, H.: Public-key cryptography and password protocols. ACM Trans. Information and System Security 2(3), 230–268 (1999)CrossRefGoogle Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    Katz, J., MacKenzie, P.D., Taban, G., Gligor, V.D.: Two-server password-only authenticated key exchange. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 1–16. Springer, Heidelberg (2005)Google Scholar
  17. 17.
    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
  18. 18.
    MacKenzie, P.D., 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
  19. 19.
    Nguyen, M.-H., Vadhan, S.: Simpler session-key generation from short random passwords. Journal of Cryptology 21(1), 52–96 (2008)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Peikert, C.: Public-key cryptosystems from the worst-case shortest vector problem. In: 41st Annual ACM Symposium on Theory of Computing (STOC), pp. 333–342. ACM Press, New York (2009)CrossRefGoogle Scholar
  21. 21.
    Peikert, C., Vaikuntanathan, V., Waters, B.: A framework for efficient and composable oblivious transfer. In: Wagner, D. (ed.) CRYPTO 2008. LNCS, vol. 5157, pp. 554–571. Springer, Heidelberg (2008); A full version, containing additional results, http://eprint.iacr.org/2007/348.pdf Google Scholar
  22. 22.
    Peikert, C., Waters, B.: Lossy trapdoor functions and their applications. In: Ladner, R.E., Dwork, C. (eds.) 40th Annual ACM Symposium on Theory of Computing (STOC), pp. 187–196. ACM Press, New York (2008)Google Scholar
  23. 23.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: 37th Annual ACM Symposium on Theory of Computing (STOC), pp. 84–93. ACM Press, New York (2005)Google Scholar
  24. 24.
    Rosen, A., Segev, G.: Chosen-ciphertext security via correlated products. In: Reingold, O. (ed.) TCC 2009. LNCS, vol. 5444, pp. 419–436. Springer, Heidelberg (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Jonathan Katz
    • 1
  • Vinod Vaikuntanathan
    • 2
  1. 1.University of Maryland 
  2. 2.IBM Research 

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