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Efficient Authentication from Hard Learning Problems

  • Eike Kiltz
  • Krzysztof Pietrzak
  • David Cash
  • Abhishek Jain
  • Daniele Venturi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6632)

Abstract

We construct efficient authentication protocols and message-authentication codes (MACs) whose security can be reduced to the learning parity with noise (LPN) problem.

Despite a large body of work – starting with the HB protocol of Hopper and Blum in 2001 – until now it was not even known how to construct an efficient authentication protocol from LPN which is secure against man-in-the-middle (MIM) attacks. A MAC implies such a (two-round) protocol.

Keywords

Authentication Protocol Random Oracle Message Authentication Code Active Attack Parallel Repetition 
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.
    The full version of this paper will be posted on the Cryptology ePrint Archive, http://eprint.iacr.org/
  2. 2.
    Agrawal, S., Boneh, D., Boyen, X.: Efficient lattice (H)IBE in the standard model. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 553–572. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  3. 3.
    Berlekamp, E., McEliece, R., van Tilborg, H.: On the inherent intractability of certain coding problems. IEEE Transactions on Information Theory 24(3), 384–386 (1978)zbMATHCrossRefGoogle Scholar
  4. 4.
    Blum, A., Furst, M.L., Kearns, M.J., Lipton, R.J.: Cryptographic primitives based on hard learning problems. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 278–291. Springer, Heidelberg (1994)Google Scholar
  5. 5.
    Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. In: 32nd ACM STOC, pp. 435–440. ACM Press, New York (May 2000)Google Scholar
  6. 6.
    Blum, A., Kalai, A., Wasserman, H.: Noise-tolerant learning, the parity problem, and the statistical query model. J. ACM 50(4), 506–519 (2003)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Boneh, D., Boyen, X.: Efficient selective-ID secure identity-based encryption without random oracles. In: Cachin, C., Camenisch, J. (eds.) EUROCRYPT 2004. LNCS, vol. 3027, pp. 223–238. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Boyen, X.: Lattice mixing and vanishing trapdoors: A framework for fully secure short signatures and more. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 499–517. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Bringer, J., Chabanne, H., Dottax, E.: HB + + : a lightweight authentication protocol secure against some attacks. In: SecPerU, pp. 28–33 (2006)Google Scholar
  10. 10.
    Cramer, R., Damgard, I.: On the amortized complexity of zero-knowledge protocols. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol. 5677, pp. 177–191. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Duc, D.N., Kim, K.: Securing HB+ against GRS man-in-the-middle attack. In: SCIS (2007)Google Scholar
  12. 12.
    Fischer, J.-B., Stern, J.: An efficient pseudo-random generator provably as secure as syndrome decoding. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 245–255. Springer, Heidelberg (1996)Google Scholar
  13. 13.
    Fürer, M.: Faster integer multiplication. SIAM J. Comput. 39(3), 979–1005 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Gilbert, H., Robshaw, M., Sibert, H.: An active attack against HB+ - a provably secure lightweight authentication protocol. Cryptology ePrint Archive, Report 2005/237 (2005), http://eprint.iacr.org/
  15. 15.
    Gilbert, H., Robshaw, M.J.B., Seurin, Y.: Good variants of hB +  are hard to find. In: Tsudik, G. (ed.) FC 2008. LNCS, vol. 5143, pp. 156–170. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Gilbert, H., Robshaw, M.J.B., Seurin, Y.: HB#: Increasing the security and efficiency of HB + . In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 361–378. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  17. 17.
    Goldreich, O., Goldwasser, S., Micali, S.: How to construct random functions. Journal of the ACM 33, 792–807 (1986)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Hopper, N.J., Blum, M.: Secure human identification protocols. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol. 2248, pp. 52–66. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Juels, A., Weis, S.A.: Authenticating pervasive devices with human protocols. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 293–308. Springer, Heidelberg (2005)Google Scholar
  20. 20.
    Katz, J., Shin, J.S.: Parallel and concurrent security of the HB and HB +  protocols. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 73–87. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  21. 21.
    Katz, J., Shin, J.S., Smith, A.: Parallel and concurrent security of the HB and HB+ protocols. Journal of Cryptology 23(3), 402–421 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  22. 22.
    Kearns, M.J.: Efficient noise-tolerant learning from statistical queries. J. ACM 45(6), 983–1006 (1998)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Levieil, É., Fouque, P.-A.: An improved LPN algorithm. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 348–359. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  24. 24.
    Munilla, J., Peinado, A.: HB-MP: A further step in the HB-family of lightweight authentication protocols. Computer Networks 51(9), 2262–2267 (2007)zbMATHCrossRefGoogle Scholar
  25. 25.
    Ouafi, K., Overbeck, R., Vaudenay, S.: On the security of hB# against a man-in-the-middle attack. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 108–124. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  26. 26.
    Pietrzak, K.: Subspace LWE (2010) (manuscript) http://homepages.cwi.nl/~pietrzak/publications/SLWE.pdf
  27. 27.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Gabow, H.N., Fagin, R. (eds.) 37th ACM STOC, pp. 84–93. ACM Press, New York (2005)Google Scholar
  28. 28.
    Schönhage, A., Strassen, V.: Schnelle Multiplikation grosser Zahlen. Computing 7 (1971)Google Scholar
  29. 29.
    Van De Graaf, J.: Towards a formal definition of security for quantum protocols. PhD thesis, Monreal, P.Q., Canada, AAINQ35648 (1998)Google Scholar
  30. 30.
    Waters, B.R.: Efficient identity-based encryption without random oracles. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 114–127. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  31. 31.
    Watrous, J.: Zero-knowledge against quantum attacks. SIAM J. Comput. 39(1), 25–58 (2009)MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© International Association for Cryptologic Research 2011

Authors and Affiliations

  • Eike Kiltz
    • 1
  • Krzysztof Pietrzak
    • 2
  • David Cash
    • 3
  • Abhishek Jain
    • 4
  • Daniele Venturi
    • 5
  1. 1.RUBochumGermany
  2. 2.CWIAmsterdamThe Netherlands
  3. 3.UCSan DiegoUSA
  4. 4.UCLos AngelesUSA
  5. 5.Sapienza UniversityRomeItaly

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