New Universal Hash Functions

  • Aysajan Abidin
  • Jan-Åke Larsson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7242)

Abstract

Universal hash functions are important building blocks for unconditionally secure message authentication codes. In this paper, we present a new construction of a class of ε-Almost Strongly Universal2 hash functions with much smaller description (or key) length than the Wegman-Carter construction. Unlike some other constructions, our new construction has a very short key length and a security parameter ε that is independent of the message length, which makes it suitable for authentication in practical applications such as Quantum Cryptography.

Keywords

Universal hash functions ε-Almost Strongly Universal hash functions authentication Quantum Cryptography 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Atici, M., Stinson, D.R.: Universal Hashing and Multiple Authentication. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 16–30. Springer, Heidelberg (1996)Google Scholar
  2. 2.
    Bennett, C.H., Brassard, G.: Quantum cryptography: Public key distribution and coin tossing. In: Proc. IEEE Int. Conf. Comput. Syst. Signal Process., Bangalore, India, pp. 175–179 (1984)Google Scholar
  3. 3.
    Bierbrauer, J., Johansson, T., Kabatianskii, G., Smeets, B.: On Families of Hash Functions via Geometric Codes and Concatenation. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 331–342. Springer, Heidelberg (1994)Google Scholar
  4. 4.
    Black, J.: Message authentication codes. Ph.D. thesis, University of California Davis, USA (2000)Google Scholar
  5. 5.
    Black, J., Halevi, S., Krawczyk, H., Krovetz, T., Rogaway, P.: UMAC: Fast and Secure Message Authentication. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 216–233. Springer, Heidelberg (1999)Google Scholar
  6. 6.
    den Boer, B.: A simple and key-economical unconditional authentication scheme. J. Comp. Sec. 2, 65–72 (1993)Google Scholar
  7. 7.
    Carter, L., Wegman, M.N.: Universal classes of hash functions. J. Comput. Syst. Sci. 18, 143–154 (1979)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the Lambert W function. Adv. Comput. Math. 5, 329–359 (1996)MathSciNetMATHCrossRefGoogle Scholar
  9. 9.
    Gemmell, P., Naor, M.: Codes for Interactive Authentication. In: Stinson, D.R. (ed.) CRYPTO 1993. LNCS, vol. 773, pp. 355–367. Springer, Heidelberg (1994)Google Scholar
  10. 10.
    Halevi, S., Krawczyk, H.: MMH: Software Message Authentication in the Gbit/Second Rates. In: Biham, E. (ed.) FSE 1997. LNCS, vol. 1267, pp. 172–189. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  11. 11.
    Johansson, T.: Bucket Hashing with a Small Key Size. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 149–162. Springer, Heidelberg (1997)Google Scholar
  12. 12.
    Kabatianskii, G., Smeets, B.J.M., Johansson, T.: On the cardinality of systematic authentication codes via error-correcting codes. IEEE Trans. Inf. Theory 42, 566–578 (1996)MathSciNetMATHCrossRefGoogle Scholar
  13. 13.
    Krawczyk, H.: LFSR-Based Hashing and Authentication. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 129–139. Springer, Heidelberg (1994)Google Scholar
  14. 14.
    Krawczyk, H.: New Hash Functions for Message Authentication. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol. 921, pp. 301–310. Springer, Heidelberg (1995)Google Scholar
  15. 15.
    Mansour, Y., Nisan, N., Tiwari, P.: The computational complexity of universal hashing. In: Ortiz, H. (ed.) Proc. STOC 1990, pp. 235–243. ACM, New York (1990)Google Scholar
  16. 16.
    Nguyen, L.H., Roscoe, A.W.: A new bound for t-wise almost universal hash functions. IACR Cryptology ePrint Archive, Report 2009/153 (2009), http://eprint.iacr.org/2009/153
  17. 17.
    Preneel, B.: Analysis and design of cryptographic hash functions. Ph.D. thesis, Katholieke Universiteit Leuven, Belgium (1993)Google Scholar
  18. 18.
    Rogaway, P.: Bucket Hashing and Its Application to Fast Message Authentication. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 29–42. Springer, Heidelberg (1995)Google Scholar
  19. 19.
    Shor, P.W., Preskill, J.: Simple proof of security of the bb84 quantum key distribution protocol. Phys. Rev. Lett. 85, 441–444 (2000)CrossRefGoogle Scholar
  20. 20.
    Stinson, D.R.: Universal Hashing and Authentication Codes. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 74–85. Springer, Heidelberg (1992)Google Scholar
  21. 21.
    Stinson, D.R.: Combinatorial techniques for universal hashing. J. Comput. Syst. Sci. 48, 337–346 (1994)MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Stinson, D.R.: On the connections between universal hashing, combinatorial designs and error-correcting codes. Congressus Numerantium 114, 7–27 (1996)MathSciNetMATHGoogle Scholar
  23. 23.
    Stinson, D.R.: Universal hash families and the leftover hash lemma, and applications to cryptography and computing. J. Combin. Math. Combin. Comput. 42, 3–31 (2002)MathSciNetMATHGoogle Scholar
  24. 24.
    Wegman, M.N., Carter, L.: New hash functions and their use in authentication and set equality. J. Comput. Syst. Sci. 22, 265–279 (1981)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Aysajan Abidin
    • 1
  • Jan-Åke Larsson
    • 1
  1. 1.Department of Electrical EngineeringLinköping UniversityLinköpingSweden

Personalised recommendations