Designs, Codes and Cryptography

, Volume 41, Issue 3, pp 343–357 | Cite as

Some constructions of systematic authentication codes using galois rings

Article

Abstract

For q = pm and m ≥ 1, we construct systematic authentication codes over finite field \(\mathbb{F}_{q}\) using Galois rings. We give corrections of the construction of [2]. We generalize corresponding systematic authentication codes of [6] in various ways.

Keywords

Authentication codes Cryptography Galois rings 

AMS Classification

94A60 94B27 14G50 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bierbrauer J, Johansson T, Kabatianskii G, Smeets B. (1994) On families of hash functions via geometric codes and concatenation. In: Stinson DR (ed) Advances in Cryptology Crypto’93, LNCS 773. Springer-Verlag, Berlin, pp 331–342Google Scholar
  2. 2.
    Bini G, (2006) A-codes from rational functions over Galois rings. Design, Code Cryptogr 39(2):207–214MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    Constantinescu I, Heise T. (1997) A metric for codes over residue class rings of integers. Problemy Peredachi Informatsii 33(3):22–28MATHMathSciNetGoogle Scholar
  4. 4.
    Ding C, Niederreiter H. (2004) Systematic authentication codes from highly nonlinear functions. IEEE Trans Inform Theory 50(10):2421–2428MathSciNetCrossRefGoogle Scholar
  5. 5.
    Greferath M, Schmidt S.E. (1999) Gray isometries for finite chain rings and a non-linear ternary (36, 312, 15) code. IEEE Trans Inform Theory 45:2522–2524MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Helleseth T, Johansson T. (1996) Universal hash functions from exponential sums over finite fields and Galois rings. In: Koblitz N (ed) Advances in Cryptology Crypto’96, LNCS 1109. Springer-Verlag, Berlin, pp 31–44Google Scholar
  7. 7.
    Helleseth T, Kumar K.V., Shanbhag A.G. (1996) Exponential sums over Galois rings and their applications Finite fields and applications (Glasgow, 1995). London Math. Soc. Lecture Note Ser., vol. 233. Cambridge University Press, Cambridge, pp 109–128Google Scholar
  8. 8.
    Kumar P.V., Helleseth T, Calderbank A.R. (1995) An upper bound for Weil exponential sums over Galois rings and applications. IEEE Trans Inform Theory 41:456–468MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    Ling S, Özbudak F. (2006) Improved bounds on Weil sums over Galois rings and homogeneous weights. In: Ythervs O (ed) Proceedings of WCC 2005, LNCS 3969. Springer-Verlag, Berlin, pp 412–426Google Scholar
  10. 10.
    Ling S, Özbudak F. (2006) Aperiodic and odd correlations of some p-ary sequences. IEICE Trans Fundamentals, E89-A, pp 2258–2263Google Scholar
  11. 11.
    Simmons G.J. (1984) Authentication theory/coding theory. In: Blankey GR, Chum D (eds) Advances in cryptology Crypto’84, LNCS 196. Springer-Verlag, Berlin, pp 411–431Google Scholar
  12. 12.
    Stinson D.R. (1994) Universal hashing and authentication codes. Design, Code Cryptogr 4:337–346Google Scholar
  13. 13.
    Stinson D.R. (1995) Cryptography: theory and practice. CRC, Boca Raton, FLGoogle Scholar
  14. 14.
    Wan Z.X. (2003) Lectures on finite fields and galois rings. World Scientific, SingaporeMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey
  2. 2.Institute of Applied MathematicsMiddle East Technical UniversityAnkaraTurkey

Personalised recommendations