Combinatorial structure of A-codes with r-fold security

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 917)


In this paper we prove two general characterization theorems for A-codes, that provide r-fold security, in terms of well-known combinatorial structures (t-designs and orthogonal arrays). We use Delsarte's linear programming method to find new bounds on the number of encoding rules for Cartesian A-codes with 1-fold and 2-folds security and show that in the latter case the bound is achieved by A-codes obtained from the dual of two well-studied error correcting codes: an MDS code and the extended Hamming code.


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  1. 1.
    D.R. Stinson, The combinatorics of authentication and secrecy codes, Journal Cryptology 2, (1990), 23–49.Google Scholar
  2. 2.
    D.R. Stinson, Combinatorial characterization of authentication codes, Lecture Notes in Comput. Sci. 576, Proceedings of Crypto 91, Springer-Verlag, 1992, 62–72.Google Scholar
  3. 3.
    P. Schobi, Perfect authentication systems for data sources with arbitrary statistics, presented at Eurocrypt '86.Google Scholar
  4. 4.
    J.H. Dinitz, D. Stinson, Contemporary Design Theory. A Collection of Surveys, A Wiley Interscience Publications, JOHN WILEY & SONS, INC, 1992.Google Scholar
  5. 5.
    J. MacWilliams, N. Sloane, The theory of error correcting codes, Noth Holland Publishing Company, 1978.Google Scholar
  6. 6.
    S. Roman, Coding and Information Theory, Springer Verlag, 1992.Google Scholar
  7. 7.
    L. Tombak, R. Safavi-Naini, Authentication codes with perfect protection Advances in Cryptology-AusCrypt'92, LNCS 718, Springer-Verlag, 1993, pp 15–26.Google Scholar
  8. 8.
    Ph. Delsarte, An algebraic approach to the association schemes of coding theory, Phillips Res. Rep. Suppl. 10,1973.Google Scholar
  9. 9.
    R.S. Rees, D.R. Stinson, Combinatorial Characterization of Authentication Codes II, personal communication.Google Scholar
  10. 10.
    C. Mitchell, M. Walker, P. Wild, The combinatorics of perfect authentication schemes, SIAM Journal of Discrete Mathematics, Vol 7, No 1, pp 102–107, 1994.Google Scholar
  11. 11.
    M. De Soete, K. Vedder, M. Walker, Cartesian Authentication Schemes, Advances in Cryptology, proc. of Eurocrypt '89, Lecture Notes in Computer Science, vol 434, Springer Verlag 1990, pp 476–490.Google Scholar
  12. 12.
    C.R. Rao, Factorial experiments derivable from combinatorial arrangements of arrays, J. Roy. Statist. Soc. 9, 128–139, 1947Google Scholar
  13. 13.
    A.Davydov, L.Tombak, Number of minimal-weight words in block codes, Problems of Information Transmission, Vol 24, No1, pp 11–24, 1988.Google Scholar
  14. 14.
    H.C.A van Tilborg, Uniformly packed Codes, Thesis, Eindhoven University of Technology (1976).Google Scholar
  15. 15.
    J. Bierbrauer, K. Gopalakrishnan and D. R. Stinson, Bounds for resilient functions and orthogonal arrays, Advances in Cryptology — Crypto '94, Proceedings (Lecture Notes in Computer Science 839), pp 247–256.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of WollongongWollongongAustralia

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