A construction for authentication / secrecy codes from certain combinatorial designs

  • D. R. Stinson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 293)


If we agree to use one of v possible messages to communicate one of k possible source states, then an opponent can successfully impersonate a transmitter with probability at least k / v, and can successfully substitute a message with a fraudulent one with probability at least (k − 1) / (v − 1). We wish to limit an opponent to these bounds. In addition, we desire that the observation of any two messages in the communication channel will give an opponent no clue as to the two source states. We describe a construction for a code which achieves these goals, and which does so with the minimum possible number of encoding rules (namely, v·(v − 1) / 2). The construction uses a structure from combinatorial design theory known as a perpendicular array.


  1. 1.
    Ernest F. Brickell, A few results in message authentication, Congressus Numerantium 43 (1984), 141–154.MathSciNetGoogle Scholar
  2. 2.
    A. Granville, A. Moisiadis and R. Rees, Nested Steiner n-gon systems and perpendicular arrays, preprint.Google Scholar
  3. 3.
    E. Gilbert, F. J. MacWilliams and N. J. A. Sloane, Codes which detect deception, Bell System Tech. J. 53 (1974), 405–424.MathSciNetzbMATHGoogle Scholar
  4. 4.
    C. Huang, E. Mendelsohn and A. Rosa, On partially resolvable t-partitions, Annals Disc. Math. 12 (1983), 169–183.Google Scholar
  5. 5.
    C. C. Lindner and D. R. Stinson, Steiner pentagon systems, Discrete Math. 52 (1984), 67–74.MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    C. C. Lindner and D. R. Stinson, The spectrum for the conjugate invariant subgroups of perpendicular arrays, Ars Combinatoria 18 (1984), 51–60.MathSciNetzbMATHGoogle Scholar
  7. 7.
    C. C. Lindner, R. C. Mullin and G. H. J. van Rees, Separable orthogonal arrays, Utilitas Math., to appear.Google Scholar
  8. 8.
    J. L. Massey, Cryptography — A selective survey, in “Digital Communications” (1986), 3–21.Google Scholar
  9. 9.
    R. C. Mullin, P. J. Schellenberg, G. H. J. van Rees and S. A. Vanstone, On the construction of perpendicular arrays, Utilitas Math. 18 (1980), 141–160.MathSciNetzbMATHGoogle Scholar
  10. 10.
    S. C. Pohlig and M. E. Hellman, An improved algorithm for computing logarithms over GF(p) and its cryptographic significance, IEEE Trans. on Inform. Theory 24 (1978), 106–110.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    P. Schobi, Perfect authentication systems for data sources with arbitrary statistics, preprint.Google Scholar
  12. 12.
    C. E. Shannon, Communication theory of secrecy systems, Bell System Tech. J. 28 (1949), 656–715.MathSciNetzbMATHGoogle Scholar
  13. 13.
    Gustavus J. Simmons, A game theory model of digital message authentication, Congressus Numerantium 34 (1982), 413–424.MathSciNetGoogle Scholar
  14. 14.
    Gustavus J. Simmons, Message Authentication: A game on hypergraphs, Congressus Numerantium 45 (1984), 161–192.MathSciNetGoogle Scholar
  15. 15.
    Gustavus J. Simmons, Authentication theory / Coding theory, in “Advances in Cryptology: Proceedings of CRYPTO 84”, Lecture Notes in Computer Science, vol. 196, 411–432, Springer Verlag, Berlin, 1985.Google Scholar
  16. 16.
    D. R. Stinson, Some constructions and bounds for authentication codes, J. of Cryptology, to appear.Google Scholar
  17. 17.
    G. H. J. van Rees, private communication.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • D. R. Stinson
    • 1
  1. 1.Department of Computer ScienceUniversity of ManitobaCanada

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