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Some constructions and bounds for authentication codes

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We investigate authentication codes, using the model described by Simmons. We review and generalize bounds on the probability that an opponent can deceive the transmitter/receiver by means of impersonation or substitution. Also, we give several constructions for authentication codes that meet one or more of these bounds with equality. These constructions use combinatorial designs, such as transversal designs, group-divisible designs, and BIBDs (balanced incomplete block designs).

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  1. [1]

    E. F. Brickell, A few results in message authentication, Congressus Numerantium, 43 (1984), 141–154.

  2. [2]

    E. N. Gilbert, F. J. Mac Williams, and N. J. A. Sloane, Codes which detect deception, Bell System Tech. J., 53 (1974), 405–424.

  3. [3]

    H. Hanani, On transversal designs, Math. Centre Tracts, 55 (1974), 42–52.

  4. [4]

    G. J. Simmons, A game theory model of digital message authentication, Congressus Numerantium, 34 (1982), 413–424.

  5. [5]

    G. J. Simmons, Message authentication: a game on hypergraphs, Congressus Numerantium, 45 (1984), 161–192.

  6. [6]

    G. J. Simmons, Authentication theory/coding theory, in Advances in Cryptology: Proceedings of CRYPTO 84, Lecture Notes in Computer Science, Vol. 196, Springer-Verlag, Berlin, 1985, pp. 411–432.

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Stinson, D.R. Some constructions and bounds for authentication codes. J. Cryptology 1, 37–51 (1988). https://doi.org/10.1007/BF00206324

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Key words

  • Authentication code
  • Combinatorial design