Skip to main content
SpringerLink
Log in

Combinatorial Characterizations of Authentication Codes II

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

For any authentication code for k source states and v messages having minimum possible deception probabilities (namely, Pd0 = k/v and Pd1 = (k - 1)/(v - 1)), we show that there must be at least v encoding rules. (This can be thought of as an authentication-code analogue of Fisher's Inequality.) We derive several properties that an extremal code must satisfy, and we characterize the extremal codes for equiprobable source states as arising from symmetric balanced incomplete block designs. We also present an infinite class of extremal codes, in which the source states are not equiprobable, derived from affine planes.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. F. Brickell, A few results in message authentication, Congressus Numer, Vol. 43(1984), pp. 141–154.

    Google Scholar 

  2. M. De Soete, K. Vedder and M. Walker, Cartesian authentication schemes: Proceedings of EUROCRYPT '89, Lecture Notes in Comput. Sci., 434(1990) pp. 476–490.

    Google Scholar 

  3. M D Soete, New homndl and nnstorntion for authentication / secrecy codes with splitting. Journal of Cryptology Vol. 6(1991) pp. 173–186.

    Google Scholar 

  4. E. N. Gilbert, F. J. MacWilliams and N. J. A. Sloane, Codes which detect deception, Bell System Tech. Journal, Vol. 53(1974) pp. 405–424.

    Google Scholar 

  5. M. Hall, Jr., Combinatorial Theory, second edition. John Wilcy & Sons (1986).

  6. J. L. Massey, Cryptography-a selective survey, In Digital Communications pp. 3–21. North-Holland (1986).

  7. C. Mitchell, M. Walker and P Wild, The combinatorics of perfect authentication schemes, SIAMJ Discrete Math. Vol. 7(1994) pp. 102 107.

    Google Scholar 

  8. U. Rosenbaum, A lower bound on authentication after having observed a sequence of messages, Journal of Cryptology, Vol. 6(1993) pp. 135 156.

    Google Scholar 

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

    Google Scholar 

  10. G. J. Simmons, Authentication theory/coding theory: Proceedings of CRYPTO '84, Lecture Notes in Comput. Sci., 196(1985) pp. 411–432.

    Google Scholar 

  11. G. J. Simmons, Anaturaltaxonomy fordigial information lthntication schemes: Poceedings of CRYPTO '87, Lecture Notes in Comput. Sci., 293(1988) pp. 269–288.

    Google Scholar 

  12. G. J. Simmons, A survey of information authentication, In Contemporary Cryptology The Science of Information Integrity, pp. 379–419. IEEE Press (1992).

  13. D. R. Stinson, Some constructions and bounds forauthentication codes, Journalof Cryptology Vol. 1 (1988) pp. 37–51.

    Google Scholar 

  14. D. R Stinson, The combinatorics of authentication and secrecy codes, Journal of Cryptology Vol. 2(1990) pp. 23–49.

    Google Scholar 

  15. D. R. Stinson, Combinatorial characterizations of authentication codes, Designs, Codes, and Cryptography Vol. 2(1992) pp175–187.

    Google Scholar 

  16. D. R. Stinson, Combinatorial designs and cryptography, In Surveys in Combinatorics, 1993, pp. 257–287. Cambridge University Press (1993).

  17. M. Walker, Information-theoretic bounds for authentication schemes, Journal of Cryptology, Vol. 2(1990) pp. 131–144.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, Newfoundland A1C 557, Canada

    Rolf S. Rees

  2. Computer Science and Engineering Department and Center for Communication and Information Science, University of Nebraska-Lincoln, Lincoln, Nebraska, 68588-0115, USA

    Douglas R. Stinson

Authors
  1. Rolf S. Rees
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Douglas R. Stinson
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rees, R.S., Stinson, D.R. Combinatorial Characterizations of Authentication Codes II. Designs, Codes and Cryptography 7, 239–259 (1996). https://doi.org/10.1023/A:1018094824862

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1018094824862

Keywords

Search

Navigation