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Combinatorial bounds and characterizations of splitting authentication codes

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Abstract

We present several generalizations of results for splitting authentication codes by studying the aspect of multi-fold security. As the two primary results, we prove a combinatorial lower bound on the number of encoding rules and a combinatorial characterization of optimal splitting authentication codes that are multi-fold secure against spoofing attacks. The characterization is based on a new type of combinatorial designs, which we introduce and for which basic necessary conditions are given regarding their existence.

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References

  1. Beth, T., Jungnickel, D., Lenz, H.: Design Theory, vols. I and II. Encyclopedia of Math. and Its Applications, vols. 69/78. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  2. Blundo, C., De Santis, A., Kurosawa, K., Ogata, W.: On a fallacious bound for authentication codes. J. Cryptol. 12, 155–159 (1999)

    Article  MATH  Google Scholar 

  3. Brickell, E.F.: A few results in message authentication. Congr. Numer. 43, 141–154 (1984)

    MathSciNet  Google Scholar 

  4. Colbourn, C.J., Dinitz, J.H. (eds.): Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton (2006)

    Google Scholar 

  5. De Soete, M.: Some constructions for authentication-secrecy codes. In: Günther, Ch.G. (ed.) Advances in Cryptology-EUROCRYPT 1988. Lecture Notes in Computer Science, vol. 330, pp. 23–49. Springer, Berlin, Heidelberg, New York (1988)

    Google Scholar 

  6. De Soete, M.: New bounds and constructions for authentication/secrecy codes with splitting. J. Cryptol. 3, 173–186 (1991)

    Article  MATH  Google Scholar 

  7. Du, B.: Splitting balanced incomplete block designs with block size 3 ×2. J. Comb. Des. 12, 404–420 (2004)

    Article  MATH  Google Scholar 

  8. Ge, G., Miao, Y., Wang, L.: Combinatorial constructions for optimal splitting authentication codes. SIAM J. Discrete Math. 18, 663–678 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  9. Gilbert, E.N., MacWilliams, F.J., Sloane, N.J.A.: Codes which detect deception. Bell Syst. Tech. J. 53, 405–424 (1974)

    MathSciNet  Google Scholar 

  10. Huber, M.: Authentication and secrecy codes for equiprobable source probability distributions. In: Proc. IEEE International Symposium on Information Theory (ISIT) 2009, pp. 1105–1109 (2009)

  11. Huber, M.: Flag-transitive Steiner Designs. Birkhäuser, Basel, Berlin, Boston (2009)

    Google Scholar 

  12. Huber, M.: Coding theory and algebraic combinatorics. In: Woungang, I., et al. (eds.) Selected Topics in Information and Coding Theory, 38 pp. World Scientific, Singapore (2010)

    Google Scholar 

  13. Johansson, T.: Lower bounds on the probability of deception in authentication with arbitration. IEEE Trans. Inf. Theory 40, 1573–1585 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  14. Kurosawa, K.: New bound on authentication code with arbitration. In: Desmedt, Y. (ed.) Advances in Cryptology-CRYPTO 1994. Lecture Notes in Computer Science, vol. 839, pp. 140–149. Springer, Berlin, Heidelberg, New York (1994)

    Google Scholar 

  15. Kurosawa, K., Obana, S.: Combinatorial bounds on authentication codes with arbitration. Designs Codes Cryptogr. 22, 265–281 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  16. Massey, J.L.: Cryptography—a selective survey. In: Biglieri, E., Prati, G. (eds.) Digital Communications, pp. 3–21. North-Holland, Amsterdam, New York, Oxford (1986)

    Google Scholar 

  17. Ogata, W., Kurosawa, K., Stinson, D.R., Saido, H.: New combinatorial designs and their applications to authentication codes and secret sharing schemes. Discrete Math. 279, 383–405 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  18. Pei, D.: Authentication Codes and Combinatorial Designs. CRC Press, Boca Raton (2006)

    MATH  Google Scholar 

  19. Schöbi, P.: Perfect authentication systems for data sources with arbitrary statistics (presented at EUROCRYPT 1986) (unpublished)

  20. Shannon, C.E.: Communication theory of secrecy systems. Bell Syst. Tech. J. 28, 656–715 (1949)

    MATH  MathSciNet  Google Scholar 

  21. Simmons, G.J.: A game theory model of digital message authentication. Congr. Numer. 34, 413–424 (1982)

    MathSciNet  Google Scholar 

  22. Simmons, G.J.: Message authentication: a game on hypergraphs. Congr. Numer. 45, 161–192 (1984)

    MathSciNet  Google Scholar 

  23. Simmons, G.J.: Authentication theory/coding theory. In: Blakley, G.R., Chaum, D. (eds.) Advances in Cryptology-CRYPTO 1984. Lecture Notes in Computer Science, vol. 196, pp. 411–432. Springer, Berlin, Heidelberg, New York (1985)

    Google Scholar 

  24. Simmons, G.J.: Message authentication with arbitration of transmitter/receiver disputes. In: Chaum, D., Price, W.L. (eds.) Advances in Cryptology-EUROCRYPT 1987. Lecture Notes in Computer Science, vol. 304, pp. 150–165. Springer, Berlin, Heidelberg, New York (1988)

    Chapter  Google Scholar 

  25. Simmons, G.J.: A Cartesian product construction for unconditionally secure authentication codes that permit arbitration. J. Cryptol. 2, 77–104 (1990)

    Article  MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  27. Stinson, D.R.: The combinatorics of authentication and secrecy codes. J. Cryptol. 2, 23–49 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  28. Stinson, D.R.: Combinatorial characterizations of authentication codes. Designs Codes Cryptogr. 2, 175–187 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  29. Stinson, D.R., Rees, R.S.: Combinatorial characterizations of authentication codes II. Designs Codes Cryptogr. 7, 239–259 (1996)

    MATH  MathSciNet  Google Scholar 

  30. Wang, J.: A new class of optimal 3-splitting authentication codes. Designs Codes Cryptogr. 38, 373–381 (2006)

    Article  MATH  Google Scholar 

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Acknowledgements

I thank the two anonymous referees for their careful reading and suggestions that helped improving the presentation of the paper. I also thank Moritz Eilers and Christoff Hische for running the computer search for Example 2.

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Authors and Affiliations

  1. Wilhelm-Schickard-Institute for Computer Science, University of Tübingen, Sand 13, 72076, Tübingen, Germany

    Michael Huber

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  1. Michael Huber
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Correspondence to Michael Huber.

Additional information

This work was supported by the Deutsche Forschungsgemeinschaft (DFG) via a Heisenberg grant (Hu954/4) and a Heinz Maier-Leibnitz Prize grant (Hu954/5).

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Huber, M. Combinatorial bounds and characterizations of splitting authentication codes. Cryptogr. Commun. 2, 173–185 (2010). https://doi.org/10.1007/s12095-010-0020-4

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