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New bound for affine resolvable designs and its application to authentication codes

  • Session 5B: Combinatorial Designs
  • Conference paper
  • First Online:
Computing and Combinatorics (COCOON 1995)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 959))

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Abstract

In this paper, we first prove that b≤ v+t− 1 for an “affine” (α 1,⋯,αt)-resolvable design, where b denotes the number of blocks, v denotes the number of symbols and t denotes the number of classes. Our inequality is an opposite to the well known inequality b≥v+t−1 for a “balanced” (α 1,⋯,αt)-resolvable design. Next, we present a more tight lower bound on the size of keys than before for authentication codes with arbitration by applying our inequality. Although this model of authentication codes is very important in practice, it has been too complicated to be analyzed. We show that the receiver's key has a structure of an affine α-resolvable design (α 1=⋯=αt=α) and v corresponds to the number of keys under a proper assumption. (Note that our inequality is a lower bound on v.)

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References

  1. R.C.Bose, “A note on the resolvability of balanced incomplete block designs”, Sankhyā, 6, 105–110. (1942)

    Google Scholar 

  2. S.S.Shrikhande and D.Raghavarao, “Affine α-resolvable incomplete block designs”, Contributions to Statistics. Presented to Prof. P.C.Mahalanobis on the occasion of his 70th birthday. Pergamon Press, pp.471–480. (1963)

    Google Scholar 

  3. D.Raghavarao, “Constructions and combinatorial problems in design of experiments”, John Wiley & Sons, Inc. (1971).

    Google Scholar 

  4. S.Kageyama, “On μ-resolvable balanced incomplete block designs”, Ann. Statist. 1, 195–203. (1973)

    Google Scholar 

  5. S.Kageyama, “Resolvability of block designs”, Ann. Statist. 4, 655–61. (1976)

    Google Scholar 

  6. D.R.Hughes & F.C.Piper, “On resolutions and Bose's theorem”, Geom. Dedicata 5, 129–33. (1976)

    Article  Google Scholar 

  7. S.Kageyama, “Some properties on resolvability of variance-balanced designs”, Geom. Dedicata 15, 289–92. (1984)

    Article  Google Scholar 

  8. R.Mukerjee & S. Kageyama, “On resolvable and affine resolvable variance balanced designs”, Biometrika, 72, 1, pp.165–172. (1985)

    Google Scholar 

  9. G.J.Simmons, “Message Authentication with Arbitration of Transmitter/Receiver Disputes”, Proceedings of Eurocrypt'87, Lecture Notes in Computer Science, LNCS 304, Springer Verlag, pp.150–16 (1987)

    Google Scholar 

  10. G.J.Simmons, “A Cartesian Product Construction for Unconditionally Secure Authentication Codes that Permit Arbitration”, Journal of Cryptology, Vol.2, no.2, 1990, pp.77–104 (1990).

    Article  Google Scholar 

  11. T.Johansson, “Lower Bounds on the Probability of Deception in Authentication with Arbitration”, In Proceedings of 1993 IEEE International Symposium on Information Theory, San Antonio, USA, January 17–22, pp.231. (1993)

    Google Scholar 

  12. T.Johansson, “Lower Bounds on the Probability of Deception in Authentication with Arbitration”, IEEE Trans. on IT, vol.40, No.5, pp.1573–1585 (1994)

    Google Scholar 

  13. T.Johansson, “On the construction of perfect authentication codes that permit arbitration”, Proceedings of Crypto'93, Lecture Notes in Computer Science, LNCS 773, Springer Verlag, pp.341–354 (1993).

    Google Scholar 

  14. K.Kurosawa, “New bound on authentication code with arbitration”, Proceedings of Crypto'94, Lecture Notes in Computer Science, LNCS 899, Springer Verlag, pp.140–149. (1994)

    Google Scholar 

  15. K.Kurosawa and S.Obana, “Combinatorial Bounds for Authentication Codes with Arbitration”, Eurocrypt'95 (to be presented)

    Google Scholar 

  16. G.J.Simmons, “A survey of Information Authentication”, in Contemporary Cryptology, The science of information integrity, ed. G.J.Simmons, IEEE Press, New York, (1992).

    Google Scholar 

  17. G.J.Simmons, “Authentication theory/coding theory”, Proceedings of Crypto'84, Lecture Notes in Computer Science, LNCS 196, Springer Verlag, pp.411–431 (1985).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical and Electronic Engineering, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152, Tokyo, Japan

    Kaoru Kurosawa

  2. Department of Mathematics, Hiroshima University, 739, Higashi-Hiroshima, Japan

    Sanpei Kageyama

Authors
  1. Kaoru Kurosawa
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  2. Sanpei Kageyama
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Editor information

Ding-Zhu Du Ming Li

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© 1995 Springer-Verlag Berlin Heidelberg

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Kurosawa, K., Kageyama, S. (1995). New bound for affine resolvable designs and its application to authentication codes. In: Du, DZ., Li, M. (eds) Computing and Combinatorics. COCOON 1995. Lecture Notes in Computer Science, vol 959. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0030844

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  • DOI: https://doi.org/10.1007/BFb0030844

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60216-3

  • Online ISBN: 978-3-540-44733-7

  • eBook Packages: Springer Book Archive

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