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On 2-level secret sharing

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Abstract

In this paper, using recent results in finite geometry, we study a certain class of 2-level shared secret schemes. We shall present upper bounds on both the number of participants in total and on the number of participants in the lower level, which constitute the only nontrivial cases, and construct examples for the extremal cases.

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References

  1. Beutelspacher A. 1990. Applications of finite geometry to cryptography. CISM Courses and Lectures No. 313, New York: Springer-Verlag Wien, pp. 161–186.

    Google Scholar 

  2. Bichara, A. and Korchmáros, G. 1982. Note on (q+2)-sets in a Galois plane of orderq.Annals of Discrete Math. 14: 117–122.

    Google Scholar 

  3. Blakley, G.R. 1979. Safeguarding cryptographic keys.Proc. NCC 48, AFIPS Press, Montvale, N.J., pp. 317–319.

    Google Scholar 

  4. Blokhuis, A., Bruen, A.A., and Thas, J.A. 1990. Arcs inPG(n,q), MDS codes and three fundamental problems of B. Segre—some extensions.Geom. Dedicate 35: 1–11.

    Google Scholar 

  5. Dembowski, P. 1968.Finite Geometries. Berlin-Heidelberg-New York: Springer-Verlag.

    Google Scholar 

  6. Hirschfeld, J.W.P. and Thas, J.A. 1991.General Galois Geometries, Oxford: Oxford Univ. Press.

    Google Scholar 

  7. Jackson, W.-A. 1989. On design which admit specific automorphisms. Ph.D. Thesis, Royal Holloway and Bedford New College, University of London.

  8. Hy, N.M. 1972. Páratlan rendű affin Galois sikok ellipszise, mint affin szabályos sokszög, (in Hungarian)Mat. Lapok 23: 303–312.

    Google Scholar 

  9. Seroussi, G. and Roth, R.M. 1986. On M.D.S. extensions of generalized Reed-Solomon codes.IEEE Transactions Inform. Theory IT-32: 349–354.

    Google Scholar 

  10. Shamir, A. How to shear a secret.Comm. ACM 22: 612–613.

  11. Simmons, G.J. 1989. How to (really) share a secret.Advances in Cryptology—CRYPTO 88, LNCS 403: 390–448.

    Google Scholar 

  12. Simmons, G.J. 1990. Sharply focused sets of lines on a conic inPG(2,q).Congressus Numerantium 73: 181–204.

    Google Scholar 

  13. Storme, L. and Szönyi, T. (k+1)-arcs inPG(n, q),n≥3, containingk points of a normal rational curve,q even. (submitted to Journal of Geometry)

  14. Storme, L. and Szőnyi, T. (k+1)-arcs inPG(n, q),n≥3, containingk points of a normal rational curve,q odd, (in preparation).

  15. Storme, L. and Thas, J.A. 1991. Generalized Reed-Solomon codes and rational curves: An improvement of results by Seroussi and Roth.Advances in Finite Geometries and Designs, Oxford-New York-Tokyo: Oxford University Press, pp. 407–419.

    Google Scholar 

  16. Szőnyi, T. 1991.k-sets inPG(2,q) having a large set of internal nuclei.Proc. “Combinatorice '88”.

  17. Wettl, F. 1987. On the nuclei of a pointset of a finite projective plane.J. of Geometry 30: 157–163.

    Google Scholar 

  18. Wettl, F. 1991. Internal nuclei ofk-sets in finite projective spaces of three dimensions.Advances in Finite Geometries and Designs, Oxford-New York-Tokyo: Oxford University Press, pp. 407–419.

    Google Scholar 

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Communicated by D. Jungnickel

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Beutelspacher, A., Wettl, F. On 2-level secret sharing. Des Codes Crypt 3, 127–134 (1993). https://doi.org/10.1007/BF01388411

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