Geometric Threshold Schemes

  • M. De Soete
Part of the International Centre for Mechanical Sciences book series (CISM, volume 313)


This paper gives constructions of infinite classes of 2, 3 and 4-threshold schemes based on finite incidence structures such as generalised quadrangles and projective planes.


Prime Power Security Level Secret Data Prob Ability Generalise Quadrangle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Beth, T., Jungnickel, D. and Lenz, H.: Design Theory, Wissenschaftsverlag Bibliographisches Institut Mannheim, 1985.Google Scholar
  2. [2]
    Beutelspacher, A. and Vedder, K.: Geometric Structures as Threshold Schemes, in: The Institute of Mathematics and its Applications, Conf. Series 20, Cryptography and Coding, ed. H. J. Beker and F. C. Piper, 1989, 255–268.Google Scholar
  3. [3]
    Blakley, G. R.: Safeguarding cryptographic keys, in: Proceedings NCC, AFIPS Press, Montvale, N.J., Vol. 48, 1979, 313–317.Google Scholar
  4. [4]
    De Soete, M. and Thas, J.A.: A coordinatisation of the generalised quadrangles of order (s, s + 2), J. Comb. Theory A, Vol. 48–1 (1988), 1–11.CrossRefGoogle Scholar
  5. [5]
    Hanssens, G. and Van Maldeghem, H.: Coordinatisation of Generalised Quadrangles, Annals of Discr. Math. 37 (1988), 195–208.Google Scholar
  6. [6]
    Hughes, D. R. and Piper, F. C.: Projective Planes, Springer Verlag, BerlinHeidelberg—New York, 1973.MATHGoogle Scholar
  7. [7]
    Hughes, D. R. and Piper, F. C.: Design Theory, Cambridge University Press, 1985.Google Scholar
  8. [8]
    Payne, S. E. and Thas, J. A.: Finite generalised quadrangles, Research Notes in Math. #110, Pitman Publ. Inc., 1984.Google Scholar
  9. [9]
    Shamir, A.: How to share a secret, Communications ACM, Vol. 22 nr. 11 (1979), 612–613.CrossRefMATHMathSciNetGoogle Scholar
  10. [10]
    Sved, M.: Baer subspaces in the n dimensional projective space, Comb. Math. Proc. Adelaide (1982), 375–391.Google Scholar

Copyright information

© Springer-Verlag Wien 1990

Authors and Affiliations

  • M. De Soete
    • 1
  1. 1.MBLE-I.S.G.BrusselBelgium

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