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Secret Sharing Schemes on Access Structures with Intersection Number Equal to One

  • Jaume Martí-Farré
  • Carles Padró
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2576)

Abstract

The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. These problems are studied in this paper for access structures with intersection number equal to one, that is, access structures such that there is at most one participant in the intersection of any two minimal qualified subsets. Examples of such access structures are those defined by finite projective planes and those defined by graphs. In this work, ideal access structures with intersection number equal to one are completely characterized and bounds on the optimal information rate are provided for the non-ideal case.

Keywords

Cryptography secret sharing schemes information rate ideal schemes 

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References

  1. 1.
    Blakley, G.R.: Safeguarding cryptographic keys. AFIPS Conference Proceedings 48 (1979) 313–317Google Scholar
  2. 2.
    Blundo, C., De Santis, A., De Simone, R., Vaccaro, U.: Tight bounds on the information rate of secret sharing schemes. Des. Codes Cryptogr. 11 (1997) 107–122zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Blundo, C., De Santis, A., Gargano, L., Vaccaro, U.: On the information rate of secret sharing schemes. Advances in Cryptology CRYPTO’92. Lecture Notes in Comput. Sci. 740 148–167Google Scholar
  4. 4.
    Blundo, C., De Santis, A., Stinson, D.R., Vaccaro, U.: Graph decompositions and secret sharing schemes. J. Cryptology 8 (1995) 39–64zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Brickell, E.F.: Some ideal secret sharing schemes. J. Combin. Math. and Combin. Comput. 9 (1989) 105–113MathSciNetGoogle Scholar
  6. 6.
    Brickell, E.F., Davenport, D.M.: On the classification of ideal secret sharing schemes. J. Cryptology 4 (1991) 123–134zbMATHGoogle Scholar
  7. 7.
    Brickell, E.F., Stinson, D.R.: Some improved bounds on the information rate of perfect secret sharing schemes. J. Cryptology 5 (1992) 153–166zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Capocelli, R.M., De Santis, A., Gargano, L., Vaccaro, U.: On the size of shares of secret sharing schemes. J. Cryptology 6 (1993) 157–168zbMATHCrossRefGoogle Scholar
  9. 9.
    Dembowski, P.: Finite geometries. Reprint of the 1968 original. Classics in Mathematics. Springer-Verlag, Berlin, 1997Google Scholar
  10. 10.
    Ito, M., Saito, A., Nishizeki, T.: Secret sharing scheme realizing any access structure. Proc. IEEE Globecom’87 (1987) 99–102Google Scholar
  11. 11.
    Jackson, W.-A., Martin, K.M.: Geometric secret sharing schemes and their duals. Des. Codes Cryptogr. 4 (1994) 83–95zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Jackson, W.-A., Martin, K.M.: Perfect secret sharing schemes on five participants. Des. Codes Cryptogr. 9 (1996) 267–286zbMATHMathSciNetGoogle Scholar
  13. 13.
    Martí-Farré, J., Padró, C.: Secret sharing schemes with three or four minimal qualified subsets. Cryptology ePrint Archive (2002) Report 2002/050, http://eprint.iacr.org/
  14. 14.
    Padró, C., Sáez, G.: Secret sharing schemes with bipartite access structure. IEEE Trans. Inform. Theory 46 (2000) 2596–2604zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Shamir, A.: How to share a secret. Commun. of the ACM 22 (1979) 612–613zbMATHMathSciNetGoogle Scholar
  16. 16.
    Stinson, D.R.: An explication of secret sharing schemes. Des. Codes Cryptogr. 2 (1992) 357–390zbMATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Stinson, D.R.: Decomposition constructions for secret-sharing schemes. IEEE Trans. Inform. Theory 40 (1994) 118–125zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Jaume Martí-Farré
    • 1
  • Carles Padró
    • 1
  1. 1.Dept. Matemàtica Aplicada IVUniversitat Politècnica de CatalunyaBarcelonaSpain

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