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Secret sharing schemes with bipartite access structure

  • Carles Padró
  • Germán Sáez
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1403)

Abstract

We study the information rate of secret sharing schemes whose access structure is bipartite. In a bipartite access structure there are two classes of participants and all participants in the same class play an equivalent role in the structure. We characterize completely the bipartite access structures that can be realized by an ideal secret sharing scheme. Both upper and lower bounds on the optimal information rate of bipartite access structures are given.

References

  1. 1.
    A. Beutelspacher and F. Wettl. On 2-Level Secret Sharing. Designs, Codes and Cryptography 3 (1993) 127–134.MATHMathSciNetCrossRefGoogle Scholar
  2. 2.
    G.R. Blakley. Safeguarding cryptographic keys. AFIPS Conference Proceedings 48 (1979) 313–317.Google Scholar
  3. 3.
    C. Blundo, A. De Santis, L. Gargano, U. Vaccaro. Tight Bounds on the Information Rate of Secret Sharing Schemes. Designs, Codes and Cryptography 11 (1997) 107–122.MATHCrossRefGoogle Scholar
  4. 4.
    C. Blundo, A. De Santis, L. Gargano, U. Vaccaro. On the Information Rate of Secret Sharing Schemes. Advances in Cryptology CRYPTO'92. Lecture Notes in Computer Science 740 148–167. Springer-Verlag.Google Scholar
  5. 5.
    C. Blundo, A. De Santis, D.R. Stinson, U. Vaccaro. Graph Decompositions and Secret Sharing Schemes. J. Cryptology 8 (1995) 39–64.MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    E.F. Brickell. Some ideal secret sharing schemes. J. Combin. Math. and Combin. Comprit, 9 (1989) 105–113.MathSciNetGoogle Scholar
  7. 7.
    E. F. Brickell, D. M. Davenport. On the Classification of Ideal Secret Sharing Schemes. J. Cryptology 4 (1991) 123–134.MATHGoogle Scholar
  8. 8.
    E.F. Brickell and D.R. Stinson. Some Improved Bounds on the Information Rate of Perfect Secret Sharing Schemes. J. Cryptology 5 (1992) 153–166.MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    R. M. Capocelli, A. De Santis, L. Gargano and U. Vaccaro. On the Size of Shares of Secret Sharing Schemes. In Advances in Cryptology-CRYPTO 91, Lecture Notes in Computer Science 576, Springer-Verlag, 101–113. To appear in J. Of Cryptology.Google Scholar
  10. 10.
    M. Ito, A. Saito and T, Nishizeki. Secret sharing scheme realizing any access structure. Proc. IEEE Globecom'87 (1987) 99–102.Google Scholar
  11. 11.
    E.D. Karnin, J.W. Greene and M.E. Hellman. On secret sharing systems. IEEE Transactions on Information Theory 29 (1983) 35–41.MATHMathSciNetCrossRefGoogle Scholar
  12. 12.
    A. Shamir. How to share a secret. Commun. of the ACM 22 (1979) 612–613.MATHMathSciNetCrossRefGoogle Scholar
  13. 13.
    G.J. Simmons. An Introduction to Shared Secret and/or Shared Control Schemes and Their Application. Contemporary Cryptology. The Science of Information Integrity. IEEE Press (1991) 441–497.Google Scholar
  14. 14.
    D.R. Stinson. An explication of secret sharing schemes. Designs, Codes and Cryptography 2 (1992) 357–390.MATHMathSciNetCrossRefGoogle Scholar
  15. 15.
    D.R. Stinson. Decomposition Constructions for Secret-Sharing Schemes. IEEE Trans. on Information Theory 40 (1994) 118–125.MATHMathSciNetCrossRefGoogle Scholar
  16. 16.
    D.R. Stinson. Cryptography: Theory and Practice. CRC Press Inc., Boca Raton (1995).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Carles Padró
    • 1
  • Germán Sáez
    • 1
  1. 1.Dep. Matemàtica Aplicada i TelemàticaUniversitat Politècnica de CatalunyaBarcelona

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