The access structure of some secret-sharing schemes

  • Ari Renvall
  • Cunsheng Ding
Session 2: Secret Sharing
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1172)


In this paper, we determine the access structure of a number of secret-sharing schemes that are based on error-correcting linear codes with respect to two approaches. Some secret-sharing, schemes based on linear codes are also constructed. The relation between the minimum distance of codes and the access structure of secret-sharing schemes is also investigated.


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  1. 1.
    G. R. Blakley, Safeguarding cryptographic keys, Proc. NCC AFIPS 1979, 313–317.Google Scholar
  2. 2.
    E. F. Brickell and D. M. Davenport, On the classification of ideal secret sharing schemes, J. Cryptology 4 (1991), 105–113. [Preliminary version in “Advances in Cryptology—Crypto'89, LNCS 435 (1990), 278–285.]Google Scholar
  3. 3.
    E. F. Brickell, Some ideal secret sharing schemes, in “Advances in Cryptology — Eurocrypt'89”, LNCS 434 (1990), 468–475.Google Scholar
  4. 4.
    C. Charnes, J. Pieprzyk and R. Safavi-Naini Conditionally secure secret sharing scheme with disenrollment capability, in “2nd ACM Conference on Computer and Communications Security,” ACM Press, 1994, 89–95.Google Scholar
  5. 5.
    E. Dawson, E. S. Mahmoodian and A. Rahilly, Orthogonal arrays and ordered threshold schemes, Australian Journal of Combinatorics 8 (1993), 27–44.Google Scholar
  6. 6.
    M. Van Dijk, A linear construction of Perfect secret sharing schemes, in “Advances in Cryptology-Eurocrypt'94”, A. De Santis, ed., LNCS 950 (1995), 23–34.Google Scholar
  7. 7.
    E. D. Karnin, J. W. Green and M. Hellman, On secret sharing systems, IEEE Trans Inform. Theory, Vol. IT-29 (1983), 644–654.Google Scholar
  8. 8.
    F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1978.Google Scholar
  9. 9.
    K. M. Martin, New secret sharing schemes from old, Journal of Combinatorial Mathematics and Combinatorial Computing 14 (1993), 65–77.Google Scholar
  10. 10.
    J. L. Massey, Minimal codewords and secret sharing, Proc. 6th Joint Swedish-Russian Workshop on Inform. Theory, Mölle, Sweden, August 22–27, 1993, 276–279.Google Scholar
  11. 11.
    J. L. Massey, Some applications of coding theory in cryptography, in “Codes and Cyphers: Cryptography and Coding IV” (Ed. P. G. Farrell). Esses, England: Formara Ltd., 1995, 33–47.Google Scholar
  12. 12.
    R. J. McEliece and D. V. Sarwate, On sharing secrets and Reed-Solomon codes, Comm. ACM 24 (1981), 583–584.Google Scholar
  13. 13.
    A. Shamir, How to share a secret, Comm. ACM 22, 1979, 612–613.Google Scholar
  14. 14.
    G. J. Simmons, How to (really) share a secret, in “Advances in Cryptology — Crypto'88”, Goldwasser, ed., LNCS 403 (1989), 390–448.Google Scholar
  15. 15.
    G. J. Simmons, Geometric shared secret and/or shared control schemes, in “Advances in Cryptology — Crypt'90”, LNCS 537 (1991), 216–241.Google Scholar
  16. 16.
    Y. Zheng, T. Hardjono and J. Seberry, Reusing shares in secret sharing schemes, The Computer Journal 37 (1994), 199–205.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Ari Renvall
    • 1
  • Cunsheng Ding
    • 1
  1. 1.Department of MathematicsUniversity of TurkuTurkuFinland

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