A nonlinear secret sharing scheme

  • 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 have described a nonlinear secret-sharing scheme for n parties such that any set of k−1 or more shares can determine the secret, any set of less than k−1 shares might give information about the secret, but it is computationally hard to extract information about the secret. The scheme is based on quadratic forms and the computation of both the shares and the secret is easy.


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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, Some ideal secret sharing schemes, in “Advances in Cryptology — Eurocrypt'89”, LNCS 434 (1990), 468–475.Google Scholar
  3. 3.
    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
  4. 4.
    E. Dawson, E. S. Mahmoodian and A. Rahilly, Orthogonal arrays and ordered threshold schemes, Australian Journal of Combinatorics 8 (1993), 27–44.Google Scholar
  5. 5.
    N. Koblitz, A Course in Number Theory and Cryptography, New York: Springer, 1985.Google Scholar
  6. 6.
    F. J. MacWiliams and N. J. A. Sloane, The Theory of Error-Correcting Codes, North-Holland, 1978.Google Scholar
  7. 7.
    R. Lidl and H. Niederreiter, Finite Fields, Cambridge University Press and Addison-Wesley, 1983.Google Scholar
  8. 8.
    K. M. Martin, New secret sharing schemes from old, Journal of Combinatorial Mathematics and Combinatorial Computing 14 (1993), 65–77.Google Scholar
  9. 9.
    A. Shamir, How to share a secret, Comm. ACM 22 (1979), 612–613.Google Scholar
  10. 10.
    G. J. Simmons, How to (really) share a secret, in “Advances in Cryptology — Crypto'88”, Goldwasser, ed., LNCS 403 (1989), 390–448.Google Scholar
  11. 11.
    G. J. Simmons, Geometric shared secret and/or shared control schemes, in “Advances in Cryptology — Crypt'90”, LNCS 537 (1991), 216–241.Google Scholar
  12. 12.
    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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