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Generalized Secret Sharing and Monotone Functions

Part of the Lecture Notes in Computer Science book series (LNCS,volume 403)


Secret Sharing from the perspective of threshold schemes has been well-studied over the past decade. Threshold schemes, however, can only handle a small fraction of the secret sharing functions which we may wish to form. For example, if it is desirable to divide a secret among four participants A, B. C, and D in such a way that either A together with B can reconstruct the secret or C together with D can reconstruct the secret, then threshold schemes (even with weighting) are provably insufficient.

This paper will present general methods for constructing secret sharing schemes for any given secret sharing function. There is a natural correspondence between the set of “generalized” secret sharing functions and the set of monotone functions, and tools developed for simplifying the latter set can be applied equally well to the former set.


  • Monotone Function
  • Secret Sharing
  • Access Structure
  • Secret Share Scheme
  • Threshold Scheme

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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© 1990 Springer-Verlag Berlin Heidelberg

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Benaloh, J., Leichter, J. (1990). Generalized Secret Sharing and Monotone Functions. In: Goldwasser, S. (eds) Advances in Cryptology — CRYPTO’ 88. CRYPTO 1988. Lecture Notes in Computer Science, vol 403. Springer, New York, NY.

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  • Print ISBN: 978-0-387-97196-4

  • Online ISBN: 978-0-387-34799-8

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