Abstract
Informally, a secret sharing scheme is a method of sharing a secret key K among a finite set of participants, in such a way that certain specified subsets of participants can compute a key. Suppose that P is the set of participants. Denote by Γ the set of subsets of participants which we desire to be able to determine the key; hence Γ ⊑ 2P. Γ is called the access structure of the secret sharing scheme. It seems reasonable to require that Γ be monotone, i.e.
For any Γ0 ⊑ 2P, define the cioswe of Γ0 to be
Note that the closure of any set of subsets is monotone.
This work performed at Sandia National Laboratories and supported by the U. S. Department of Energy under contract number DE-AC04-76DP00789
Research supported by NSERC operating grant A9287 and by the Center for Communication and Information Science, University of Nebraska
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© 1991 Springer-Verlag Berlin Heidelberg
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Brickell, E.F., Stinson, D.R. (1991). Some Improved Bounds on the Information Rate of Perfect Secret Sharing Schemes. In: Menezes, A.J., Vanstone, S.A. (eds) Advances in Cryptology-CRYPTO’ 90. CRYPTO 1990. Lecture Notes in Computer Science, vol 537. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-38424-3_17
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