A Perfect Secret Sharing Scheme for (r-1, r)-Uniform Hypergraph-Based Access Structures.
Yichun Wang, Justie Su-Tzu Juan · FCS · 2007
A secret sharing scheme is a method to distribute a secret among a set of participants, such that only qualified subsets of the participants can recover the secret. A secret sharing scheme is perfect if any unqualified subset obtains no information regarding the master key. The collection of qualified subsets is called access structure. In a hypergraph, if the size of edges is equal to r, the hypergraph is called an r-uniform hypergraph. An r-uniform hypergraph-based access structure is an access structure which using an r-uniform hypergraph to show the access structure, where a vertex denote a participant and the edge set denote the minimal access structure of a secret sharing scheme. Given any r-uniform hypergraph G and Γ is the G-based access structure, this paper proposes a perfect secret sharing scheme for Γ, and this scheme is the most efficient secret sharing scheme for Γ up to now.