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An ideal secret sharing scheme is a method of sharing a secret key in somekey space among a finite set of participants in such a way that only theauthorized subsets of participants can reconstruct the secret key from theirshares which are of the same length as that of the secret key. The set of allauthorized subsets of participants is the access structure of the secretsharing scheme. In this paper, we derive several properties and restate thecombinatorial characterization of an ideal secret sharing scheme inBrickell-Stinson model in terms of orthogonality of its representative array.We propose two practical models, namely the parallel and hierarchical models,for access structures, and then, by the restated characterization, we discusssufficient conditions on finite geometries for ideal secret sharing schemes torealize these access structure models. Several series of ideal secret sharingschemes realizing special parallel or hierarchical access structure model areconstructed from finite projective planes.

Ideal Secret Sharing Schemes: Combinatorial Characterizations, Certain Access Structures, and Related Geometric Problems