1994 | OriginalPaper | Buchkapitel
Nonperfect Secret Sharing Schemes and Matroids
verfasst von : Kaoru Kurosawa, Koji Okada, Keiichi Sakano, Wakaha Ogata, Shigeo Tsujii
Erschienen in: Advances in Cryptology — EUROCRYPT ’93
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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This paper shows that nonperfect secret sharing schemes (NSS) have matroid structures and presents a direct link between the secret sharing matroids and entropy for both perfect and nonperfect schemes. We define natural classes of NSS and derive a lower bound of |Vi| for those classes. “Ideal” nonperfect schemes are defined baaed on this lower bound. We prove that every such ideal secret sharing scheme has a matroid structure. The rank function of the matroid is given by the entropy divided by some constant. It satisfies a simple equation which represents the access level of each subset of participants.