1993 | ReviewPaper | Chapter
Nonperfect secret sharing schemes
Authors : Wakaha Ogata, Kaoru Kurosawa, Shigeo Tsujii
Published in: Advances in Cryptology — AUSCRYPT '92
Publisher: Springer Berlin Heidelberg
Included in: Professional Book Archive
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A nonperfect secret sharing scheme (NSS) consists of a family of access subsets Γ1, a family of semi-access subsets Γ2 and a family of non-access subsets Γ3. In an NSS, it is possible that ¦Vi¦<¦S¦, where ¦Vi¦ is the size of the share and ¦S¦ is the size of the secret. This paper characterizes nonperfect secret sharing schemes. First, we show that (Γ1, Γ2, Γ3) is realizable if and only if Γ1 is monotone and Γ1 ∪ Γ2 is monotone. Then, we derive a lower bound of ¦Vi¦ in terms of a distance between Γ1 and Γ3. Finally, we show a condition for (Γ1, Γ2, Γ3) to achieve ¦V i ¦=¦S¦/2 for all i.