Abstract
A nonperfect secret sharing scheme (NSS) consists of a family of access subsets Γ 1, a family of semi-access subsets Γ 2 and a family of non-access subsets Γ 3. In an NSS, it is possible that ¦V i¦<¦S¦, where ¦V i¦ 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 (Γ 1, Γ 2, Γ 3) is realizable if and only if Γ 1 is monotone and Γ 1 ∪ Γ 2 is monotone. Then, we derive a lower bound of ¦V i¦ in terms of a distance between Γ 1 and Γ 3. Finally, we show a condition for (Γ 1, Γ 2, Γ 3) to achieve ¦V i ¦=¦S¦/2 for all i.
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© 1993 Springer-Verlag Berlin Heidelberg
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Ogata, W., Kurosawa, K., Tsujii, S. (1993). Nonperfect secret sharing schemes. In: Seberry, J., Zheng, Y. (eds) Advances in Cryptology — AUSCRYPT '92. AUSCRYPT 1992. Lecture Notes in Computer Science, vol 718. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57220-1_52
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DOI: https://doi.org/10.1007/3-540-57220-1_52
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