Abstract
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.
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© 1994 Springer-Verlag Berlin Heidelberg
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Kurosawa, K., Okada, K., Sakano, K., Ogata, W., Tsujii, S. (1994). Nonperfect Secret Sharing Schemes and Matroids. In: Helleseth, T. (eds) Advances in Cryptology — EUROCRYPT ’93. EUROCRYPT 1993. Lecture Notes in Computer Science, vol 765. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48285-7_11
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DOI: https://doi.org/10.1007/3-540-48285-7_11
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