文章基本信息

标题：Determining the Optimal Contrast for Secret Sharing Schemes in Visual Cryptography
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作者：Matthias Krause ; Hans Ulrich Simon
期刊名称：Electronic Colloquium on Computational Complexity
印刷版ISSN：1433-8092
出版年度：2000
卷号：2000
出版社：Universität Trier, Lehrstuhl für Theoretische Computer-Forschung
摘要：This paper shows that the largest possible contrast C(k,n) in a k-out-of-n secret sharing scheme is approximately 4^(-(k-1)). More precisely, we show that 4^(-(k-1)) <= C_{k,n} <= 4^(-(k-1))}n^k/(n(n-1)...(n-(k-1))). This implies that the largest possible contrast equals 4^(-(k-1)) in the limit when n approaches infinity. For large n, the above bounds leave almost no gap. For values of n that come close to k, we will present alternative bounds (being tight for n=k). The proofs of our results proceed by revealing a central relation between the largest possible contrast in a secret sharing scheme and the smallest possible approximation error in problems occuring in Approximation Theory.
关键词：Keywords: Approximation Theory, cryptography, Secret Sharing Schemes for Visual Cryptography