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- 2015
对3条超边的超圈存取结构最优信息率的一点注记
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Abstract:
摘要： 将含有3条超边的超圈存取结构分为两类:一类是任意一条超边都没有属于自己的独立点集;另一类是至少存在一条超边有属于自己的独立点集。对第一类超圈存取结构,用Shamir方案构造了一个理想的秘密共享方案,从而证明了其最优信息率等于1;对第二类超圈存取结构用信息论和λ-分解方法证明了其最优信息率等于2/3。给出了参与者人数为6、7且含有3条超边共86种互不同构的超圈存取结构,并计算了其最优信息率。
Abstract: The hypercycle access structures with three hyperedges is divided into two kinds:one kind is that any hyperedge has no its own independent point set, another kind is that there is at least one hyperedge which has its own independent point set. By using Shamir-threshold scheme, an ideal secret sharing scheme is constructed, and it is proved that the optimal information rate of the first kind of hypercycle access structures are equal to 1; Using information theory and λ-decomposition method, it is shown that the optimal information rate of the second kind of hypercycle access structures are equal to 2/3. Eighty-six hypercycle access structures with three hyperedges on six and seven participants, in which all of each other are not isomorphic, and their optimal information rates are calculated
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