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An impossibility result on graph secret sharing

机译：图秘密共享的不可能结果

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A perfect secret sharing scheme based on a graph G is a randomized distribution of a secret among the vertices of the graph so that the secret can be recovered from the information assigned to vertices at the endpoints of any edge, while the total information assigned to an independent set of vertices is independent (in statistical sense) of the secret itself. The efficiency of a scheme is measured by the amount of information the most heavily loaded vertex receives divided by the amount of information in the secret itself. The (worst case) information ratio of G is the infimum of this number. We calculate the best lower bound on the information ratio for an infinite family of graphs the entropy method can give. We argue that almost all existing constructions for secret sharing schemes are special cases of the generalized vector space construction. We give direct constructions of this type for the first two members of the family, and show that for the other members no such construction exists which would match the bound yielded by the entropy method.
机译：基于图G的完美秘密共享方案是秘密在图的各个顶点之间的随机分布，以便可以从分配给任意边缘端点的顶点的信息中恢复秘密，而将总信息分配给任意一个端点。独立的一组顶点独立于秘密本身（在统计意义上）。方案的效率由负载最大的顶点接收的信息量除以秘密本身中的信息量来衡量。 G的（最坏情况）信息比率是该数字的最小值。我们为熵方法可以提供的无穷系列图计算信息比率的最佳下限。我们认为，几乎所有现有的秘密共享方案构造都是广义向量空间构造的特例。我们为家庭的前两个成员给出了这种类型的直接构造，并表明对于其他成员，不存在这样的构造，该构造将与熵方法产生的界匹配。

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