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Secret Sharing, Rank Inequalities, and Information Inequalities

机译:秘密共享,等级不平等和信息不平等

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Beimel and Orlov proved that all information inequalities on four or five variables, together with all information inequalities on more than five variables that are known to date, provide lower bounds on the size of the shares in secret sharing schemes that are at most linear on the number of participants. We present here another two negative results about the power of information inequalities in the search for lower bounds in secret sharing. First, we prove that all information inequalities on a bounded number of variables can only provide lower bounds that are polynomial on the number of participants. Second, we prove that the rank inequalities that are derived from the existence of two common informations can provide only lower bounds that are at most cubic in the number of participants.
机译:Beimel和Orlov证明,关于四个或五个变量的所有信息不平等,以及迄今为止已知的五个以上变量的所有信息不平等,为秘密共享计划中的份额大小提供了下限,而秘密共享方案的份额最多是线性的。参加人数。我们在这里提出了另外两个关于信息不平等在秘密共享中寻找下界的能力的否定结果。首先,我们证明了一定数量的变量上的所有信息不等式只能提供下限,该下限是参与者数量的多项式。其次,我们证明了从两个公共信息的存在中得出的秩不等式只能提供下限,该下限最多等于参与者人数的立方。

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