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Optimal complexity of secret sharing schemes with four minimal qualified subsets

机译：具有四个最小合格子集的秘密共享方案的最佳复杂性

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摘要

The complexity of a secret sharing scheme is defined as the ratio between the maximum length of the shares and the length of the secret. This paper deals with the open problem of optimizing this parameter for secret sharing schemes with general access structures. Specifically, our objective is to determine the optimal complexity of the access structures with exactly four minimal qualified subsets. Lower bounds on the optimal complexity are obtained by using the known polymatroid technique in combination with linear programming. Upper bounds are derived from decomposition constructions of linear secret sharing schemes. In this way, the exact value of the optimal complexity is determined for several access structures in that family. For the other ones, we present the best known lower and upper bounds.
机译：秘密共享方案的复杂度定义为份额的最大长度与秘密长度之间的比率。本文讨论了针对具有通用访问结构的秘密共享方案优化此参数的开放问题。具体来说，我们的目标是确定具有四个最小合格子集的访问结构的最佳复杂性。最佳复杂度的下限是通过使用已知的多类拟态技术与线性编程结合而获得的。上限是从线性秘密共享方案的分解构造中得出的。这样，可以为该系列中的几个访问结构确定最佳复杂度的确切值。对于其他，我们提出了最著名的下限和上限。

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