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首页> 外文会议>International Conference on Security and Cryptography for Networks(SCN 2006); 20060906-08; Maiori(IT) >Ideal Secret Sharing Schemes Whose Minimal Qualified Subsets Have at Most Three Participants
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Ideal Secret Sharing Schemes Whose Minimal Qualified Subsets Have at Most Three Participants

机译：最小合格子集最多具有三个参与者的理想秘密共享计划

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摘要

One of the main open problems in secret sharing is the characterization of the access structures of ideal secret sharing schemes. As a consequence of the results by Brickell and Davenport, every one of those access structures is related in a certain way to a unique matroid. We study this open problem for access structures with rank three, that is, structures whose minimal qualified subsets have at most three participants. We prove that all access structures with rank three that are related to matroids with rank greater than three are ideal. After the results in this paper, the only open problem in the characterization of the ideal access structures with rank three is to characterize the matroids with rank three that can be represented by an ideal secret sharing scheme.
机译：秘密共享中的主要开放问题之一是理想秘密共享方案的访问结构的特征。由于Brickell和Davenport的研究结果，这些访问结构中的每一个都以某种方式与唯一的拟阵线相关。我们研究了具有第3级访问结构的开放问题，即，其最小合格子集最多具有3个参与者的结构。我们证明与等级大于3的拟阵有关的所有等级3的访问结构都是理想的。根据本文的结果，表征第三级的理想访问结构的唯一开放问题是表征可以由理想秘密共享方案表示的第三级的拟阵。

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