Efficient Explicit Constructions of Multipartite Secret Sharing Schemes
Efficient Explicit Constructions of Multipartite Secret Sharing Schemes
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DOI：
10.1007/978-3-030-34621-8_18
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发表时间：
2019-12
影响因子：
2.5
通讯作者：
Qi Chen;Chunming Tang;Zhiqiang Lin
中科院分区：
文献类型：
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作者：
Qi Chen;Chunming Tang;Zhiqiang Lin
多方秘密共享方案是指具有多方访问结构的方案，其中参与者的集合被分成几个部分，并且同一部分中的所有参与者都扮演相同的角色。由于多方秘密共享可以看作是门限秘密共享的一种自然和有用的推广，多方接入结构的秘密共享方案受到了广泛的关注。本文研究了理想多方秘密共享方案的有效和显式构造。文献中大多数理想的多方秘密共享方案都可以分为分层的和分区的两类。主要结果是理想分层存取结构的构造，包含每一个理想分层存取结构作为特例的族，如析取分层阈值存取结构和合取分层阈值存取结构，三族划分存取结构的构造，以及两族划分存取结构的构造.在多部秘密共享方案、多拟阵和拟阵之间关系的基础上，利用线性代数技术，提出了一种构造实现这些访问结构的理想线性方案的有效方法.
Multipartite secret sharing schemes are those having a multipartite access structure, in which the set of participants is divided into several parts and all participants in the same part play an equivalent role. Secret sharing schemes for multipartite access structures have received considerable attention due to the fact that multipartite secret sharing can be seen as a natural and useful generalization of threshold secret sharing. This work deals with efficient and explicit constructions of ideal multipartite secret sharing schemes. Most ideal multipartite secret sharing schemes in the literature can be classified as either hierarchical or compartmented. The main results are the constructions for ideal hierarchical access structures, a family that contains every ideal hierarchical access structure as a particular case such as the disjunctive hierarchical threshold access structure and the conjunctive hierarchical threshold access structure, the constructions for three families of compartmented access structures, and the constructions for two families compartmented access structures with compartments. We present an efficient method to construct ideal linear schemes realizing these access structures by linear algebraic techniques on the basis of the relationship between multipartite secret sharing schemes, polymatroids and matroids.