Efficient explicit constructions of compartmented secret sharing schemes
Efficient explicit constructions of compartmented secret sharing schemes
复制标题
分段秘密共享方案的高效显式构建
DOI：
10.1007/s10623-019-00657-2
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Lin Zhiqiang
中科院分区：
文献类型：
--
作者：
Chen Qi;Tang Chunming;Lin Zhiqiang
多方秘密共享方案一直是秘密共享领域的一个重要研究对象。多部访问结构的两个有趣的家族是分层访问结构和分隔访问结构。本文研究了理想的分区秘密共享方案的有效和明确的构造，而大多数已知的构造要么是低效的，要么是随机的。针对三种类型的分隔访问结构，即具有上界的分隔访问结构、具有下界的分隔访问结构和具有上下界的分隔访问结构，构造了理想的线性秘密共享方案.在文献中存在一些构造实现这些分隔存取结构的理想线性方案的方法，但这些方法通常效率低下，因为必须确定许多矩阵的非奇异性以检查方案的正确性。我们的构造不需要做这些计算。我们的方法来构建理想的线性计划实现这些访问结构结合联合收割机基于多项式的技术与Gabidulin码。Gabidulin码在构造中起着重要的作用，它们的性质意味着我们的方法是有效的。
Multipartite secret sharing schemes have been an important object of study in the area of secret sharing schemes. Two interesting families of multipartite access structures are hierarchical access structures and compartmented access structures. This work deals with efficient and explicit constructions of ideal compartmented secret sharing schemes, while most of the known constructions are either inefficient or randomized. We construct ideal linear secret sharing schemes for three types of compartmented access structures, such as compartmented access structures with upper bounds, compartmented access structures with lower bounds, and compartmented access structures with upper and lower bounds. There exist some methods to construct ideal linear schemes realizing these compartmented access structures in the literature, but those methods are inefficient in general because non-singularity of many matrices has to be determined to check the correctness of the scheme. Our constructions do not need to do these computations. Our methods to construct ideal linear schemes realizing these access structures combine polymatroid-based techniques with Gabidulin codes. Gabidulin codes play a fundamental role in the constructions, and their properties imply that our methods are efficient.