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秘密共享是指在多个参与者之间共享一个主秘密,即分发给每个参与者一个子秘密,使得只有授权集中的参与者才能联合从他们的子秘密中恢复主秘密.所有授权集的集合称为存取结构.理想的存取结构具有的特性是秘密共享领域中主要的开放性问题之一,并且该问题与拟阵论有着密切的联系,即每一个理想的存取结构都是与拟阵相关联的.由于每个拟阵都是多部的且有一个对应的离散多拟阵,通过对离散多拟阵的秩函数进行研究,给出并证明了一个新的多部存取结构为理想的充分条件,并且将这一结论分别应用于m部拟阵(m≤3),进而得到与二部以及三部拟阵相关联的存取结构均为理想的一个新的证明方法.这些结论对于解决哪些拟阵导出理想的存取结构这一开放性问题将是一个新的贡献.
Secret sharing refers to the sharing of a master secret among multiple participants, that is, distributing to each participant a sub-secret, so that only participants in an authorized collective can jointly restore the master secret from their sub-secret. The collection is called access structure, and the ideal access structure has the characteristics of one of the main open problems in the field of secret sharing, and the problem is closely related to pseudo-theory that every ideal access structure is Associated with quasi-matrices. Since each quasi-matrices is multi-part and has a corresponding discrete multivariate matrix, the rank function of discrete multivariable quasi-matrices is studied and a new multi-part store Taking the sufficient and sufficient conditions of the structure as the ideal, and applying this conclusion to the m-partial m-ary matrices (m≤3) respectively, and then obtaining the access structures associated with the two and three pseudo-mosaics as the ideal new proof Method.These conclusions will be a new contribution to solve the open problem of which matroid leads to the ideal access structure.