Secret sharing is a general method for distributing sensitive data among the participants of a system such that only a collection of predefined qualified coalitions can recover the secret data. One of the most widely used special cases is threshold secret sharing, where every subset of participants of size above a given number is qualified. In this short note, we propose a general construction for a generalized threshold scheme, called conjunctive hierarchical secret sharing, where the participants are divided into disjoint levels of hierarchy, and there are different thresholds for all levels, all of which must be satisfied by qualified sets. The construction is the first method for arbitrary parameters based on finite geometry arguments and yields an improvement in the size of the underlying finite field in contrast with the existing results using polynomials.

密钥共享是在系统参与者之间分发敏感数据的通用方法，这样只有一组预定义的合格联盟才能恢复密钥数据。最广泛使用的特殊情况之一是阈值秘密共享，其中大小超过给定数字的每个参与者子集都符合条件。在这个简短的笔记中，我们提出了一个广义阈值方案的一般结构，称为联合分层秘密共享，其中参与者被划分为不相交的层次结构级别，并且所有级别都有不同的阈值，所有这些阈值都必须由合格的集合满足。该构造是基于有限几何参数的任意参数的第一种方法，与使用多项式的现有结果相比，底层有限场的大小有所改进。