Generalized Secret Sharing with Linear Hierarchical Secrets

Generalized secret sharing is a method of constructing secret sharing from the perspective of access structure. In this paper, we propose a novel solution for achieving generalized secret sharing with linear hierarchical secrets. We use a matrix to model the relationship related to the access structure and transfer the matrix to modular arithmetic, which is calculated by Chinese Remainder Theorem. The participants in the corresponding access structures can cooperate with each other to produce secrets in monotonous levels. We prove that shared secrets can be efficient and reconstructed only by the qualified subset of participants; unqualified participants cannot reconstruct the corresponding shared secret.