Hierarchical Secret-Sharing Scheme Based on XOR Operations

Abstract

Hierarchical secret-sharing schemes (HSSSs) are known for the manner in which they share a secret among a group of participants partitioned into levels. First, we developed a fast HSSS that requires a minimal number of higher-level participants for recovering the secret. Next, in HSSSs, depending on the allocation of participant identities, there exists a specific case in which the secret cannot be recovered in spite of the presence of an authorized subset. For practical use, this traditional allocation issue should be eliminated in advance by adopting some simple condition. In this paper, we propose an XOR-based HSSS that can be applied to any level. It theoretically resolves the allocation issue for threshold k=3 with a simple condition and is therefore ideal for practical use. We also present an evaluation of our software implementation.