({1,3},n) Hierarchical Secret Sharing Scheme Based on XOR Operations for a Small Number of Indispensable Participants

Abstract

Blakley and Shamir independently introduce the basic idea of a (k, n) threshold secret sharing scheme in 1979. Shamir also recognize the concept of a hierarchical scheme, and suggests accomplishing the scheme by giving the participants of the more capable levels a greater number of shares. Some of hierarchical secret sharing schemes are known in the way that the secret is shared among a group of participants that is partitioned into levels. We look at hierarchical secret sharing schemes in the purpose of the ease of deleting the secret after it is distributed, that is, the reliability of data deletion depends on the deletion of the shares of the indispensable participants, and focus on providing a fast method and practicality. In this paper, we introduce Fujii et al.'s XOR-based secret sharing scheme and Kurihara et al.'s XOR-based secret sharing scheme, and propose a perfect and ideal ({1,3},n) hierarchical secret sharing scheme based on Fujii et al.'s XOR-based secret sharing scheme for a small number of indispensable participants to place practicality. Our implementation system on a PC with Intel Celeron G1820 2.70GHz and 3.6GB RAM can recover the secret in the processing of around 7.0Gbps.