An Ideal Compartmented Secret Sharing Scheme Based on Linear Homogeneous Recurrence Relations

Abstract

Multipartite secret sharing schemes are those that have multipartite access structures. The set of the participants in those schemes is divided into several parts, and all the participants in the same part play the equivalent role. One type of such access structure is the compartmented access structure. We propose an ideal and efficient compartmented multi-secret sharing scheme based on the linear homogeneous recurrence (LHR) relations. In the construction phase, the shared secrets are hidden in some terms of the linear homogeneous recurrence sequence. In the recovery phase, the shared secrets are obtained by solving those terms in which the shared secrets are hidden. When the global threshold is $t$, our scheme can reduce the computational complexity from $O(n^{t-1})$ to $O(n^{\max(t_i-1)}\log n)$, where $t_i<t$. The security of the proposed scheme is based on Shamir\u27s threshold scheme. Moreover, it is efficient to share the multi-secret and to change the shared secrets in the proposed scheme. That is, the proposed scheme can improve the performances of the key management and the distributed system