A label graph based verifiable secret sharing scheme for general access structures

TLDR: A verifiable secret sharing scheme realizing general access structures is proposed that can resist possible internal attack performed by malicious participants, who want to obtain additional shares or provide a fake share to other participants.

Abstract: Secret sharing is that a dealer distributes a piece of information (called a share) about a secret to each participant such that authorized subsets of participants can reconstruct the secret but unauthorized subsets of participants cannot determine the secret. In this paper, an access structure can be represented by a label graph G, where a vertex denotes a participant and a complete subgraph of G corresponds to a minimal authorized subset. The vertices of G are labeled into distinct vectors uniquely determined by the maximum prohibited structure. Based on such a label graph, a verifiable secret sharing scheme realizing general access structures is proposed. A major advantage of this scheme is that it applies to any access structure, rather than only structures rep-resentable as previous graphs, i.e., the access structures of rank two. Furthermore, verifiability of the proposed scheme can resist possible internal attack performed by malicious participants, who want to obtain additional shares or provide a fake share to other participants.