Recursive General Secret Sharing Scheme Based on Authorized Subsets

Abstract

The basic idea of secret sharing is that a dealer distributes a piece of information about a secret to each participant in such a way that authorized subsets of participants can reconstruct the secret but unauthorized subsets of participants cannot determine the secret. We propose a new secret sharing scheme realizing general access structures, which is based on authorized subsets. The proposed scheme is perfect and can reduce the number of shares distributed to one specified participant. In the implementation of secret sharing schemes for general access structures, an important issue is the number of shares distributed to each participant. We can apply the proposed scheme to the same access structure recursively. That is, the proposed scheme can reduce the number of shares distributed to another participant once again by applying the proposed scheme recursively. We apply the proposed scheme to all access structures on five participants in order to evaluate the efficiency of the proposed scheme.Index Terms-Secret sharing scheme, general access structure, ( , )-threshold scheme.∈ Γ, ⊂ ′ ⊂ ⟹ ′ ∈ Γ.Let Γ 0 be a family of the minimal sets in Γ, called the minimal access structure. Γ 0 is denoted by Γ 0 = { ∈ Γ ∶ ′ ⊄ for all ′ ∈ Γ − { }}.