International Association
for Cryptologic Research

An ideal conjunctive hierarchical secret sharing scheme, constructed based on the Maximum Distance Separable (MDS) codes, is proposed in this paper. The scheme, what we call, is computationally perfect. By computationally perfect, we mean, an authorized set can always reconstruct the secret in polynomial time whereas for an unauthorized set this is computationally hard. Also, in our scheme, the size of the ground field is independent of the parameters of the access structure. Further, it is efficient and requires $O(n^3)$, where $n$ is the number of participants.

Keywords: Computationally perfect, Ideal, Secret sharing scheme, Conjunctive hierarchical access structure, Disjunctive hierarchical access structure, MDS code.