Ideal and Perfect Secret Sharing for Fault-Tolerant Distributed Access Control of Secure Data via Nondominated Bicoteries

A perfect secret sharing scheme permits a secret to be shared among participants so that only qualified subsets of participants can reconstruct the secret, but any unqualified subset has absolutely no information about the secret. In this paper, we first show that the general secret sharing scheme with a coterie access structure is perfect if the coterie is nondominated (ND). We then propose a perfect secret sharing scheme with an ND bicoterie access structure for the access control of secure data. The proposed scheme has the merits of having two types of quorums: one type to grant and the other to revoke the access of the secure data. This provides us more flexibility for the distributed access control of the secure data. Since there are a large number of different quorums consisting of few participants, the proposed scheme is fault-tolerant in the sense that it still works even when some participants are not available. We also propose an ideal and perfect secret sharing scheme with an ND grid bicoterie access structure. The proposed scheme is optimal (ideal) in the sense that its shares have the same