Unconditionally-secure ideal robust secret sharing schemes for threshold and multilevel access structure

摘要

An n-player (t, δ)-secure robust secret sharing scheme is a (t, n)-threshold secret sharing scheme with the additional property that the secret can be recovered, with probability at least 1 - δ, from the set of all shares even if up to t players provide incorrect shares. The existing constructions of robust secret sharing schemes for the range n/3 ≤ t < n/2 have the share size larger than the secret size. An important goal in this area is to minimize the share size. In the paper, we propose a new unconditionally-secure robust secret sharing scheme for the case n ≥ 2t + 2 with share size equal to the secret size. This is the minimum possible size as dictated by the perfect secrecy of the scheme. We further extend our scheme to realize a class of multilevel access structures that satisfy a special condition. The property that the share size is equal to secret size is preserved in the extended scheme. The proposed scheme is the first known robust secret sharing scheme realizing multilevel access structure.