Unconditionally-Secure Robust Secret Sharing with Minimum Share Size

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 discuss our results and propose directions for future research.