Unconditionally-Secure Robust Secret Sharing with Minimum Share Size

An n-player (t,δ)-secure threshold 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 threshold 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 threshold 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.

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