An Efficient Robust Secret Sharing Scheme with Optimal Cheater Resiliency

In this paper, we consider the problem of (t, δ) robust secret sharing secure against rushing adversary. We design a simple t-out-ofn secret sharing scheme, which can reconstruct the secret in presence of t cheating participants except with probability at most δ, provided t < n/2. The later condition on cheater resilience is optimal for the case of public reconstruction of the secret, on which we focus in this work. Our construction improves the share size of Cevallos et al. (EUROCRYPT2012) robust secret sharing scheme by applying the “authentication tag compression” technique devised by Carpentieri in 1995. Our improvement is by a constant factor that does not contradict the asymptotic near-optimality of the former scheme. To the best of our knowledge, the proposed scheme has the smallest share size, among other efficient rushing (t, δ) robust secret sharing schemes with optimal cheater resilience.