Improved Robust Secret-Sharing for Honest-Majority Preprocessing-MPC

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We design a novel robust secret-sharing scheme in the honest-majority setting for $n$ parties that allows constant communication per opening per party when amortized over $\Theta(n)$ simultaneous openings. We attain this scheme by a novel application of list decoding of folded Reed-Solomon codes. This was stated as an open problem by Escudero and Fehr (2023), who could obtain this amortized complexity only for $\Theta(n^2)$ simultaneous openings. Additionally, the dealing of such shares for