### Nearly Optimal Robust Secret Sharing against Rushing Adversaries

Robust secret sharing is a strengthening of standard secret sharing that allows the shared secret to be recovered even if some of the shares being used in the reconstruction have been adversarially modified. In this work, we study the setting where out of all the n shares, the adversary is allowed to adaptively corrupt and modify up to t shares, where $$n = 2t+1$$ (Note that if the adversary is allowed to modify any more shares, then correct reconstruction would be impossible.). Further, we deal with rushing adversaries, meaning that the adversary is allowed to see the honest parties’ shares before modifying its own shares.

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