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Recently Gennaro et al. (ACNS ’16) presented a threshold-optimal signature algorithm for DSA. Threshold-optimality means that if security is set so that it is required to have servers to cooperate to sign, then it is sufficient to have honest servers in the network. Obviously threshold optimality compromises robustness since if , a single corrupted player can prevent the group from signing. Still, in their protocol, up to t corrupted players cannot produce valid signatures. Their protocol requires six rounds which is already an improvement over the eight rounds of the classic threshold DSA of Gennaro et al. (Eurocrypt ’99) (which is not threshold optimal since if robust and if not).

We present a new and improved threshold-optimal DSA signature scheme, which cuts the round complexity to four rounds. Our protocol is based on the observation that given an encryption …