Bingo: Adaptivity and Asynchrony in Verifiable Secret Sharing and Distributed Key Generation.

We present Bingo , an adaptively secure and optimally resilient packed asynchronous verifiable secret sharing (PAVSS) protocol that allows a dealer to share f + 1 secrets with a total communication complexity of O ( λ n 2 ) words, where λ is the security parameter and n is the number of parties. Using Bingo , we obtain an adaptively secure validated asynchronous Byzantine agreement (VABA) protocol that uses O ( λ n 3 ) expected words and constant expected time, which we in turn use to construct an adaptively secure high-threshold asynchronous distributed key generation (ADKG) protocol that uses O ( λ n 3 ) expected words and constant expected time. To the best of our knowledge, our ADKG is the first to allow for an adaptive adversary while matching the asymptotic complexity of the best known static ADKGs.