Asymptotically Optimal Adaptive Asynchronous Common Coin and DKG with Silent Setup

We present the first optimal-resilient, adaptively secure asynchronous common coin protocol with $O(\lambda n^2)$ communication complexity and $O(1)$ rounds, requiring only a public silent setup. Our protocol immediately implies a sequence of quadratic-communication, constant-round asynchronous Byzantine agreement protocols, and also asynchronous distributed key generation with a silent setup. Along the way, we formulate a new primitive called asynchronous subset alignment, and introduce a simple framework to reason about specific composition security suitable for asynchronous common coin, enhancing security and functionality of silent-setup threshold encryption, which may be of independent interests.