Not a COINcidence: Sub-Quadratic Asynchronous Byzantine Agreement WHP
share
King and Saia were the first to break the quadratic word complexity bound for Byzantine Agreement in synchronous systems against an adaptive adversary, and Algorand broke this bound with near-optimal resilience in the eventual-synchrony model. Yet the question of asynchronous sub-quadratic Byzantine Agreement remained open. To the best of our knowledge, we are the first to answer this question in the affirmative. A key component of our solution is a novel shared coin algorithm based on a VRF, without any further trusted setup. A second essential ingredient is VRF-based committee sampling, which we formalize and utilize in the asynchronous model for the first time. Our algorithms work against a delayed-adaptive adversary, which cannot perform after-the-fact removals but has full control of Byzantine processes and full information about communication in earlier rounds. Using committee sampling and our shared coin, we solve Byzantine Agreement with high probability, with a word complexity of O(n) and O(1) expected time, breaking the O(n^2) bit barrier for asynchronous Byzantine Agreement.
READ FULL TEXT