Closing the Efficiency Gap Between Synchronous and Network-Agnostic Consensus

In the consensus problem, n parties want to agree on a common value, even if some of them are corrupt and arbitrarily misbehave. If the parties have a common input m, then they must agree on m. Protocols solving consensus assume either a synchronous communication network, where messages are delivered within a known time, or an asynchronous network with arbitrary delays. Asynchronous protocols only tolerate \(t_a < n/3\) corrupt parties. Synchronous ones can tolerate \(t_s < n/2\) corruptions with setup, but their security completely breaks down if the synchrony assumptions are violated. Network-agnostic consensus protocols, as introduced by Blum, Katz, and Loss [TCC’19], are secure regardless of network conditions, tolerating up to \(t_s\) corruptions with synchrony and \(t_a\) without, under provably optimal assumptions \(t_a \le t_s\) and \(2t_s + t_a < n\) . Despite efforts to improve their efficiency, all known network-agnostic protocols fall short of the asymptotic complexity of state-of-the-art purely synchronous protocols. In this work, we introduce a novel technique to compile any synchronous and any asynchronous consensus protocols into a network-agnostic one. This process only incurs a small constant number of overhead rounds, so that the compiled protocol matches the optimal round complexity for synchronous protocols. Our compiler also preserves under a variety of assumptions the asymptotic communication complexity of state-of-the-art synchronous and asynchronous protocols. Hence, it closes the current efficiency gap between synchronous and network-agnostic consensus. As a plus, our protocols support \(\ell \) -bit inputs, and can be extended to achieve communication complexity \(\mathcal {O}(n^2\kappa + \ell n)\) under the assumptions for which this is known to be possible for purely synchronous protocols.