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 ta < n/3 corrupt parties. Synchronous ones can tolerate ts < 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 ts corruptions with synchrony and ta without, under provably optimal assumptions ta ≤ ts and 2ts + ta < 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 asymptomatic communication complexity of state-of-theart synchronous and asynchronous protocols. Hence, it closes the current efficiency gap between synchronous and network-agnostic consensus.

As a plus, our protocols support ℓ-bit inputs, and can be extended to achieve communication complexity O(n 2 κ + ℓn) under the assumptions for which this is known to be possible for purely synchronous protocols.

⋆ This is the full version of a paper appearing in Eurocrypt 2024.