Consensus enables n processes to agree on a common valid L-bit value, despite t < n/3 processes being faulty and acting arbitrarily. A long line of work has been dedicated to improving the worst-case communication complexity of consensus in partial synchrony. This has recently culminated in the worst-case word complexity of O(n^2). However, the worst-case bit complexity of the best solution is still O(n^2 L + n^2 kappa) (where kappa is the security parameter), far from the \Omega(n L + n^2) lower bound. The gap is significant given the practical use of consensus primitives, where values typically consist of batches of large size (L > n). This paper shows how to narrow the aforementioned gap while achieving optimal linear latency. Namely, we present a new algorithm, DARE (Disperse, Agree, REtrieve), that improves upon the O(n^2 L) term via a novel dispersal primitive. DARE achieves O(n^{1.5} L + n^{2.5} kappa) bit complexity, an effective sqrt{n}-factor improvement over the state-of-the-art (when L > n kappa). Moreover, we show that employing heavier cryptographic primitives, namely STARK proofs, allows us to devise DARE-Stark, a version of DARE which achieves the near-optimal bit complexity of O(n L + n^2 poly(kappa)). Both DARE and DARE-Stark achieve optimal O(n) latency.

翻译：共识算法使得n个进程能够就一个有效的通用L位值达成一致，尽管存在t < n/3个进程可能发生故障并任意行为。大量研究工作致力于优化部分同步环境下共识的最坏情况通信复杂度，最新进展将最坏情况字复杂度降至O(n²)。然而，现有最优解决方案的最坏情况比特复杂度仍为O(n²L + n²κ)（其中κ为安全参数），远未达到Ω(nL + n²)的理论下界。考虑到共识原语在实际应用中通常涉及大尺寸值块（L > n），这一差距尤为显著。本文展示了如何在实现最优线性延迟的同时缩小上述差距：我们提出一种新算法DARE（Disperse, Agree, REtrieve），通过创新性的分散原语优化了O(n²L)项。DARE将比特复杂度降至O(n^1.5 L + n^2.5 κ)，当L > nκ时，相较于现有最优方案实现了√n量级的改进。此外，我们证明采用更强的加密原语（即STARK证明）可设计出DARE-Stark版本，该版本实现了接近最优的O(nL + n² poly(κ))比特复杂度。DARE与DARE-Stark均能达到最优的O(n)延迟。