Every Bit Counts in Consensus (2306.00431v2)

Abstract: 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.