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(n²). However, the worst-case bit complexity of the best solution is still O(n²L + n²κ) (where κ is the security parameter), far from the Ω(nL + n²) 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. Namely, we present a new algorithm, DARE (Disperse, Agree, REtrieve), that improves upon the O(n²L) term via a novel dispersal primitive. DARE achieves O(n^{1.5}L + n^{2.5}κ) bit complexity, an effective √n-factor improvement over the state-of-the-art (when L > nκ). 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(nL + n²poly(κ)). Both DARE and DARE-Stark achieve optimal O(n) worst-case latency.
@InProceedings{civit_et_al:LIPIcs.DISC.2023.13, author = {Civit, Pierre and Gilbert, Seth and Guerraoui, Rachid and Komatovic, Jovan and Monti, Matteo and Vidigueira, Manuel}, title = {{Every Bit Counts in Consensus}}, booktitle = {37th International Symposium on Distributed Computing (DISC 2023)}, pages = {13:1--13:26}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-301-0}, ISSN = {1868-8969}, year = {2023}, volume = {281}, editor = {Oshman, Rotem}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.13}, URN = {urn:nbn:de:0030-drops-191399}, doi = {10.4230/LIPIcs.DISC.2023.13}, annote = {Keywords: Byzantine consensus, Bit complexity, Latency} }
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