DARE to Agree: Byzantine Agreement With Optimal Resilience and Adaptive Communication

Byzantine Agreement (BA) enables n processes to reach consensus on a common valid Lo-bit value, even in the presence of up to t < n faulty processes that can deviate arbitrarily from their prescribed protocol. Despite its significance, the optimal communication complexity for key variations of BA has not been determined within the honest majority regime (n = 2t +1), for both the worst-case scenario and the adaptive scenario, which accounts for the actual number f ≤ t of failures. We introduce ada-Dare (Adaptively Disperse, Agree, Retrieve), a novel universal approach to solve BA efficiently. Let κ represent the size of the cryptographic objects required to solve BA when t > n/3. Different instantiations of ada-Dare achieve near-optimal adaptive bit complexity of O(nLo + n(f + 1)κ) for both strong multi-valued validated BA (SMVBA) and interactive consistency (IC). By definition, for IC, Lo = nLin where Lin is the size of an input value. These results achieve optimal O(n(Lo + f)) word complexity and significantly improve the previous best results by up to a linear factor, depending on Lo and f.