Byzantine Agreement (BA) allows a set of π parties to agree on a value even when up to π‘ of the parties involved are corrupted. While previous works have shown that, for β-bit inputs, BA can be achieved with the optimal communication complexity βπ for...Communication-Optimal Convex Agreement β’ February 16th, 2024
This gave rise to the notion of Convex Agreement (CA), introduced by Vaidya and Garg [PODCβ13], which requires the honest partiesβ outputs to be in the convex hull of the honest inputs. Unfortunately, all existing CA protocols incur a communication complexity of at least Ξ© βπ2 . In this work, we introduce the first CA protocol with the optimal communication of βπ bits for inputs in Z of size β = Ξ© π π2 log π , where π is the security parameter.
