Player-Centric Byzantine Agreement

Most of the existing feasibility results on Byzantine Agreement (BA) are of an all-or-nothing fashion: in Broadcast they address the question whether or not there exists a protocol which allows any player to broadcast his input. Similarly, in Consensus the question is whether or not consensus can be reached which respects pre-agreement on the inputs of all correct players. In this work, we introduce the natural notion of player-centric BA which is a class of BA primitives, denoted as PCBA = {PCBA(C)}(C subset of P), parametrized by subsets C of the player set. For each primitive PCBA(C) is an element of PCBA the validity is defined on the input(s) of the players in C. Broadcast (with sender p) and Consensus are special (extreme) cases of PCBA primitives for C = {p} and C = P, respectively.We study feasibility of PCBA in the presence of a general (aka non-threshold) mixed (active/passive) adversary, and give a complete characterization for perfect, statistical, and computational security. Our results expose an asymmetry of Broadcast which has, so far, been neglected in the literature: there exist non-trivial adversaries which can be tolerated for Broadcast with sender some p(i) is an element of P but not for some other p(j) is an element of P being the sender. Finally, we extend the definition of PCBA by adding fail corruption to the adversary's capabilities, and give exact feasibility bounds for computationally secure PCBA(P) (aka Consensus) in this setting. This answers an open problem from ASIACRYPT 2008 concerning feasibility of computationally secure multi-party computation in this model.