Multi-Valued Byzantine Broadcast: the $t < n$ Case
Martin Hirt and Pavel Raykov
All known protocols implementing broadcast from synchronous point-to-point channels tolerating any $t < n$ Byzantine corruptions have communication complexity at least $\Omega(\ell n^2)$. We give cryptographically secure and information-theoretically secure protocols for $t < n$ that communicate $O(\ell n)$ bits in order to broadcast sufficiently long $\ell$ bit messages. This matches the optimal communication complexity bound for any protocol allowing to broadcast $\ell$ bit messages. While broadcast protocols with the optimal communication complexity exist in cases where $t < n/3$ (by Liang and Vaidya in PODC '11) or $t < n/2$ (by Fitzi and Hirt in PODC '06), this paper is the first to present such protocols for $t < n$.