Paper 2015/352

Broadcast from Minicast Secure Against General Adversaries

Pavel Raykov

Abstract

Byzantine broadcast is a distributed primitive that allows a specific party to consistently distribute a message among $n$ parties in the presence of potential misbehavior of up to $t$ of the parties. The celebrated result of \cite{PSL80} shows that broadcast is achievable from point-to-point channels if and only if $t<n/3$. The following two generalizations have been proposed to the original broadcast problem. In~\cite{FM98} the authors considered a \emph{general adversary} characterized by the sets of parties that can be corrupted. It was shown that broadcast is achievable from point-to-point channels if and only if no three possible corrupted sets can cover the whole party set. In~\cite{CFFLMM05} the notion of point-to-point channels has been extended to the $$-minicast channels allowing to locally broadcast among any subset of $$ parties. It has been shown that broadcast secure against adversaries corrupting up to $$ parties is achievable from $$-minicast if and only if $$. In this paper we combine both generalizations by considering the problem of achieving broadcast from $$-minicast channels secure against general adversaries. Our main result is a condition on the possible corrupted sets such that broadcast is achievable from $$-minicast if and only if this condition holds.