Broadcast from Minicast Secure Against General Adversaries

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 [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 [FM98] the authors considered a 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 [CFF + 05] the notion of point-to-point channels has been extended to the b-minicast channels allowing to locally broadcast among any subset of b parties. It has been shown that broadcast secure against adversaries corrupting up to t parties is achievable from b-minicast if and only if t < b-1/b+1 n. In this paper we combine both generalizations by considering the problem of achieving broadcast from b-minicast channels secure against general adversaries. Our main result is a condition on the possible corrupted sets such that broadcast is achievable from b-minicast if and only if this condition holds.