Broadcast from Minicast Secure Against General Adversaries

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 [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 $t < \frac{b-1}{b+1}n$.

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.

The unabridged version of this paper appears in [Ray15]. P. Raykov – Supported by ISF grant 1155/11, Israel Ministry of Science and Technology (grant 3-9094), GIF grant 1152/2011, and the Check Point Institute for Information Security.