Byzantine broadcast is a primitive which allows a specific party to distribute a message consistently among n parties, even if up to t parties exhibit malicious behaviour. In the classical model with a complete network of bilateral authenticated channels, the seminal result of Pease et al. [Pease et al., 1980] shows that broadcast is achievable if and only if t < n/3. There are two generalizations suggested for the broadcast problem - w.r.t. the adversarial model and the communication model. Fitzi and Maurer [Fitzi and Maurer, 1998] consider a (non-threshold) general adversary that is characterized by the subsets of parties that could be corrupted, and show that broadcast can be realized from bilateral channels if and only if the union of no three possible corrupted sets equals the entire set of n parties. On the other hand, Considine et al. [Considine et al., 2005] extend the standard model of bilateral channels with the existence of b-minicast channels that allow to locally broadcast among any subset of b parties; the authors show that in this enhanced model of communication, secure broadcast tolerating up to t corrupted parties is possible if and only if t < (b-1)/(b+1) n. These generalizations are unified in the work by Raykov [Raykov P., 2015], where a tight condition on the possible corrupted sets such that broadcast is achievable from a complete set of b-minicasts is shown.

This paper investigates the achievability of broadcast in general networks, i.e., networks where only some subsets of minicast channels may be available, thereby addressing open problems posed in [Jaffe et al., 2012; Raykov P., 2015]. Our contributions include: 1) proposing a hierarchy over all possible general adversaries for a clean analysis of the broadcast problem in general networks, 2) showing the infeasibility of a prominent technique - used to achieve broadcast in general 3-minicast networks [Ravikant et al., 2004] - with regard to higher b-minicast networks, and 3) providing some necessary conditions on general networks for broadcast to be possible while tolerating general adversaries.