Problems of unconditionally secure communication have been studied extensively in network models. Dolev-Dwork-Waarts-Yung considered the Byzantine threats model, in which the adversary can only take over a number of nodes bounded by a threshold. They studied two cases:
all communication links (edges in the graph) are two-way communication,
all communication links are one-way communication, and there is no feedback.
The node sets that the adversary can take over was generalized by Hirt-Maurer to an adversary structure. At PODC 2002, Kumar-Goundan-Srinathan-Rangan generalized Dolev-Dwork-Waarts-Yung’s first scenario to the case of a general adversary structure. In this paper we generalize Dolev-Dwork-Waarts-Yung’s second scenario to the case of a general adversary structure. As in Dolev-Dwork-Waarts-Yung, our work relies on the use of secret sharing.