In this thesis, we study perfectly secure message transmission in directed networks in which nodes and communication channels may be faulty. Following [6], we abstract away the network and consider that sender and receiver are connected by some number of channels. While [6] assumed that channels are either all directed from sender to receiver or all bidirectional, we are interested in the case that there might be both bidirectional channels and directional ones from sender to receiver or vice versa. We find necessary and sufficient conditions for perfeclty secure communication in this model. We also present an efficient algorithm which relies on no complexity-theoretic assumption. Interpreting those channels in our abstracted model as vertex disjoint paths between sender and receiver in the underlying directed network, we can apply our algorithm to the general directed network.
