On perfectly secret message transmission in digraphs tolerating dual failures.

Consider a synchronous distributed network which is partly controlled by an adversary. In a Perfectly Secret Message Transmission(PSMT) protocol, the sender S wishes to transmit a message to the receiver R such that the adversary learns nothing about the message. We characterize the set of directed graphs that admit PSMT protocols tolerating a dual failure model where up to t p nodes are passively corrupted and further up to any t f nodes may fail.