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We study perfectly secure message transmission (PSMT) from a sender S to a receiver R in the general adversary model. In this model, instead of being bounded by a threshold, the Byzantine adversary in a network is characterized by an adversary structure. By regarding monotone general access structures as linear codes, we introduce some new properties that allow us to design efficient PSMT protocols. We give a number of efficient PSMT protocols in both undirected and directed network graphs. These protocols comprehensively improve the transmission complexity of some previous results in this area. More significantly, as all of our protocols are executed in either 3 or 2 rounds, our result is the first, in the context of PSMT in the general adversary model, to have constant round complexity when using interaction.

General Perfectly Secure Message Transmission Using Linear Codes