This paper characterizes the secret message capacity of three networks wheretwo unicast sessions share some of the communication resources. Each networkconsists of erasure channels with state feedback. A passive eavesdropper isassumed to wiretap any one of the links. The capacity achieving schemes as wellas the outer bounds are formulated as linear programs. The proposed strategiesare then numerically evaluated and shown to achieve higher rate performances(up to a double single- or sum-rate) with respect to alternative strategies,where the network resources are time-shared among the two sessions. Theseresults represent a step towards the secure capacity characterization forgeneral networks. They also show that, even in configurations for which networkcoding does not offer benefits in absence of security, it can become beneficialunder security constraints.
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