Multicasting with untrusted relays: A noncoherent secure network coding approach

We consider the problem of multicasting information from a source to a destination over a multihop network of intermediate relays. However, some of the relays are untrustworthy and may be subject to eavesdropping. The source wishes to enlist their help while keeping the message secret against the eavesdropper. By employing random linear network coding at the relays, the problem is modeled as a noncoherent wiretap channel and is examined in terms of its secrecy capacity. The input distribution is optimized using an efficient projection-based gradient decent algorithm. The untrusted relay recruitment problem is also examined based on the derived secrecy capacity. An interesting scenario is analyzed where each potentially insecure relay may be randomly eavesdropped with a certain probability. Our asymptotic analysis reveals that, with enough untrusted relays, there exists a threshold on the eavesdropping probability below which all untrusted relays should be recruited.