  This paper focuses on Byzantine attack detection for Gaussian two-way relay
network. In this network, two source nodes communicate with each other with the
help of an amplify-and-forward relay which may perform Byzantine attacks by
forwarding altered symbols to the sources. For simple investigating the
detectability of attacks conducted in Gaussian channels, we focus on the MA
channel of the network, while assuming the BC channel is noiseless. Upon such
model, we propose a attack detection scheme implemented in the sources.
Specifically, we consider a open wireless propagation environment that allows
the symbols, forwarded by the relay, to go through a continuous channel and
arrive to the sources. With the observations of the source, we develop a
detection scheme for the source by comparing the joint empirical distribution
of its received and transmitted signals with the known channel statistics. The
main contribution of this paper is to prove that if and only if the Gaussian
relay network satisfies a non-manipulable channel condition, the proposed
detection scheme can detect arbitrary attacks that allows the stochastic
distributions of altered symbols to vary arbitrarily and depend on each other.
No pre-shared secret or secret transmission is needed for the detection.
Furthermore, we also prove that for the considered Gaussian two-way relay
networks, the non-manipulable channel condition is always satisfied. This
result indicates that arbitrary attacks conducted in MA Gaussian channels are
detectable by only using observations, while providing a base for attack
detection in more general Gaussian networks.
