Network Equivalence in the Presence of an Eavesdropper

TL;DR

This paper demonstrates that for networks with noisy wiretap channels where the eavesdropper can tap only one channel at a time, the secrecy capacity is equivalent to a noiseless model, but this does not hold when multiple channels are compromised simultaneously.

Contribution

It establishes a separation principle between wiretap channel coding and secure network coding for single-channel eavesdropping scenarios, and explores limitations when multiple channels are accessed.

Findings

Secrecy capacity equals that of a noiseless network when eavesdropper taps one channel.

Separation between channel coding and network coding holds in the single-channel eavesdropper case.

The separation does not hold when the eavesdropper can access multiple channels at once.

Abstract

We consider networks of noisy degraded wiretap channels in the presence of an eavesdropper. For the case where the eavesdropper can wiretap at most one channel at a time, we show that the secrecy capacity region, for a broad class of channels and any given network topology and communication demands, is equivalent to that of a corresponding network where each noisy wiretap channel is replaced by a noiseless wiretap channel. Thus in this case there is a separation between wiretap channel coding on each channel and secure network coding on the resulting noiseless network. We show with an example that such separation does not hold when the eavesdropper can access multiple channels at the same time, for which case we provide upper and lower bounding noiseless networks.