Secret message capacity of a line network

TL;DR

This paper characterizes the maximum secure communication rate in a line network with erasure channels and feedback, considering various levels of private randomness at intermediate nodes, and provides algorithms to achieve these capacities.

Contribution

It is the first work to determine the secrecy capacity of arbitrary-sized networks with imperfect channels and feedback, covering different randomness scenarios.

Findings

Characterized secret message capacity for single and multiple eavesdropped channels.

Developed polynomial-time algorithms achieving these capacities.

Provided outer bounds for networks with multiple eavesdropped channels.

Abstract

We investigate the problem of information theoretically secure communication in a line network with erasure channels and state feedback. We consider a spectrum of cases for the private randomness that intermediate nodes can generate, ranging from having intermediate nodes generate unlimited private randomness, to having intermediate nodes generate no private randomness, and all cases in between. We characterize the secret message capacity when either only one of the channels is eavesdropped or all of the channels are eavesdropped, and we develop polynomial time algorithms that achieve these capacities. We also give an outer bound for the case where an arbitrary number of channels is eavesdropped. Our work is the first to characterize the secrecy capacity of a network of arbitrary size, with imperfect channels and feedback. As a side result, we derive the secret key and secret message capacity of an one-hop network, when the source has limited randomness.