# On Secure Network Coding for Multiple Unicast Traffic

## TL;DR

This paper explores secure network coding for multiple unicast traffic, establishing capacity bounds and designing schemes that achieve optimal secure transmission rates in various network topologies.

## Contribution

It provides the first characterization of the secure capacity region for multiple unicast traffic with an external adversary, including optimal schemes for two destinations.

## Key findings

- Outer bound on secure capacity region derived for arbitrary networks.
- Secure schemes match the outer bound for two destinations.
- Numerical verification shows schemes are optimal for certain network classes.

## Abstract

This paper investigates the problem of secure communication in a wireline noiseless scenario where a source wishes to communicate to a number of destinations in the presence of a passive external adversary. Different from the multicast scenario, where all destinations are interested in receiving the same message, in this setting different destinations are interested in different messages. The main focus of this paper is on characterizing the secure capacity region, when the adversary has unbounded computational capabilities, but limited network presence. First, an outer bound on the secure capacity region is derived for arbitrary network topologies and general number of destinations. Then, secure transmission schemes are designed and analyzed in terms of achieved rate performance. In particular, for the case of two destinations, it is shown that the designed scheme matches the outer bound, hence characterizing the secure capacity region. It is also numerically verified that the designed scheme matches the outer bound for a special class of networks with general number of destinations, referred to as combination network. Finally, for an arbitrary network topology with general number of destinations, a two-phase polynomial time in the network size scheme is designed and its rate performance {is} compared with the capacity-achieving scheme for networks with two destinations.