# Secure Multi-Source Multicast

## TL;DR

This paper addresses secure multi-source multicast by characterizing the rate region under individual security, demonstrating that full capacity can be achieved without increasing field size, thus advancing secure network coding.

## Contribution

It provides a complete characterization of the rate region for secure MSM under individual security and proves capacity achievement at the cut-set bound.

## Key findings

- Capacity is achievable at the cut-set bound.
- Field size remains similar to non-secure MSM.
- Complete rate region characterization for individual security.

## Abstract

The principal mission of Multi-Source Multicast (MSM) is to disseminate all messages from all sources in a network to all destinations. MSM is utilized in numerous applications. In many of them, securing the messages disseminated is critical. A common secure model is to consider a network where there is an eavesdropper which is able to observe a subset of the network links, and seek a code which keeps the eavesdropper ignorant regarding all the messages. While this is solved when all messages are located at a single source, Secure MSM (SMSM) is an open problem, and the rates required are hard to characterize in general. In this paper, we consider Individual Security, which promises that the eavesdropper has zero mutual information with each message individually. We completely characterize the rate region for SMSM under individual security, and show that such a security level is achievable at the full capacity of the network, that is, the cut-set bound is the matching converse, similar to non-secure MSM. Moreover, we show that the field size is similar to non-secure MSM and does not have to be larger due to the security constraint.