# Two-Multicast Channel with Confidential Messages

## TL;DR

This paper investigates the secrecy capacity of a two-transmitter, two-receiver multicast channel with an eavesdropper, extending known techniques and deriving bounds for secure communication in various channel configurations.

## Contribution

It introduces new inner and outer bounds for the secrecy rates of the two-multicast channel, generalizing several existing results and providing conditions where bounds meet.

## Key findings

- Inner bounds recover known results for multiple-access wiretap and broadcast channels.
- Outer bounds are derived for both degraded and non-degraded channels.
- An auxiliary result on minimal randomness for secrecy is presented.

## Abstract

Motivated in part by the problem of secure multicast distributed storage, we analyze secrecy rates for a channel in which two transmitters simultaneously multicast to two receivers in the presence of an eavesdropper. Achievable rates are calculated via extensions of a technique due to Chia and El Gamal and the method of output statistics of random binning. Outer bounds are derived for both the degraded and non-degraded versions of the channel, and examples are provided in which the inner and outer bounds meet. The inner bounds recover known results for the multiple-access wiretap channel, broadcast channel with confidential messages, and the compound MAC channel. An auxiliary result is also produced that derives an inner bound on the minimal randomness necessary to achieve secrecy in multiple-access wiretap channels.