# Byzantine agreement implies Broadcast channel [Consesus]

I am not sure if this is the right place to ask but I will give it a try. If not, let me know and I will ask somewhere else :)

We discussed the byzantine agreement and broadcast channel in class. We showed that broadcast implies byzantine agreement if $t < \frac{n}{2}$, where $t$ are dishonest parties and $n$ are the honest parties.

We designed a protocol for the byzantine agreement

1. All parties send input $p_i$ over broadcast channel
2. Parties output majority of received values

All parties receive same message $p_i$ via broadcast channel -> Majority is unique.

Now I have to show that byzantine implies broadcast. That means I have to design a broadcast protocol which uses Byzantine agreement as subroutine. At the end we have to explain why it satisfies the security properties of the broadcast channel.

I am stuck with designing the protocol. From what I understood is the byzantine agreement based on point-to-point channels. I had the idea to have it based on a PKI structure. Each sender owns the public key of the other parties, encrypts the message and sends it.

This would simulate a point-to-point channel, but on the other hand it means a lot calculation and time. Not sure if the last point is important to consider in this kind of view but I took it into consideration due to the "Termination" security property.

Would be nice if someone is able to help me.