Modelling broadcast functionality in Universally Composable Framework
UC broadcast can be defined by a functionality $\mathcal{F}_{\textrm{BC}}$, which upon receiving a message $x$ from party $P_i$, sends $(x, P_i)$ to all parties and the adversary. 

This is formally given in, e.g. Section 3.2 of a paper by Goldwasser and Lindell. However, many higher-level protocols use broadcast without explicitly specifying the functionality, because it is so straightforward.

That paper also contains the following, very simple echo-broadcast protocol for any $t &lt; n$ corruptions:


$P_i$ sends $x$ to all other parties
Every other party re-sends $x$ to everybody else and checks that they received the same values.
If any value is inconsistent, abort. Otherwise, output $x$.


This is secure in a slightly weaker model, where a corrupt party may force some honest parties to abort; however, any honest party who does not abort will learn the correct output.