Fig. 2. The anonymous broadcast protocol
Real-life experiment. We have parties $P_1, \dots, P_n$ with messages $m_1, \dots, m_n$ that they want to broadcast anonymously. An adversary $\mathcal{A}$ with input $z$ controls a fixed set of these parties. $\mathcal{A}$ also controls the scheduling in the protocol, in other words, $\mathcal{A}$ decides when to proceed to the next phase, and within each phase $\mathcal{A}$ activates parties adaptively. When activated a party receives the contents of the message board, computes its input according to the protocol, and posts it on the message board. Control then passes back to $\mathcal{A}$. In the end, $\mathcal{A}$ outputs some string $s$ and halts.
We denote by $\text{Exp}_{P_1, \dots, P_n, \mathcal{A}}^{\text{real}}(m_1, \dots, m_n; z)$ the distribution of outputs $(s, \text{cont. messages})$ from the experiment, where cont is the content of the message board, and messages is a sorted list of messages from cont.
Simulation. Again, we have a trusted party $T$ and a simulator $S$. $T$ controls the message board and has as input $m_1, \dots, m_n$ and a list of corrupted parties. During the execution of the protocol it expects $S$ to provide witnesses for correctness of the actions performed by corrupted parties. When only one honest party re-