Someone trusted prepares random material for everyone in advance, then steps away.
Why it matters: Makes the later computation fast and secure, as long as the dealer was honest.
On the map: hands out correlated randomness before the computation, then leaves
An entity that generates correlated randomness for the participants before a computation and then leaves[1]. It must not collude with anyone or leak what it handed out.
In practice the dealer is usually replaced by a computational offline phase or by trusted hardware.
If any of these breaks, this breaks too.
If this breaks, these break with it.