Broadcast-Optimal Four-Round MPC in the Plain Model

The prior works of Cohen, Garay and Zikas (Eurocrypt 2020), Damg degrees ard, Magri, Ravi, Siniscalchi and Yakoubov (Crypto 2021) and Damgard, Ravi, Siniscalchi and Yakoubov (Eurocrypt 2023) study 2-round Multi-Party Computation (where some form of set-up is required). Motivated by the fact that broadcast is an expensive resource, they focus on so-called broadcast optimal MPC, i.e., they give tight characterizations of which security guarantees are achievable, if broadcast is available in the first round, the second round, both rounds, or not at all. This work considers the natural question of characterizing broadcast optimal MPC in the plain model where no set-up is assumed. We focus on 4-round protocols, since 4 is known to be the minimal number of rounds required to securely realize any functionality with black-box simulation. We give a complete characterization of which security guarantees, (namely selective abort, selective identifiable abort, unanimous abort and identifiable abort) are feasible or not, depending on the exact selection of rounds in which broadcast is available.