Broadcast-Optimal Two Round MPC with an Honest Majority

This paper closes the question of possibility two-round MPC protocols achieving different security guarantees with and without availability broadcast in any given round. Cohen et al. [CGZ20] study this dishonest majority setting; we complete picture by studying honest setting. In setting, both rounds, it is known that strongest guarantee—guaranteed output delivery—is achievable [GLS15]. We show that, first round only, guaranteed delivery still achievable. Given second give a new construction achieves identifiable abort, fairness—and thus delivery—are not Finally, if only peer-to-peer channels are available, weakest guarantee—selective abort—is one for corruption thresholds $$t> 1$$ $$t=1$$ $$n=3$$ . On other hand, already selective abort can be achieved these cases. remaining cases, i.e., $$t= $$n\ge 4$$ , [IKP10, IKKP15] (and all weaker guarantees) possible.