Four-round MPC ⇒ MPC with expected-time simulation

Fully-black-box reduction · standard model · folklore · security loss: none

Statement

A four-round plain-model protocol that securely computes $f$ with selective abort against $n-1$ corruptions, with a black-box simulator running in expected polynomial time (four-round MPC), followed by one round in which every party broadcasts whether it aborted and every party outputs $\perp$ if any party reports an abort or broadcasts nothing, securely computes $f$ with unanimous abort against $n-1$ corruptions, with a simulator running in expected polynomial time (MPC with expected polynomial-time simulation) — folklore.

Sketch

All honest parties see the same broadcast messages in the last round, so they output $\perp$ together or output together. The simulator runs the four-round simulator, in expected polynomial time, derives each honest party’s last-round broadcast from whether that simulator lets the party receive its output, runs $\mathcal{A}$ for the corrupted parties’ last-round broadcasts, and tells the trusted party to abort for all if any broadcast reports an abort or is missing — folklore.