Secure channels ⇒ MPC with abort and honest majority ($t<n/2$) (CGH+18)

Free reduction · standard model · CGH+18

Statement

Over secure point-to-point channels, every functionality given as an arithmetic circuit has an $n$-party protocol that is information-theoretically secure with abort against a malicious adversary corrupting any $t<n/2$ of the parties (honest majority with abort). It does not achieve fairness: the adversary may receive its output while the honest parties do not. Its method for verifying that the adversary does not cheat costs about twice the semi-honest protocol in some settings, with variants for small and large fields instantiated from replicated and from Shamir secret sharing — CGH+18.

Notes

• For three parties, one semi-honest corruption and Boolean circuits, the semi-honest protocol has each party send a single bit per AND gate and nothing for XOR gates — AFL+16; a modification of that protocol is secure against malicious adversaries — FLNW17.
• Every arithmetic circuit $C$ over $\mathbb{F}$ compiles into a randomized circuit of size $O(|C|)$ on which the effect of any additive attack on the wires can be simulated, up to statistical distance $O(|C|/|\mathbb{F}|)$, by an additive attack on its inputs and outputs, so running a passive-secure protocol whose active attacks are additive on the compiled circuit gives security against active adversaries — GIP+14.
• With guaranteed output delivery the threshold $t<n/2$ is reached over secure channels with a broadcast channel (Secure channels ⇒ MPC with honest majority ($t<n/2$) (Rabin–Ben-Or)) — RB89.