COM ⇒ MPC

COM implies MPC.

Statement

Migrated verbatim from commitment-scheme § Other results:

COM is complete for MPC in the semi-honest model: any two-party functionality can be computed given a commitment scheme — GMW87

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

SUSPECTED MATHEMATICAL ERROR (reported, not fixed): GMW87’s semi-honest two-party protocol is built from OBLIVIOUS TRANSFER, not from commitments; commitments appear in the GMW compiler that lifts semi-honest security to malicious security. As stated, ‘commitments imply semi-honest 2PC’ would place OT inside Minicrypt (commitments follow from OWFs), contradicting the Impagliazzo-Rudich black-box separation.
‘complete for’ is not one of the directions in the target model and is untyped here — completeness (everything reduces to it) is not the same as an implication.
The citation is attached to a claim the cited paper does not make in this form.