Rabin OT ⇔ OT

Rabin OT is equivalent to OT.

Statement

Migrated verbatim from oblivious-transfer § Rabin OT:

Introduced by Rab81, Rabin’s OT is a simpler variant where the sender transmits a single message $x$ and the receiver obtains it with probability $1/2$, receiving $\perp$ otherwise — without the sender learning which outcome occurred. Rabin OT and 1-out-of-2 OT are equivalent; each implies the other by efficient reductions.

Notes

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:

• The citation [[Rab81]] attaches to ‘Introduced by’, NOT to the equivalence claim; the equivalence (‘each implies the other by efficient reductions’) is effectively uncited (the standard citation, Crepeau87, is absent from content/References).
• [[Rab81]] is a bare wikilink to an alias, not the canonical ‘[[KEY - Full Title|KEY]]’ form used everywhere else (it resolves via the alias ‘Rab81’ on ‘Rabin81 - How to Exchange Secrets with Oblivious Transfer.md’).
• ‘rabin-ot’ has no page; it is a variant section on this page.
• Equivalence should be migrated as TWO reductions (rabin-ot ⇒ OT and OT ⇒ rabin-ot).