No fully-black-box reduction from OT to PKE

Unconditional · against fully-black-box reductions · GKM+00

Statement

There is no fully-black-box construction of PKE, taken as a trapdoor predicate (single-bit PKE), from OT: the two primitives are incomparable under black-box reductions, by oracle separations following IR89 — GKM+00. A multi-bit scheme restricted to one-bit messages is a trapdoor predicate, so no fully-black-box construction of multi-bit PKE from OT exists either — folklore.

Notes

• A restricted, strengthened form of each primitive does imply the other — GKM+00.
• The converse separation: PKE ⇏ OT — GKM+00.