No fully-black-box reduction from OIHF to OT

Unconditional · against fully-black-box reductions · BH26

Statement

There is no fully-black-box construction of OT from an OIHF: a random oracle yields an OIHF (ROM ⇒ OIHF) — BH26 — so such a construction would compose into a fully-black-box construction of OT, hence of key agreement, from a random oracle alone, which IR89 rules out.

Notes

• BH26’s reduction from an OIHF to OT is non-black-box (OIHF ⇒ OT) and so gets around the barrier; standard-model OIHFs are known only from Cryptomania assumptions, so the Minicrypt–Cryptomania separation stands for black-box constructions — BH26.