OIHF ⇒ OT

Free reduction · standard model · BH26

Statement

An OIHF implies OT via a non-black-box reduction — BH26. The reduction cannot be fully black-box (barrier): OIHFs exist relative to a random oracle (ROM ⇒ OIHF), while no fully-black-box construction of OT from a random oracle exists — IR89.

Notes

• Conversely, OT implies OIHFs — BH26.
• Standard-model OIHFs are known only from Cryptomania assumptions, so the result does not place OT in Minicrypt — BH26.