[BH26] How to Steal Oblivious Transfer from Minicrypt

Authors: Cruz Barnum, David Heath | Venue: ePrint 2026 | Source

Abstract

We introduce Oblivious Interactive Hash Functions (OIHFs), a new cryptographic primitive that sits between Minicrypt and Cryptomania. We show: (1) OIHFs can be constructed from a random oracle (placing them in Minicrypt); (2) OIHFs imply oblivious transfer via a non-black-box reduction; and (3) OIHFs can be constructed from oblivious transfer. The non-black-box implication of OT from OIHFs challenges the classical 36-year-old separation between Minicrypt and Cryptomania established by Impagliazzo and Rudich. However, constructing OIHFs in the standard model (without a random oracle) currently requires Cryptomania assumptions, so the full separation remains intact for black-box constructions.