OIHF ⇒ OT
Statement
Migrated verbatim from random-oracle-model § Known Results:
- OIHFs bridge Minicrypt and Cryptomania non-black-box — Barnum and Heath introduced Oblivious Interactive Hash Functions (OIHFs), a primitive that can be constructed from a random oracle, yet implies OT via a non-black-box reduction BH26. This partially bridges the classical separation between Minicrypt (one-way functions, PRFs, etc.) and Cryptomania (public-key primitives including OT), though the non-black-box OT construction from a standard-model OIHF currently requires Cryptomania assumptions.
Notes
Recorded during migration and not fixed — these are claims about the source text, not changes to it:
- CLASS IS LOAD-BEARING: dropping class:‘non-black-box’ would put this edge in direct conflict with the Impagliazzo-Rudich black-box separation of OT from symmetric primitives.
- The bullet immediately qualifies the headline — a standard-model OIHF ‘currently requires Cryptomania assumptions’ — a side condition the sub-edge cannot carry, and which was recorded as a separate record.
- oblivious-interactive-hash-function has no wiki page.
- COMPOSITE: two links (RO ⇒ OIHF construction; OIHF ⇒ OT via a non-black-box reduction) collapsed into one bullet — must be split.
- “oblivious-interactive-hash-function” (OIHF) has no wiki page.
- The second link is explicitly non-black-box; the class must survive migration or the record contradicts the Impagliazzo–Rudich barrier.
- The bullet immediately walks the headline back (“currently requires Cryptomania assumptions” in the standard model) — recorded as a separate record.