ROM ⇒ OIHF

ROM implies OIHF.

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

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

  • oblivious-interactive-hash-function has no wiki page.
  • The hypothesis is a MODEL, not an object: ‘a random oracle’ is an idealized primitive, so this edge’s hypothesis is model-shaped and duplicates the information in the model field.
  • The reduction class for this link is not stated on the 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.