Hash function + iO ⇒ PKE
Hash function together with iO implies PKE.
Statement
Migrated verbatim from impagliazzos-five-worlds § Obfustopia:
Indistinguishability obfuscation (iO) together with OWFs defines an even richer world beyond Cryptomania, sometimes called Obfustopia. iO is an extremely powerful primitive: combined with OWFs, it implies PKE, digital signatures, NIZK proofs without a CRS, functional encryption for all circuits, deniable encryption, and much more — SW14.
Migrated verbatim from indistinguishability-obfuscation § Other results:
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.
This relation is stated on 2 pages; the statements above are all of them.
Recorded during migration and not fixed — these are claims about the source text, not changes to it:
- CONJUNCTIVE and DISJUNCTIVELY BUNDLED: “combined with OWFs, it implies PKE, digital signatures, NIZK proofs without a CRS, functional encryption for all circuits, deniable encryption, and much more” is one hypothesis SET {iO, OWF} with five separate conclusions; this record isolates {iO, OWF} ⇒ PKE.
- “and much more” is an unbounded, untypeable tail that a migration must drop.
- OWF hypothesis is again the hash-function page alias.