Hash function + iO ⇒ DS

Hash function together with iO implies DS.

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.

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:

• 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} ⇒ digital signatures.
• “and much more” is an unbounded, untypeable tail that a migration must drop.
• OWF hypothesis is again the hash-function page alias.