PCS ⇒ NIZK

PCS implies NIZK.

Statement

Migrated verbatim from polynomial-commitment § Other results:

• Any polynomial commitment with $O(1)$ proof size implies the existence of a succinct NIZK for NP — standard

Notes

source: folklore: the claim carried no citation on the page it was migrated from, and none was invented.

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:

• Uncited, flagged ’— standard’ (folklore exception).
• SUSPECTED MATHEMATICAL ERROR (recorded, not fixed): an O(1)-proof-size polynomial commitment does not by itself imply a succinct NIZK for NP — a polynomial IOP/PIOP (and a setup/ROM for non-interactivity, plus zero-knowledge, which evaluation binding does not provide) is also required. This is not folklore-obvious and should not carry the ’— standard’ label.
• Conclusion ‘succinct NIZK for NP’ spans two wiki objects ([[non-interactive-zero-knowledge]] and [[succinct-argument]]) and is not wikilinked at all.