Arithmetization + NIZK + PCS ⇒ SNARK

Arithmetization together with NIZK together with PCS implies SNARK.

Statement

Migrated verbatim from succinct-argument § Other results:

• NIZK proofs can be made succinct using polynomial commitments and arithmetization — 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:

• Genuinely conjunctive (three hypotheses together), but the claim is vague: ‘can be made succinct’ does not name a theorem, and the folklore label ’— standard’ covers a construction that is not really folklore.
• Overlaps with line 94, which states the same two-step recipe with the NIZK hypothesis dropped — the page gives two incompatible ingredient lists for the same construction.