SNARK ⇒ NIZK

SNARK implies NIZK.

Statement

Migrated verbatim from non-interactive-zero-knowledge § zk-SNARK:

zk-SNARK

A Succinct Non-interactive ARgument of Knowledge (zk-SNARK) is a NIZK argument with the additional properties that:

  • The proof is short (polylogarithmic in the circuit size)
  • Verification is fast (polylogarithmic in the statement size)
  • The prover has knowledge soundness (a witness can be extracted)

See SNARKs for more detail.

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:

  • Definitional containment (a zk-SNARK is a NIZK argument with extra properties) rather than a stated reduction; recorded because it is a Variations-section ‘implies’.
  • No citation for the succinctness/knowledge-soundness properties listed.
  • SUSPECT: ‘Verification is fast (polylogarithmic in the statement size)’ - SNARK verification is polylogarithmic in the circuit/witness size but necessarily at least linear in the statement length. Report only; do not fix.