Bilinear pairing ⇒ SNARK

Bilinear pairing implies SNARK.

Statement

Migrated verbatim from succinct-argument § zk-SNARK:

A SNARK with zero-knowledge. The verifier learns nothing about the witness beyond the validity of the statement. Groth16 is the canonical pairing-based zk-SNARK with constant proof size (3 group elements) and millisecond verification — Gro16.

Notes

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• The hypothesis is only implicit (‘pairing-based’); the actual assumption is stated elsewhere on the page as knowledge-of-exponent (line 89) or the generic/algebraic group model (line 95). As written the hyperedge has no assumption.
• INTERNAL INCONSISTENCY: this line says ‘3 group elements’ while line 89 says ‘3 ${\mathbb{G}}_1$ elements + 1 ${\mathbb{G}}_2$ element’ (= 4). Groth16 proofs are 2 ${\mathbb{G}}_1$ + 1 ${\mathbb{G}}_2$ = 3 elements, so line 89 appears to be the erroneous one. Reported, not fixed.
• ‘pairings’ resolves to a Glossary page, not an assumption page — a hypothesis slot filled by a glossary entry.