BDH ⇒ NIZK

Statement

Migrated verbatim from bilinear-map-assumptions § Known Results:

DLIN (Decision Linear) assumption: a generalization of BDDH; more conservative and used in e.g. Groth-Sahai proofs — standard

Migrated verbatim from non-interactive-zero-knowledge § Other results:

Pairing-based NIZK (Groth-Sahai proofs, Groth16) achieves constant or logarithmic proof size — Gro16

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

This relation is stated on 2 pages; the statements above are all of them.

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

Groth-Sahai proofs marked standard; GS08 is attributable and missing.
Conclusion typed as NIZK; Groth-Sahai is specifically a NIZK proof system for pairing-product equations in the CRS model.
Two constructions bundled (Groth-Sahai proofs and Groth16) under a single Gro16 citation; Groth-Sahai (GS08) is uncited and has no reference page.
The hypothesis (‘pairing-based’) is not a named assumption; Groth16 additionally needs a knowledge-of-exponent-style assumption or the generic/algebraic group model, which is not stated - arguably model should be generic-group.
SUSPECT: Groth-Sahai proofs are not constant-size in general (they are constant per equation, linear in the number of equations). Report only.