BDH ⇒ AC

BDH implies AC.

Statement

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

BDDH → short signatures (Boneh-Lynn-Shacham BLS), VRFs, and anonymous credential schemes — standard

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:

anonymous-credentials has no wiki page; identifier invented.
Uncited; ’- standard’ misapplied.
Pairing-based anonymous credentials rest on q-type / LRSW-style assumptions rather than BDDH, so the hypothesis is doubtful (recorded, not fixed).
Three conclusions bundled (BLS signatures, VRFs, anonymous credentials) — must be split.
SUSPECTED MATHEMATICAL ERROR: BLS short signatures are proved under (co-)CDH / gap-DH in pairing groups, not under decisional BDH; a decisional assumption is the wrong hypothesis for an unforgeability result.
Marked standard where BLS01 and the VRF literature are attributable.
verifiable-random-function and anonymous-credentials have no pages.