DLOG ⇒ DDH

DLOG implies DDH.

Statement

Migrated verbatim from algebraic-group-model § Key Results:

• DDH ${\le }_{\mathrm{AGM}}$ DLOG: DDH reduces tightly to DLOG in the AGM.

Notes

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:

• SUSPECTED MATHEMATICAL / ATTRIBUTION ERROR (reported, not fixed): AGM reductions work by extracting a representation from the group elements an adversary outputs. A DDH distinguisher outputs only a bit, so the standard AGM extraction does not apply, and ‘DDH reduces tightly to DLOG in the AGM’ is not a straightforward FKL18 result. This is precisely the kind of AGM claim KZ22 (cited at line 43 of this same page) argues does not go through. Verify against FKL18 before migrating.
• The direction of '${\le }_{\mathrm{AGM}}$' is ambiguous: read as ‘DDH reduces to DLOG’ the hypothesis is DLOG hardness and the conclusion DDH hardness, but the bullet does not say which object is assumed hard.
• No citation on the bullet; inherited from the line 28 lead-in.