SXDH (Symmetric External Diffie-Hellman) ⇒ BDH

SXDH (Symmetric External Diffie-Hellman) implies BDH.

Statement

Migrated verbatim from bilinear-map-assumptions:

Assumes DDH is hard in both ${\mathbb{G}}_1$ and ${\mathbb{G}}_2$ of an asymmetric pairing. Stronger than BDDH; used for efficiently instantiating Groth-Sahai proofs.

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:

• Stronger than BDDH is the only statement of direction; no citation.
• SUSPECTED IMPRECISION: SXDH is stated for asymmetric (Type 3) pairings whereas BDDH is stated on this page for symmetric pairings, so the two are not directly comparable.