CDH ⇒ BDH

CDH implies BDH.

Statement

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

  • BDH is implied by CDH in the generic group model, but no standard-model reduction is known

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:

  • No citation.
  • SUSPECTED ERROR: hardness of BDH in the generic (bilinear) group model is an unconditional lower bound, not a reduction from CDH.
  • Direction looks reversed: BDH hardness is normally seen to imply CDH hardness, since an algorithm for CDH in the pairing group breaks BDH.