BDH ⇒ HIBE

BDH implies HIBE.

Statement

Migrated verbatim from attribute-based-encryption § Other results:

• The dual system encryption technique of Wat09 gives adaptively secure IBE, HIBE, and ABE under simple pairing-based assumptions — Wat09

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:

• Same umbrella-hypothesis problem as the IBE sub-edge.
• HIBE is not wikilinked on this bullet although the page exists.
• Multi-conclusion bullet (IBE, HIBE, ABE) rather than a chain — must still be split into three reductions, one per conclusion. ‘isComposite’ is used here in that sense.
• ‘simple pairing-based assumptions’ is vague and unlinked (Wat09 uses decisional bilinear Diffie-Hellman and decisional linear); the hypothesis cannot be pinned to a specific assumption node.
• IBE and HIBE targets are not wikilinked on this bullet even though both pages exist.