BDH ⇒ ABE
Statement
Migrated verbatim from attribute-based-encryption § Other results:
- GPSW06 introduced KP-ABE and gave the first construction for monotone formulas, proving selective security under DBDH — GPSW06
Migrated verbatim from attribute-based-encryption § Other results:
- Wat11 gave the first CP-ABE with a standard-model proof of selective security under DBDH — Wat11
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.
This relation is stated on 3 pages; the statements above are all of them.
Citations disagree across pages: [object Object]
Recorded during migration and not fixed — these are claims about the source text, not changes to it:
- DBDH is named in bare prose with no wikilink; the assumption lives on content/Assumptions/bilinear-map-assumptions.md, whose aliases include ‘BDDH’ but NOT ‘DBDH’, so the obvious wikilink would not resolve.
- Conclusion is selectively secure KP-ABE, not full ABE — the security notion is part of the conclusion and has no node in the model.
- SURPRISING WIKILINK TARGET: the reference filename says ‘Ciphertext-Policy Attribute-Based Encryption from Subset Cover’, but that reference page’s own H1 and BibTeX title the paper ‘Ciphertext-Policy Attribute-Based Encryption: An Expressive, Efficient, and Provably Secure Realization’ (PKC 2011, eprint 2008/290). The filename appears to be wrong.
- DBDH named in bare prose with no wikilink (see line 173).
- SUSPECTED OVER-ATTRIBUTION (reported, not corrected): Wat09’s title and results cover IBE and HIBE; adaptively secure ABE via dual system encryption is Lewko-Okamoto-Sahai-Takashima-Waters 2010, which has no reference page. The bullet attaches ABE to the wrong citation.
- Same umbrella-hypothesis problem as the other two sub-edges.
- 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.