BDH ⇒ HVE
Statement
Migrated verbatim from hidden-vector-encryption § Other results:
- BW07 introduced HVE and gave constructions for conjunctive, subset, and range queries, proved attribute-hiding under the decisional bilinear Diffie-Hellman and decisional linear assumptions — BW07
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:
- GENUINELY CONJUNCTIVE: {decisional bilinear Diffie-Hellman, decisional linear} together. But both map to the single page content/Assumptions/bilinear-map-assumptions.md (aliases BDDH and DLIN), so the conjunction collapses to one hypothesis node in the current wiki.
- SURPRISING WIKILINK TARGET: the filename ‘BW07 - Conjunctive Normal Form Encryption and Attribute Based Encryption’ does not match the paper — that reference page’s own H1 and BibTeX give ‘Conjunctive, Subset, and Range Queries on Encrypted Data’ (Boneh-Waters, TCC 2007, eprint 2006/465).
- Neither assumption is wikilinked.
- REPAIR PATCH: Arity sweep. Wiki L104: ”… proved attribute-hiding under the decisional bilinear Diffie-Hellman and decisional linear assumptions —
[[BW07]]”. GENUINE CONJUNCTION: BW07 needs both assumptions together; “and” here joins two assumptions used in one proof, not two alternative constructions. The extractor collapsed both onto the single page slug bilinear-map-assumptions, leaving arity 1 with conjunctive:true. Repair: hypotheses [“bddh”,“dlin”], conjunctive:true — both strings are declared aliases in the frontmatter of content/Assumptions/bilinear-map-assumptions.md (lines 5 and 7), so neither slug is invented. Recorded: both aliases currently resolve to the SAME page, so until DBDH and DLIN get separate nodes this conjunction has two parallel edges to one node.