-Linear assumption ⇒ ABE
[[bilinear-map-assumptions#k-linear-assumption|-Linear assumption]] implies ABE.
Statement
Migrated verbatim from attribute-based-encryption § Other results:
- RW13 gives large-universe KP-ABE and CP-ABE constructions for any monotone formula under variants of the -linear assumption — RW13
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:
- ‘variants of the -linear assumption’ is vague — ‘variants of’ cannot be typed as a hypothesis node.
- k-Lin has no page of its own: content/Assumptions/decisional-diffie-hellman.md has a ’## k-Lin’ section that is a bare TODO, and content/Assumptions/bilinear-map-assumptions.md discusses k-Lin/DLIN. Nothing is wikilinked here.
- Two conclusions (KP-ABE and CP-ABE) collapse into one slug because both are aliases of attribute-based-encryption.