ABE ⇒ Fuzzy IBE

ABE implies Fuzzy IBE.

Statement

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

• ABE (KP-ABE) generalizes Fuzzy IBE: threshold-$t$ overlap policies are monotone formulas

Migrated verbatim from fuzzy-identity-based-encryption § Other results:

• Fuzzy IBE is subsumed by KP-ABE: a threshold-$t$ formula over $|\mathcal{U}|$ attributes is expressible as a monotone Boolean formula

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.

This relation is stated on 2 pages; the statements above are all of them.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

• No citation (the natural one is SW05/GPSW06); not flagged as folklore per house style.
• Duplicated on content/Primitives/fuzzy-identity-based-encryption.md line 80 (‘Fuzzy IBE is subsumed by KP-ABE’) — the two pages assert the same edge and should merge to one relation.
• Threshold-$t$ over a universe of size $u$ has monotone formula size polynomial in $u$ only for small universes; the one-line justification hides that.
• No citation.
• Duplicate of content/Primitives/attribute-based-encryption.md line 169 (same edge stated from the other endpoint).
• ‘is subsumed by’ reverses the arrow relative to word order (ABE ⇒ FIBE).