ABE ⇒ BE

ABE implies BE.

Statement

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

• ABE (CP-ABE) subsumes BE: set-membership policies $f^{\ast }(x)=[x\in S^{\ast }]$ are a special case of monotone DNF

Migrated verbatim from broadcast-encryption § Other results:

• BE is a special case of CP-ABE with set-membership policies: the access policy $f^{\ast }(x)=[x\in S^{\ast }]$ is a monotone DNF 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.
• Duplicated on content/Primitives/broadcast-encryption.md line 80 (same edge asserted from the other side).
• The reduction is syntactic only: generic CP-ABE gives ciphertexts of size proportional to the policy, i.e. $\Omega (|S^{\ast }|)$, which defeats the succinctness that motivates BE. The bullet does not note this.
• Duplicate of content/Primitives/attribute-based-encryption.md line 171 — same edge stated on both endpoints’ pages.
• Surface phrasing ‘BE is a special case of CP-ABE’ reverses the implication direction relative to the arrow (CP-ABE ⇒ BE); a naive migration would get the direction backwards.