Hash function + PRF ⇒ Symmetric CP-ABE

Hash function together with PRF implies Symmetric CP-ABE.

Statement

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

• Symmetric CP-ABE, where also the encryptor must hold attributes satisfying the ciphertext policy, admits an IND-CCA2-secure open-universe construction from collision-resistant hash functions and a $\mathsf{PRF}$, with no bilinear map or lattice hardness assumption — LS26

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: {collision-resistant hash function, PRF} ⇒ symmetric CP-ABE. Must not be split into two separate single-hypothesis reductions.
• The conjunction is arguably redundant (CRHF ⇒ OWF ⇒ PRF), so a normalizing migration might collapse it; recorded as stated.
• ‘collision-resistant hash functions’ is bare prose — [[hash-function]] (which carries the CRH alias) is not wikilinked.
• Conclusion ‘symmetric-cp-abe’ has no slug; it is defined only in the ’## Symmetric CP-ABE’ Variations section of this page.