Fuzzy IBE ⇒ IBE

Fully-black-box reduction · standard model · folklore · security loss: tight (the IBE adversary is forwarded unchanged)

Statement

A Fuzzy IBE scheme (SW05) over attribute universe $\mathcal{U}$ with threshold $t=1$, restricted to singleton attribute sets, is an IBE scheme with identity space $\mathcal{U}$: a key for $\omega =\{id\}$ decrypts a ciphertext for ${\omega }^{\prime }=\{{id}^{\prime }\}$ iff $id={id}^{\prime }$. If the Fuzzy IBE is IND-FIBE-CPA-secure, the IBE is IND-ID-CPA-secure with the same advantage — folklore.

Sketch

Every IBE adversary is, unchanged, a Fuzzy IBE adversary: its key queries for identities $id\ne {id}^{\ast }$ are singletons with $|\{id\}\cap \{{id}^{\ast }\}|=0<t$, so IBE admissibility is Fuzzy IBE admissibility.