Anonymous HIBE ⇒ HIBE

Fully-black-box reduction · standard model · folklore

Statement

Every anonymous HIBE is itself a HIBE: anonymity requires ciphertexts to hide the recipient identity vector $\overrightarrow{id}$ in addition to the payload — folklore.

Sketch

The construction is the identity; a HIBE adversary is forwarded unchanged to the anonymous HIBE game, whose payload-indistinguishability requirement it breaks with the same advantage.