ABSTRACT
This chapter provides the details of the hierarchical identity based encryption (HIBE). It presents the preliminaries starting from the general construction of HIBE and discusses the generic group model. HIBE allows a root PKG to distribute the workload by delegating private key generation and identity authentication to lower-level PKGs. Decryption works only when the tag values of the ciphertext and decrypting key are unequal. If the simulator attempted to test semi-functionality of key for itself by creating a semi-functional ciphertext for the same identity, it would only be able to create one with an equal tag, and hence decryption would unconditionally fail. A variant of semi-functional keys introduced is called nominally semi-functional keys. In such case, when a nominally semi-functional key is used to decrypt a semi-functional ciphertext, the interaction of the two semifunctional components results in cancelation and decryption is successful.
