Abstract: As of Hierarchical Identity Based Encryption (HIBE) systems, there are two important tasks should be accomplished properly, the first one is to establish logically hierarchical relationship between entities in the hierarchy tree, which is essentially accomplished through private key derivation by delegating responsibilities to lower-level PKGs and the other task is to achieve encryption privacy of ciphertext targeting an intended recipient. In this study, mechanisms of private key derivation in HIBE systems are classified, which explicitly define how and to what extent an entity in the hierarchy takes its level PKGs role of generating valid private keys for its descendants in the hierarchy. Moreover, a new delegation mechanism, authorized delegation is introduced, which can prevent any entity from deriving private keys for its descendants with use of its private key and delegate the responsibility of generating private keys for a specified entity through authorization by distributing a specific secret to an entity as an ancestor of the specified entity by the root PKG (primitive authorization) or some other authorized entities (chained authorization). As for encryption privacy of ciphertext in a HIBE system, which measures the possibility that ciphertexts targeting an entity are successfully decrypted by its ancestors or descendants, the encryption privacy is studied from two distinct perspectives, i.e., private key derivation perspective and private key legitimacy perspective. Furthermore, dominated encryption privacy and dedicated encryption privacy are defined and discussed from private key legitimacy perspective.