The paper presents a Hierarchical Identity Based Encryption (HIBE) system where the ciphertext consists of just three group elements, and decryption requires only two bilinear map computations, regardless of the hierarchy depth. The system is efficient and secure, with selective-ID security proven in the standard model and full security in the random oracle model. Key applications include forward secure public key and identity-based cryptosystems, efficient public key broadcast systems, and mechanisms for encrypting to the future. The system supports limited delegation, allowing users to be given restricted private keys that only allow delegation to bounded depth. The authors also discuss extensions, such as sublinear size private keys at the cost of some ciphertext expansion.The paper presents a Hierarchical Identity Based Encryption (HIBE) system where the ciphertext consists of just three group elements, and decryption requires only two bilinear map computations, regardless of the hierarchy depth. The system is efficient and secure, with selective-ID security proven in the standard model and full security in the random oracle model. Key applications include forward secure public key and identity-based cryptosystems, efficient public key broadcast systems, and mechanisms for encrypting to the future. The system supports limited delegation, allowing users to be given restricted private keys that only allow delegation to bounded depth. The authors also discuss extensions, such as sublinear size private keys at the cost of some ciphertext expansion.