We provide a general framework for constructing identity-based and broadcast encryption systems. In particular, we construct a general encryption system called
from which many systems with a variety of properties follow. The ciphertext size in all these systems is independent of the number of users involved and is just three group elements. Private key size grows with the complexity of the system. One application of these results gives the first
system with short ciphertexts. Broadcast HIBE solves a natural problem having to do with identity-based encrypted email.