As an intermediate model between conventional PKC and ID-PKC CL-PKC can avoid the heavy overhead of certificate management in traditional PKC as well as the key escrow problem in ID-PKC altogether. Since the introduction of CL-PKC many concrete constructions security models and applications have been proposed during the last decade. Differing from the other books on the market this one provides rigorous treatment of CL-PKC. Definitions precise assumptions and rigorous proofs of security are provided in a manner that makes them easy to understand.