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.