Zhen (University of Electronic Science and Technology of China, Chengdu, Sichuan, People’s Republic of China) Qin & Athanasios V. (Lulea University of Technology, Sweden) Vasilakos 
Introduction to Certificateless Cryptography [PDF ebook] 

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.