Certificateless cryptography combines the best of traditional public-key cryptography and the ID-based paradigm. There is no need to get and verify certificates, and the secret keys are not under the key generation center (KGC)'s escrow.

This chapter focuses on giving a complete survey of secure certificateless encryption (CLE) schemes in the literature. In particular, we discuss the techniques behind addressing special security concerns in certificateless paradigm, which include key replacement attack, decryption capabilities for arbitrary public keys (as considered in strongly-secure CLE), partial decryption capabilities (as considered in security-mediated certificateless encryption, or SMCLE) and malicious KGC attack. We also examine some less obvious efficiency issues, in which we compare specific CLE constructions with the normal public key encryption approach.