Certificateless cryptography is a variant of ID-based cryptography intended to prevent the key escrow problem. Ordinarily, keys are generated by a certificate authority or a key generation center (KGC) who is given complete power and is implicitly trusted. To prevent a complete breakdown of the system in the case of a compromised KGC, the key generation process is split between the KGC and the user. The KGC first generates a key pair, where the private key is now the partial private key of the system. The remainder of the key is a random value generated by the user, and is never revealed to anyone, not even the KGC. All cryptographic operations by the user are performed by using a complete private key which involves both the KGC's partial key, and the user's random secret value. One disadvantage of this is that the identity information no longer forms the entire public key.
To encrypt a message to another user, three pieces of information are needed: 1) the other user's public key and 2) identity, and also 3) the third party's public information. To decrypt, a user just needs to use their private key.
For tight security, a certificateless system has to prove its security against two types of adversaries. Type 1 Adversary- Refers to any third party who can fake the user's public keys, corresponding to the user's random secret value. Type 2 Adversary- Refers to a compromised or malicious KGC, who has access to the partial public and private keys of all users.