Survey on certificateless public key cryptography

In the notion of traditional public key infrastructure (PKI), we need to deliver public keys in an authentic way. More precisely, digital certificate binds a public key with the identity of its owner. However, significant overhead is associated with managing digital certificates. For this reason, the new notion called "identity-based public key cryptography" (ID-PKC) in which bitstring of user identity (could be name, email addresses, etc) is directly being the public key. The private key generator (PKG) is responsible for creating users private keys according to their public keys (identities). As a result, the need of certificates is eliminated because the authenticity of the public key is highly achieved. On the other hand, key escrow issue exists since PKG is able to find (calculate) any user?s private key. Can you imagine what a malicious or compromised PKG can do? In order to overcome this issue a new paradigm which is certificateless public key cryptography (CL-PKC) is introduced in which the private key is partially determined by the key generating centre (KGC). In this paper we study the first CL-PKC scheme which is proposed by Al-Riyami and Paterson.