Certificateless encryption scheme secure in standard model

The scheme introduced by Hwang and Liu in 2008 is shown to be insecure against the key replacement attack. A more practical attack model is introduced, and according to this model, an efficient certificateless encryption scheme is presented which is IND-CCA secure against both Type I and Type II attackers without random oracle. This encryption scheme can defend against the malicious key generation center attack, and can reach Girault's trusted level 3 as in traditional public key infrastructure-based cryptography. This certificateless encryption scheme has a shorter public key than other schemes in the standard model.