A supplement to Liu et al.'s certificateless signcryption scheme in the standard model

Recently, Liu et al. proposed the first certificateless signcryption scheme without random oracles and proved it was semantically secure in the standard model. However, Selvi et al. launched a fatal attack to its confidentiality by replacing users’ public keys, thus pointed out this scheme actually doesn’t reach the semantic security as claimed. In this paper, we come up with a rescue scheme based on Liu et al.’s original proposal. A Schnorr-based onetime signature is added to each user’s public key, which is used to resist Selvi et al.’s attack. In addition, according to the mistake made in Liu et al.’s security proof, we also show that our improvement is really secure in the standard model under the intractability of the decisional bilinear DiffieHellman assumption.