Further observations on certificateless public key encryption

Certificateless public key encryption can be classi.ed into two types, namely, CLE and CLE†, both of which were introduced by Al-Riyami and Paterson in Asiacrypt 2003. Most works about certicateless public key encryption belong to CLE, where the partial secret key is uniquely determined by an entity's identity. In CLE†, an entity's partial secret key is not only determined by the identity information but also by his/her (partial) public key. Such techniques can enhance the resilience of certificateless public key encryption against a cheating KGC. In this paper, we .rst formalize the security de.nitions of CLE†. After that, we demonstrate the gap between the security model of CLE† and CLE, by showing the insecurity of a CLE† scheme proposed by Lai and Kou in PKC 2007. We give an attack that can successfully break the indistinguishability of their CLE† scheme, although their scheme can be proved secure in the security model of CLE. Therefore, it does not su.ce to consider the security of CLE† in the security model of CLE. Finally, we show how to secure Lai-Kou's scheme by providing a new scheme with the security proof in the model of CLE†.