Certificateless cryptography (CL-PKC) is a concept that aims at enjoying the advantages of identity based cryptography without suffering from its inherent key escrow. Several methods were recently suggested to generically construct a certificateless encryption (CLE) scheme by combining identity based schemes with ordinary public key cryptosystems. Whilst the security of one of these generic compositions was proved in a relaxed security model, we show that all them are insecure against chosen-ciphertext attacks in the strongest model of Al-Riyami and Paterson. We show how to easily fix these problems and give a method to achieve generic CLE constructions which are provably CCA-secure in the random oracle model. We finally propose a new efficient pairing-based scheme that performs better than previous proposals without precomputation. We also prove its security in the random oracle model.
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