Is it possible to have CBE from CL-PKE?

Abstract

Recently, Al-Riyami and Paterson proposed a generic conversion from CL-PKE (Certificateless Public Key Encryption) to CBE (Certificate Based Encryption) and claimed that the derived CBE scheme is secure and even more efficient than the original scheme of Gentry. In this paper, we show that their conversion is wrong due to the flaw of the security proof. It leads the new concrete CBE scheme by Al-Riyami and Paterson to be invalidated. In addition, our result supports the impossibility to relate both notions in any directions.