Certificate-based encryption (CBE) and certificateless encryption (CLE) are proposed to lessen the certificate management problem in a traditional public-key encryption setting. Although they are two different notions, CBE and CLE are closely related and possess several common features. The encryption in CBE and CLE does not require authenticity verification of the recipient's public key. The decryption in both notions requires two secrets that are generated by the third party and the public key owner, respectively. Recently a generic conversion from CLE to CBE was given, but unfortunately its security proof is flawed. This paper provides an elaborate security model of CBE, based on which a provably secure generic construction of CBE from CLE is proposed. A concrete instantiation is also presented to demonstrate the application of our generic construction. © 2012 The Author 2012. Published by Oxford University Press on behalf of The British Computer Society. All rights reserved.