We consider public key encryption (PKE) schemes with auxiliary input, that is, the adversary is given any computationally uninvertible function of the secret key. Previous result only achieves security under chosen-plaintext attacks (CPA). In this paper, we construct public key encryption schemes that are secure under chosen-ciphertext attacks even when the adversary is given any computationally uninvertible function of the secret key as an auxiliary input. We follow the Naor–Yung ‘double encryption’ paradigm and generally transform any chosen-plaintext attack secure public key encryption into a chosen-ciphertext attack secure one in the auxiliary input model. Copyright © 2012 John Wiley & Sons, Ltd.