This paper addresses the security of authenticated encryption schemes in the public key setting. We present two new notions of authenticity that are stronger than the integrity notions given in the symmetric setting \cite{bn00}. We also show that chosen-ciphertext attack security (IND-CCA) in the public key setting is not obtained in general from the combination of chosen-plaintext security (IND-CPA) and integrity of ciphertext (INT-CTXT), which is in contrast to the results shown in the symm...