On-Line Authenticated Encryption (OAE) combines confidentiality with data integrity and is on-line computable. Most block cipher-based schemes for Authenticated Encryption can be run online and are provably secure against nonce-respecting adversaries. But they fail badly for more general adversaries. This is not a theoretical observation only – in practice, the reuse of nonces is a frequent issue1 . In recent years, cryptographers developed misuse-resistant schemes for Authenticated Encryption. These guarantee excellent security even against general adversaries which are allowed to reuse nonces. Their disadvantage is that encryption can be performed in an off-line way, only. This paper considers OAE schemes dealing both with nonce-respecting and with general adversaries. It introduces McOE, an efficient design for OAE schemes. The construction is based on a ’simple’ block cipher and is on-line computable. It provably guarantees reasonable security against general adversaries as...