Submission 5: A sufficient condition for key-privacy

The notion of key privacy for encryption schemes was defined formally by Bellare, Boldyreva, Desai and Pointcheval in Asiacrypt 2001. This notion seems useful in settings where anonymity is important. In this short note we describe a (very simple) sufficient condition for key privacy. In a nutshell, a scheme that provides data privacy is guaranteed to provide also key privacy if the distribution of a *random encryption of a random message* is independent of the public key that is used for the encryption.