We consider user conditional privacy preservation in the context of public key encryption. Unlike the full privacy preservation, our conditional one ensures that the message sender’s as well as the intended receiver’s privacy are well preserved while their legitimation can still be verified; besides, the actual sender of an encrypted message can only be identified by the intended receiver. Furthermore, considering the practical scenario where the communication channels between some senders and receivers are controlled with a blacklist (BL), we address the issue how a message sender proves the legitimation of the communication channel with its intended communicator according to the BL. Previous works only partially solve the former problem and there exists no solution addressing the two aforementioned problems simultaneously. In this paper, we present an encryption scheme which keeps not only the transmitted message confidential but also the user’s conditional privacy preserved. Besides, given the BL, our scheme also empowers the message sender the capability to give a proof of the legitimation of the communication channel with its communication partner without leaking their identities. In other words, only message senders form unblocked communication channels are able to produce such a proof. We provide the security models for our scheme and prove its security under the random oracle model.