Two protocols of quantum direct communication with authentication [Phys. Rev. A 73 (2006) 042305] were recently indicated to be insecure against the authenticator Trent attacks [Phys. Rev. A 75 (2007) 026301]. We present two efficient protocols by using four Pauli operations, which are secure against inner Trent attacks as well as outer Eve attacks. Finally, we generalize them to multiparty quantum direction communication.