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