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