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 using 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.
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