High Efficiency of Two Efficient QSDC with Authentication Is at the Cost of Their Security

Two efficient protocols of quantum secure direct communication with authentication Chin. Phys. Lett. 25(2008) 2354 were recently proposed by Liu et al. to improve the efficiency of two protocols presented in Phys. Rev. A 75(2007)026301 by four Pauli operations. We show that the high efficiency of the two protocols is at the expense of their security. The authenticator Trent can reach half the secret by a particular attack strategy in the first protocol. In the second protocol, not only Trent but also an eavesdropper outside can elicit half-information about the secret from the public declaration.