  We analyze the security of the two-way continuous-variable quantum key
distribution protocol in reverse reconciliation against general two-mode
attacks, which represent all accessible attacks at fixed channel parameters.
Rather than against one specific attack model, the expression of secret key
rates of the two-way protocol are derived against all accessible attack models.
It is found that there is an optimal two-mode attack to minimize the
performance of the protocol in terms of both secret key rates and maximal
transmission distances. We identify the optimal two-mode attack, give the
specific attack model of the optimal two-mode attack and show the performance
of the two-way protocol against the optimal two-mode attack. Even under the
optimal two-mode attack, the performances of two-way protocol are still better
than the corresponding one-way protocol, which shows the advantage of making a
double use of the quantum channel and the potential of long-distance secure
communication using two-way protocol.
