  Two-way Gaussian protocols have the potential to increase quantum key
distribution (QKD) protocols' secret-key rates by orders of
magnitudes~[Phys.~Rev.~A {\bf 94}, 012322 (2016)]. Security proofs for two-way
protocols, however, are underdeveloped at present. In this paper, we establish
a security proof framework for the general coherent attack on two-way Gaussian
protocols in the asymptotic regime. We first prove that coherent-attack
security can be reduced to collective-attack security for all two-way QKD
protocols. Next, we identify two different constraints that each provide
intrusion parameters which bound an eavesdropper's coherent-attack information
gain for any two-way Gaussian QKD protocol. Finally, we apply our results to
two such protocols.
