  We consider a man-in-the-middle attack on two-way quantum key distribution
ping-pong and LM05 protocols in which an eavesdropper copies all messages in
the message mode, while being undetectable in the mode. Under the attack there
is therefore no disturbance in the message mode and the mutual information
between the sender and the receiver is always constant and equal to one and
messages copied by the eavesdropper are always genuine. An attack can only be
detected in the control mode but the level of detection at which the protocol
should be aborted is not defined. We examine steps of the protocol to evaluate
its security and find that the protocol should be redesigned. We also compare
it with the security of a one-way asymmetric BB84-like protocol in which one
basis serves as the message mode and the other as the control mode but which
does have the level of detection at which the protocol should be aborted
defined.
