  Recently, a "counterfactual" quantum key distribution scheme was proposed by
Tae-Gon Noh [1]. In this scheme, two legitimate distant peers may share secret
keys even when the information carriers are not traveled in the quantum
channel. We find that this protocol is equivalent to an entanglement
distillation protocol (EDP). According to this equivalence, a strict security
proof and the asymptotic key bit rate are both obtained when perfect single
photon source is applied and Trojan-horse attack can be detected. We also find
that the security of this scheme is deeply related with not only the bit error
rate but also the yields of photons. And our security proof may shed light on
security of other two-way protocols.
