Security proof of counterfactual quantum cryptography against general intercept-resend attacks and its vulnerability

Counterfactual quantum cryptography, recently proposed by Noh, is featured with no transmission of signal parti- cles. This exhibits evident security advantages, such as its immunity to the well-known photon-number-splitting attack. In this paper, the theoretical security of counterfactual quantum cryptography protocol against the general intercept- resend attacks is proved by bounding the information of an eavesdropper Eve more tightly than in Yin＇s proposal [Phys. Rev. A 82 042335 （2010）]. It is also shown that practical counterfactual quantum cryptography implementations may be vulnerable when equipped with imperfect apparatuses, by proving that a negative key rate can be achieved when Eve launches a time-shift attack based on imperfect detector efficiency.