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 particles. 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.