Eavesdropping on counterfactual quantum key distribution with finite resources

A striking scheme called “counterfactual quantum cryptography” gives a conceptually new approach to accomplish the task of key distribution. It allows two legitimate parties to share a secret even though a particle carrying secret information is not, in fact, transmitted through the quantum channel. Since an eavesdropper cannot directly access the entire quantum system of each signal particle, the protocol seems to provide practical security advantages. However, here we propose an eavesdropping method which works on the scheme in a finite key scenario. We show that, for practical systems only generating a finite number of keys, the eavesdropping can obtain all of the secret information without being detected. We also present a improved protocol as a countermeasure against this attack.

Figure 1

Configuration of the counterfactual QKD scheme in the absence of Eve. S, single photon source; C, optical circulator; BS, beam splitter; OD, optical delay line; FM, Faraday mirror; PBS, polarization beam splitter; SW, optical switch; OL, optical loop; ${\mathrm{D}}_0$,${\mathrm{D}}_1$,${\mathrm{D}}_2$, detectors.

Figure 2

Principle of the proposed attack scheme. S, single photon source; C, optical circulator; ${\mathrm{BS}}_1$, ${\mathrm{BS}}_{{\text{E}}_i}(i=0,1,...,n)$, beam splitters; OD, ${\mathrm{OD}}_E$, optical delay lines; ${\mathrm{PM}}_{\text{E}}$, phase modulator; FM, Faraday mirror; PBS, polarization beam splitter; SW, optical switch; OL, optical loop; ${\text{D}}_0,{\text{D}}_1,{\text{D}}_2,{\text{D}}_{{\text{E}}_i}(i=0,1,...,n)$, detectors.

Figure 3

Schematic of the simplified eavesdropping scheme. S, single photon source; C, optical circulator; ${\mathrm{BS}}_1,{\text{BS}}_{{\text{E}}_0},{\text{BS}}_{{\text{E}}_1}$, beam splitters; OD,${\mathrm{OD}}_{\text{E}}$, optical delay lines; ${\mathrm{PM}}_{\text{E}}$, phase modulator; FM, Faraday mirror; PBS, polarization beam splitter; SW, optical switch; OL, optical loop; ${\mathrm{D}}_0,{\text{D}}_1,{\text{D}}_2,{\text{D}}_{{\text{E}}_0},{\text{D}}_{{\text{E}}_1}$, detectors.

Figure 4

Probability of Eve being revealed as a function of the raw key length; parameters used: $n=1\times {10}^8$ and $r_{{\text{E}}_c}=1\times {10}^{-2}$. The six curves correspond to six different values of $r_{{\text{E}}_0}$.

Figure 5

Configuration of the improved counterfactual QKD scheme. SPR, switchable polarization rotator; S, single photon source; C, optical circulator; BS, beam splitter; OD, optical delay line; FM, Faraday mirror; PBS, polarization beam splitter; SW, optical switch; OL, optical loop; ${\mathrm{D}}_0,{\text{D}}_1,{\text{D}}_2$, detectors.