Abstract

The physical imperfections of quantum key distribution systems compromise their information-theoretic security. By exploiting the imperfections on the detection unit, an eavesdropper can launch various detector-control attacks to steal the secret key. Recently, in Optica 6, 1178 (2019) [CrossRef]   entitled “Robust countermeasure against detector control attack in a practical quantum key distribution system,” Qian et al. proposed a countermeasure using variable attenuators in the detection unit that was claimed to be effective against detector-control attacks with or without blinding light. We comment on this paper, disputing this countermeasure by showing that their assumptions for proving this effectiveness are unrealistic.

© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

The ideal model of quantum key distribution (QKD) protocol has been proved to be information-theoretically secure [1,2]. However, the implementation of a real-life QKD system shows some deviations from its ideal model, which can be exploited by an eavesdropper to steal the secret key. Studies for preventing such attacks play an important role in building highly reliable QKD communication links. In the recent paper [3], Qian et al. proposed a countermeasure that was claimed to be effective to any detector-control attack. Here we show that this countermeasure is unreliable in practice, because the assumptions behind their paper are not realizable in a real-life QKD system.

Qian et al. divide detector-control attacks into two kinds: a non-blinding detector-control attack and a blinding detector-control attack. In the attack without blinding, Eve intercepts the signals from Alice, measures them in a randomly chosen basis, and resends a trigger pulse encoded by her measurement result at the end of Bob’s gate signal when Bob’s avalanche photodiodes (APD) show superlinearity [4,5]. A full trigger pulse makes Bob’s APD corresponding to Eve’s measurement result click with a high probability ${P_f}$. Half-trigger pulses reach both of Bob’s APDs in the opposite basis and cause clicks only with low probability ${P_h}$. Thus, Eve steals almost all of the secret key by controlling Bob’s detection events. In the blinding detector-control attack, Eve injects bright light to Bob to blind his APDs and then uses a similar intercept-resend strategy to eavesdrop the information [6].

Qian et al. add a variable attenuator (VA) in front of each of Bob’s APDs. The attenuation value of each VA switches to 0 dB or 3 dB randomly. Bob monitors ${R_0}$, ${R_3}$, ${e_0}$, and ${e_3}$, which indicates the detection rate of an APD under 0 dB and 3 dB attenuation and quantum bit error rate (QBER) under 0 dB and 3 dB attenuation, respectively. An alarm is triggered if at least one of the following criteria fails:

$$1 \lt \frac{{{R_0}}}{{{R_3}}} \lt 2,$$
$$\{{e_0},{e_3}\} \lt 11\% .$$

Qian et al. proved that these criteria cannot be satisfied simultaneously under a non-blinding detector-control attack, which provides the reliability of their countermeasure. However, we find that three assumptions at the foundation of their proof are unrealistic.

The first assumption is that Eve always uses the intercept-resend strategy in each round of communication. However, a wiser Eve can just attack a portion of the rounds, while passing Alice’s photons in the rest of the rounds. It is an obvious fact that if the portion used by Eve is decreased to small enough, the monitored values will finally converge into a valid range. As can be seen from the simulation shown in Fig. 1, if Eve uses a lossless channel and passes 78% of Alice’s signals while launching a non-blinding detector-control attack in the rest of the rounds by trigger pulses of ${P_{f,0}} = 8\%$, ${P_{f,3}} = 4\%$, ${P_{h,0}} = 4\%$, and ${P_{h,3}} = 2\%$, then both Eqs. (1) and (2) are satisfied simultaneously. The experimental parameters we used in the simulation are the dark count rate ${Y_0} = 1.7 \times {10^{- 6}}$, the error rate of a detector ${e_{{\rm det}}} = 3.3\%$, the error rate of the background ${e_0} = 0.5$, the transmittance in Bob’s side ${\eta _{{\rm Bob}}} = 0.1$, and the channel transmittance ${t_{{AB}}}{= 10^{- \alpha l/10}}$, where $\alpha = 0.21\;{\rm dB}/{\rm km}$ is the loss coefficient of the quantum channel.

 

Fig. 1. (a) $\frac{{{R_0}}}{{{R_3}}}$, (b) $e_0^s$ and $e_3^s$ under a non-blinding detector-control attack versus the rate that Eve passes Alice’s photons without any intervention. Eve uses a lossless channel to launch the partial attack. Eve uses trigger pulses of ${P_{f,0}} = 8\%$, ${P_{f,3}} = 4\%$, ${P_{h,0}} = 4\%$, and ${P_{h,3}} = 2\%$. The green region indicates the valid range of the monitored parameter. The dotted lines indicate that $\frac{{{R_0}}}{{{R_3}}}$ is in valid range with a pass rate of approximately 0%, while QBER is in the valid range with a pass rate of 78%.

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Moreover, to keep the total gain matching to the expected value of the original normal working QKD system to further hide her existence, Eve can add attenuation to the attacked channel. For example, given the lossy channel of the original QKD system is 8 km, Eve can just use the aforementioned partial attack with a 3 dB attenuator to maintain the original gain of the QKD system, and meanwhile the monitored values in Eqs. (1) and (2) also keep in their valid ranges. The lower bound of the real secure key rate under this attack can be evaluated by the following tailored Gottesman–Lo–Lutkenhaus–Preskill (GLLP) formula:

$$R_L^{{\rm attack}} = \frac{1}{2}p\{{e^{- u}}Y_1^{{\rm attack}}(1 - {H_2}(e_1^{{\rm attack}})) - {Q_\omega}{f_{{\rm EC}}}{H_2}({E_\omega})\} ,$$
where $u = 0.6$ is the average photon number of the signal state, $p = 78\%$ is the proportion of non-attacked communications, $Y_1^{{\rm attack}}/e_1^{{\rm attack}}$ is the contribution of the single photon to the gain/QBER, ${Q_\omega}/{E_\omega}$ is the gain/QBER during the communications according to Ref. [7], ${f_{{\rm EC}}} = 1.2$ is the error correction factor, and ${H_2}$ is the Shannon entropy function. Thus, $R_L^{{\rm attack}} = 0.0016$ bit/pulse, which is lower than the key rate without this attack, ${R_L} = 0.002$ bit/pulse, calculated by the original GLLP formula [8]. The simulation result shows that this partial attack indeed eavesdrops a certain amount of key in this example. Therefore, the analysis above indicates that this countermeasure is far from perfectly securing each bit.

The second assumption is ${P_{f,3}} = {P_{h,0}}$. Apparently, it holds for each APD individually. However, a detection efficiency mismatch between the two APDs is widely found in practical QKD systems [911]. Thus, the detection efficiencies of two APDs at the detection time window are unavoidably different as shown in Fig. 2. As a result, under a non-blinding detector-control attack, the triggering probability of a full trigger pulse on APD ‘${+}$’ with a 3 dB VA and that of a half-trigger pulse on APD ‘${-}$’ with a 0 dB VA might not be the same. That is, $P_{f,3}^ + \ne P_{h,0}^ -$, where the superscript represents the corresponding state of the APD. Thus, this assumption does not hold between two APDs. Furthermore, this fact is also confirmed in Ref. [3]. Qian et al. chose two different attacking positions (at the falling edge of 0.74 ns and 0.88 ns) for two APDs to make ${P_{f,3}} = {P_{h,0}}$ seem to hold between two APDs. This choice implies that, even in their experimental QKD system, the triggering probabilities of two APDs are not perfectly the same at a certain timing, and thus the assumption ${P_{f,3}} = {P_{h,0}}$ does not hold between two APDs. Any derived results based on this unrealistic assumption are not reliable. Therefore, the countermeasure proposed in Ref. [3] cannot warrant an unconditional security to a non-blinding detector-control attack. We believe this assumption should be extended to a more precise form, which can be written as

$$\begin{split} P_{f,0}^ + &\ge P_{f,3}^ + = P_{h,0}^ + \ge P_{h,3}^ +, \\ P_{f,0}^ - &\ge P_{f,3}^ - = P_{h,0}^ - \ge P_{h,3}^ -,\\ P_{f,0}^H &\ge P_{f,3}^H = P_{h,0}^H \ge P_{h,3}^H, \\ P_{f,0}^V &\ge P_{f,3}^V = P_{h,0}^V \ge P_{h,3}^V,\end{split}$$
and the effectiveness of their countermeasure should be reconsidered upon this assumption.
 

Fig. 2. Detection efficiency mismatch at the detection time window of Bob. As a 3 dB attenuator weakens a pulse of full power to half power, this detection efficiency mismatch directly implies the violation of the assumption ${P_{f,3}} = {P_{h,0}}$ between two detectors.

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The third assumption is that the attenuation value of a VA is perfectly binary in {0 dB, 3 dB} for each gate. However, according to Fig. 5 of Ref. [3], the switching of a VA’s attenuation value undergoes a rising edge or a falling edge, during which the attenuation value is in an intermediate value between 0 dB and 3 dB. Moreover, as can be seen from Fig. 5 of Ref. [3], these edges can be wider than a gate signal. Thus, for gate signals under these edges, the attenuation value is neither 0 dB nor 3 dB, which violates the third assumption. As the third assumption is also unrealistic, the security of their countermeasure based on this assumption may be compromised in practice.

For any blinding detector-control attack, Qian et al. claims that the aforementioned countermeasure is still effective. In Fig. 5 of Ref. [3], they show that the switching of a VA’s attenuation value leads to an abrupt change on the intensity of the continuous-wave (c.w.) blinding light arriving at the APD, which makes the output signal of the APD exceed the discrimination voltage and then causes a random click. These random clicks increase the QBER and yield of the QKD system significantly and trigger the alarm. However, a blinding detector-control attack cannot be restricted to be only a c.w. blinding attack. The pulse illumination attack proposed by Wu et al. in recent research is a more resilient blinding detector-control attack [12]. In this attack, Eve only injects groups of bright blinding pulses to Bob’s APDs. The first blinding pulse in each group causes a random click leading to a dead time, which has been considered in the hacking model in Ref. [12]. As the dead time covers the duration of the blinding-pulse group, random clicks caused by VA switching during this group are concealed. After the dead time, there is a blinded period due to the remaining photocurrent generated by the blinding-pulse group ahead, which is hackable for Eve. As no blinding light is injected to Bob during the blinded period, VA switching cannot introduce any random clicks during this time slot. Thus, the countermeasure proposed in Ref. [3] cannot hinder a carefully modulated pulse illumination attack. Therefore, strictly speaking, the countermeasure proposed by Qian et al. is not effective for all attacks with blinding light.

In conclusion, in Ref. [3], Eve is assumed to be too weak, and some significant practical factors of a QKD system have not been taken into consideration. Therefore, the security of their countermeasure under a tough detector-control attack is not guaranteed. We believe that the results shown in Ref. [3] should be rechecked under realistic assumptions, and a further experiment matching a real-life attacking scenario is needed to verify the effectiveness of their countermeasure.

Funding

National Natural Science Foundation of China (61901483, 11674397, 61601476, 61632021); National Key Research and Development Program of China (2019QY0702).

Disclosures

The authors declare that there are no competing interests.

REFERENCES

1. B. Zhao, B. Liu, C. Wu, W. Yu, and I. You, “A tutorial on quantum key distribution,” in 10th International Conference on Broadband and Wireless Computing, Communication and Applications (BWCCA) (2015), pp. 370–374.

2. B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016). [CrossRef]  

3. Y.-J. Qian, D.-Y. He, S. Wang, W. Chen, Z.-Q. Yin, G.-C. Guo, and Z.-F. Han, “Robust countermeasure against detector control attack in a practical quantum key distribution system,” Optica 6, 1178–1184 (2019). [CrossRef]  

4. L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011). [CrossRef]  

5. C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011). [CrossRef]  

6. L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4, 686–689 (2010). [CrossRef]  

7. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005). [CrossRef]  

8. D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Inf. Comput. 4, 325–360 (2004). [CrossRef]  

9. V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006). [CrossRef]  

10. V. Makarov, A. Anisimov, and J. Skaar, “Erratum: Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 78, 019905 (2008). [CrossRef]  

11. A. Huang, S. Sajeed, P. Chaiwongkhot, M. Soucarros, M. Legré, and V. Makarov, “Testing random-detector-efficiency countermeasure in a commercial system reveals a breakable unrealistic assumption,” IEEE J. Quantum Electron. 52, 1–11 (2016). [CrossRef]  

12. Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

References

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  1. B. Zhao, B. Liu, C. Wu, W. Yu, and I. You, “A tutorial on quantum key distribution,” in 10th International Conference on Broadband and Wireless Computing, Communication and Applications (BWCCA) (2015), pp. 370–374.
  2. B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016).
    [Crossref]
  3. Y.-J. Qian, D.-Y. He, S. Wang, W. Chen, Z.-Q. Yin, G.-C. Guo, and Z.-F. Han, “Robust countermeasure against detector control attack in a practical quantum key distribution system,” Optica 6, 1178–1184 (2019).
    [Crossref]
  4. L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
    [Crossref]
  5. C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
    [Crossref]
  6. L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4, 686–689 (2010).
    [Crossref]
  7. X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
    [Crossref]
  8. D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Inf. Comput. 4, 325–360 (2004).
    [Crossref]
  9. V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
    [Crossref]
  10. V. Makarov, A. Anisimov, and J. Skaar, “Erratum: Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 78, 019905 (2008).
    [Crossref]
  11. A. Huang, S. Sajeed, P. Chaiwongkhot, M. Soucarros, M. Legré, and V. Makarov, “Testing random-detector-efficiency countermeasure in a commercial system reveals a breakable unrealistic assumption,” IEEE J. Quantum Electron. 52, 1–11 (2016).
    [Crossref]
  12. Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

2019 (1)

2016 (2)

B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016).
[Crossref]

A. Huang, S. Sajeed, P. Chaiwongkhot, M. Soucarros, M. Legré, and V. Makarov, “Testing random-detector-efficiency countermeasure in a commercial system reveals a breakable unrealistic assumption,” IEEE J. Quantum Electron. 52, 1–11 (2016).
[Crossref]

2011 (2)

L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
[Crossref]

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
[Crossref]

2010 (1)

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4, 686–689 (2010).
[Crossref]

2008 (1)

V. Makarov, A. Anisimov, and J. Skaar, “Erratum: Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 78, 019905 (2008).
[Crossref]

2006 (1)

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
[Crossref]

2005 (1)

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

2004 (1)

D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Inf. Comput. 4, 325–360 (2004).
[Crossref]

Anisimov, A.

V. Makarov, A. Anisimov, and J. Skaar, “Erratum: Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 78, 019905 (2008).
[Crossref]

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
[Crossref]

Chaiwongkhot, P.

A. Huang, S. Sajeed, P. Chaiwongkhot, M. Soucarros, M. Legré, and V. Makarov, “Testing random-detector-efficiency countermeasure in a commercial system reveals a breakable unrealistic assumption,” IEEE J. Quantum Electron. 52, 1–11 (2016).
[Crossref]

Chen, H.

Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

Chen, W.

Ding, J.

Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

Elser, D.

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
[Crossref]

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4, 686–689 (2010).
[Crossref]

Fu, X.

Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

Gottesman, D.

D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Inf. Comput. 4, 325–360 (2004).
[Crossref]

Guo, G.-C.

Han, Z.-F.

He, D.-Y.

Huang, A.

A. Huang, S. Sajeed, P. Chaiwongkhot, M. Soucarros, M. Legré, and V. Makarov, “Testing random-detector-efficiency countermeasure in a commercial system reveals a breakable unrealistic assumption,” IEEE J. Quantum Electron. 52, 1–11 (2016).
[Crossref]

Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

Jain, N.

L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
[Crossref]

Legré, M.

A. Huang, S. Sajeed, P. Chaiwongkhot, M. Soucarros, M. Legré, and V. Makarov, “Testing random-detector-efficiency countermeasure in a commercial system reveals a breakable unrealistic assumption,” IEEE J. Quantum Electron. 52, 1–11 (2016).
[Crossref]

Leuchs, G.

L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
[Crossref]

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
[Crossref]

Liu, B.

B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016).
[Crossref]

B. Zhao, B. Liu, C. Wu, W. Yu, and I. You, “A tutorial on quantum key distribution,” in 10th International Conference on Broadband and Wireless Computing, Communication and Applications (BWCCA) (2015), pp. 370–374.

Lo, H.-K.

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Inf. Comput. 4, 325–360 (2004).
[Crossref]

Lütkenhaus, N.

D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Inf. Comput. 4, 325–360 (2004).
[Crossref]

Lydersen, L.

L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
[Crossref]

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
[Crossref]

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4, 686–689 (2010).
[Crossref]

Ma, X.

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

Makarov, V.

A. Huang, S. Sajeed, P. Chaiwongkhot, M. Soucarros, M. Legré, and V. Makarov, “Testing random-detector-efficiency countermeasure in a commercial system reveals a breakable unrealistic assumption,” IEEE J. Quantum Electron. 52, 1–11 (2016).
[Crossref]

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
[Crossref]

L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
[Crossref]

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4, 686–689 (2010).
[Crossref]

V. Makarov, A. Anisimov, and J. Skaar, “Erratum: Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 78, 019905 (2008).
[Crossref]

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
[Crossref]

Marøy, Ø.

L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
[Crossref]

Marquardt, C.

L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
[Crossref]

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
[Crossref]

Palmieri, F.

B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016).
[Crossref]

Preskill, J.

D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Inf. Comput. 4, 325–360 (2004).
[Crossref]

Qi, B.

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

Qian, Y.-J.

Qiang, X.

Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

Sajeed, S.

A. Huang, S. Sajeed, P. Chaiwongkhot, M. Soucarros, M. Legré, and V. Makarov, “Testing random-detector-efficiency countermeasure in a commercial system reveals a breakable unrealistic assumption,” IEEE J. Quantum Electron. 52, 1–11 (2016).
[Crossref]

Skaar, J.

L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
[Crossref]

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
[Crossref]

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4, 686–689 (2010).
[Crossref]

V. Makarov, A. Anisimov, and J. Skaar, “Erratum: Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 78, 019905 (2008).
[Crossref]

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
[Crossref]

Soucarros, M.

A. Huang, S. Sajeed, P. Chaiwongkhot, M. Soucarros, M. Legré, and V. Makarov, “Testing random-detector-efficiency countermeasure in a commercial system reveals a breakable unrealistic assumption,” IEEE J. Quantum Electron. 52, 1–11 (2016).
[Crossref]

Su, J.

B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016).
[Crossref]

Sun, S.-H.

Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

Wang, S.

Wiechers, C.

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
[Crossref]

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4, 686–689 (2010).
[Crossref]

Wittmann, C.

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
[Crossref]

L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
[Crossref]

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4, 686–689 (2010).
[Crossref]

Wu, C.

B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016).
[Crossref]

B. Zhao, B. Liu, C. Wu, W. Yu, and I. You, “A tutorial on quantum key distribution,” in 10th International Conference on Broadband and Wireless Computing, Communication and Applications (BWCCA) (2015), pp. 370–374.

Wu, J.

Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

Wu, Z.

Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

Xu, P.

Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

Yin, Z.-Q.

You, I.

B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016).
[Crossref]

B. Zhao, B. Liu, C. Wu, W. Yu, and I. You, “A tutorial on quantum key distribution,” in 10th International Conference on Broadband and Wireless Computing, Communication and Applications (BWCCA) (2015), pp. 370–374.

Yu, W.

B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016).
[Crossref]

B. Zhao, B. Liu, C. Wu, W. Yu, and I. You, “A tutorial on quantum key distribution,” in 10th International Conference on Broadband and Wireless Computing, Communication and Applications (BWCCA) (2015), pp. 370–374.

Zhao, B.

B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016).
[Crossref]

B. Zhao, B. Liu, C. Wu, W. Yu, and I. You, “A tutorial on quantum key distribution,” in 10th International Conference on Broadband and Wireless Computing, Communication and Applications (BWCCA) (2015), pp. 370–374.

Zhao, Y.

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

IEEE J. Quantum Electron. (1)

A. Huang, S. Sajeed, P. Chaiwongkhot, M. Soucarros, M. Legré, and V. Makarov, “Testing random-detector-efficiency countermeasure in a commercial system reveals a breakable unrealistic assumption,” IEEE J. Quantum Electron. 52, 1–11 (2016).
[Crossref]

IEEE Trans. Ind. Electron. (1)

B. Zhao, B. Liu, C. Wu, W. Yu, J. Su, I. You, and F. Palmieri, “A novel NTT-based authentication scheme for 10-GHz quantum key distribution systems,” IEEE Trans. Ind. Electron. 63, 5101–5108 (2016).
[Crossref]

Nat. Photonics (1)

L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, “Hacking commercial quantum cryptography systems by tailored bright illumination,” Nat. Photonics 4, 686–689 (2010).
[Crossref]

New J. Phys. (1)

C. Wiechers, L. Lydersen, C. Wittmann, D. Elser, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “After-gate attack on a quantum cryptosystem,” New J. Phys. 13, 013043 (2011).
[Crossref]

Optica (1)

Phys. Rev. A (4)

L. Lydersen, N. Jain, C. Wittmann, Ø. Marøy, J. Skaar, C. Marquardt, V. Makarov, and G. Leuchs, “Superlinear threshold detectors in quantum cryptography,” Phys. Rev. A 84, 032320 (2011).
[Crossref]

X. Ma, B. Qi, Y. Zhao, and H.-K. Lo, “Practical decoy state for quantum key distribution,” Phys. Rev. A 72, 012326 (2005).
[Crossref]

V. Makarov, A. Anisimov, and J. Skaar, “Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 74, 022313 (2006).
[Crossref]

V. Makarov, A. Anisimov, and J. Skaar, “Erratum: Effects of detector efficiency mismatch on security of quantum cryptosystems,” Phys. Rev. A 78, 019905 (2008).
[Crossref]

Quantum Inf. Comput. (1)

D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, “Security of quantum key distribution with imperfect devices,” Quantum Inf. Comput. 4, 325–360 (2004).
[Crossref]

Other (2)

B. Zhao, B. Liu, C. Wu, W. Yu, and I. You, “A tutorial on quantum key distribution,” in 10th International Conference on Broadband and Wireless Computing, Communication and Applications (BWCCA) (2015), pp. 370–374.

Z. Wu, A. Huang, H. Chen, S.-H. Sun, J. Ding, X. Qiang, X. Fu, P. Xu, and J. Wu, “Hacking single-photon avalanche detector in quantum key distribution via pulse illumination,” arXiv 2002.09146 (2020).

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Figures (2)

Fig. 1.
Fig. 1. (a) $\frac{{{R_0}}}{{{R_3}}}$, (b) $e_0^s$ and $e_3^s$ under a non-blinding detector-control attack versus the rate that Eve passes Alice’s photons without any intervention. Eve uses a lossless channel to launch the partial attack. Eve uses trigger pulses of ${P_{f,0}} = 8\%$, ${P_{f,3}} = 4\%$, ${P_{h,0}} = 4\%$, and ${P_{h,3}} = 2\%$. The green region indicates the valid range of the monitored parameter. The dotted lines indicate that $\frac{{{R_0}}}{{{R_3}}}$ is in valid range with a pass rate of approximately 0%, while QBER is in the valid range with a pass rate of 78%.
Fig. 2.
Fig. 2. Detection efficiency mismatch at the detection time window of Bob. As a 3 dB attenuator weakens a pulse of full power to half power, this detection efficiency mismatch directly implies the violation of the assumption ${P_{f,3}} = {P_{h,0}}$ between two detectors.

Equations (4)

Equations on this page are rendered with MathJax. Learn more.

1 < R 0 R 3 < 2 ,
{ e 0 , e 3 } < 11 % .
R L a t t a c k = 1 2 p { e u Y 1 a t t a c k ( 1 H 2 ( e 1 a t t a c k ) ) Q ω f E C H 2 ( E ω ) } ,
P f , 0 + P f , 3 + = P h , 0 + P h , 3 + , P f , 0 P f , 3 = P h , 0 P h , 3 , P f , 0 H P f , 3 H = P h , 0 H P h , 3 H , P f , 0 V P f , 3 V = P h , 0 V P h , 3 V ,

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