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Energy-time attack on detectors in quantum key distribution

Konstantin Zaitsev1,2,3,4,*, Vladimir Bizin3,5, Dmitriy Kuzmin4,6,7, and Vadim Makarov1,3,4

  • *Contact author: zaitsev20k@gmail.com
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Phys. Rev. A 114, 012601 – Published 6 July, 2026

DOI: https://doi.org/10.1103/nmdx-c94q

Abstract

Quantum key distribution is unbreakable in theory but may be hacked via imperfections in its hardware implementations. While many imperfections have been mitigated by countermeasures and advanced security proofs, several remain unsolved. One of these is a superlinear behavior in single-photon detectors, when the click probability rises faster with the photon number of an incoming light pulse than expected from individual independent photon detections. Here we test an avalanche single-photon detector sinusoidally gated at 312.5 MHz for superlinearity. Its click probability is moderately superlinear. However, we notice that the click timing depends strongly on the incoming pulse energy. The click occurs progressively earlier, shifting more than 2 ns as the energy rises over a wide 50-dB range. An attacker might use this energy-time effect to conditionally toggle the click between adjacent key bit slots, violating an implicit assumption in the security proofs and rendering them inapplicable. We propose two attacks that exploit this flaw.

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References (72)

  1. J. P. Dowling and G. J. Milburn, Quantum technology: The second quantum revolution, Philos. Trans. R. Soc. London Ser. A 361, 1655 (2003).
  2. R. L. Rivest, A. Shamir, and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Commun. ACM 21, 120 (1978).
  3. P. W. Shor, Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer, SIAM J. Comput. 26, 1484 (1997).
  4. C. H. Bennett and G. Brassard, Quantum cryptography: Public key distribution and coin tossing, in Procceedings of the International Conference on Computers, Systems, and Signal Processing (IEEE, New York, 1984), pp. 175–179.
  5. G. Brassard, N. Lütkenhaus, T. Mor, and B. C. Sanders, Limitations on practical quantum cryptography, Phys. Rev. Lett. 85, 1330 (2000).
  6. V. Makarov, A. Anisimov, and J. Skaar, Effects of detector efficiency mismatch on security of quantum cryptosystems, Phys. Rev. A 74, 022313 (2006) [Erratum: 78, 019905(E) (2008)].
  7. Y. Zhao, C.-H. F. Fung, B. Qi, C. Chen, and H.-K. Lo, Quantum hacking: Experimental demonstration of time-shift attack against practical quantum-key-distribution systems, Phys. Rev. A 78, 042333 (2008).
  8. F. Xu, B. Qi, and H.-K. Lo, Experimental demonstration of phase-remapping attack in a practical quantum key distribution system, New J. Phys. 12, 113026 (2010).
  9. L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, Hacking commercial quantum cryptography systems by tailored bright illumination, Nat. Photon. 4, 686 (2010).
  10. I. Gerhardt, Q. Liu, A. Lamas-Linares, J. Skaar, C. Kurtsiefer, and V. Makarov, Full-field implementation of a perfect eavesdropper on a quantum cryptography system, Nat. Commun. 2, 349 (2011).
  11. S.-H. Sun, M.-S. Jiang, and L.-M. Liang, Passive Faraday-mirror attack in a practical two-way quantum-key-distribution system, Phys. Rev. A 83, 062331 (2011).
  12. N. Jain, C. Wittmann, L. Lydersen, C. Wiechers, D. Elser, C. Marquardt, V. Makarov, and G. Leuchs, Device calibration impacts security of quantum key distribution, Phys. Rev. Lett. 107, 110501 (2011).
  13. H. Weier, H. Krauss, M. Rau, M. Fürst, S. Nauerth, and H. Weinfurter, Quantum eavesdropping without interception: An attack exploiting the dead time of single-photon detectors, New J. Phys. 13, 073024 (2011).
  14. H.-W. Li, S. Wang, J.-Z. Huang, W. Chen, Z.-Q. Yin, F.-Y. Li, Z. Zhou, D. Liu, Y. Zhang, G.-C. Guo, W.-S. Bao, and Z.-F. Han, Attacking a practical quantum-key-distribution system with wavelength-dependent beam-splitter and multiwavelength sources, Phys. Rev. A 84, 062308 (2011).
  15. M.-S. Jiang, S.-H. Sun, C.-Y. Li, and L.-M. Liang, Wavelength-selected photon-number-splitting attack against plug-and-play quantum key distribution systems with decoy states, Phys. Rev. A 86, 032310 (2012).
  16. P. Jouguet, S. Kunz-Jacques, and E. Diamanti, Preventing calibration attacks on the local oscillator in continuous-variable quantum key distribution, Phys. Rev. A 87, 062313 (2013).
  17. N. Jain, E. Anisimova, I. Khan, V. Makarov, C. Marquardt, and G. Leuchs, Trojan-horse attacks threaten the security of practical quantum cryptography, New J. Phys. 16, 123030 (2014).
  18. S. Sajeed, I. Radchenko, S. Kaiser, J.-P. Bourgoin, A. Pappa, L. Monat, M. Legré, and V. Makarov, Attacks exploiting deviation of mean photon number in quantum key distribution and coin tossing, Phys. Rev. A 91, 032326 (2015).
  19. M. Rau, T. Vogl, G. Corrielli, G. Vest, L. Fuchs, S. Nauerth, and H. Weinfurter, Spatial mode side channels in free-space QKD implementations, IEEE J. Sel. Top. Quantum Electron. 21, 6600905 (2015).
  20. S. Sajeed, P. Chaiwongkhot, J.-P. Bourgoin, T. Jennewein, N. Lütkenhaus, and V. Makarov, Security loophole in free-space quantum key distribution due to spatial-mode detector-efficiency mismatch, Phys. Rev. A 91, 062301 (2015).
  21. V. Makarov, J.-P. Bourgoin, P. Chaiwongkhot, M. Gagné, T. Jennewein, S. Kaiser, R. Kashyap, M. Legré, C. Minshull, and S. Sajeed, Creation of backdoors in quantum communications via laser damage, Phys. Rev. A 94, 030302(R) (2016).
  22. K. I. Yoshino, M. Fujiwara, K. Nakata, T. Sumiya, T. Sasaki, M. Takeoka, M. Sasaki, A. Tajima, M. Koashi, and A. Tomita, Quantum key distribution with an efficient countermeasure against correlated intensity fluctuations in optical pulses, npj Quantum Inf. 4, 8 (2018).
  23. A. Huang, S. H. Sun, Z. Liu, and V. Makarov, Quantum key distribution with distinguishable decoy states, Phys. Rev. A 98, 012330 (2018).
  24. A. Huang, Á. Navarrete, S.-H. Sun, P. Chaiwongkhot, M. Curty, and V. Makarov, Laser-seeding attack in quantum key distribution, Phys. Rev. Appl. 12, 064043 (2019).
  25. A. Huang, A. Mizutani, H.-K. Lo, V. Makarov, and K. Tamaki, Characterization of state-preparation uncertainty in quantum key distribution, Phys. Rev. Appl. 19, 014048 (2023).
  26. P. Ye, W. Chen, G.-W. Zhang, F.-Y. Lu, F.-X. Wang, G.-Z. Huang, S. Wang, D.-Y. He, Z.-Q. Yin, G.-C. Guo, and Z.-F. Han, Induced-photorefraction attack against quantum key distribution, Phys. Rev. Appl. 19, 054052 (2023).
  27. F.-Y. Lu, P. Ye, Z.-H. Wang, S. Wang, Z.-Q. Yin, R. Wang, X.-J. Huang, W. Chen, D.-Y. He, G.-J. Fan-Yuan, G.-C. Guo, and Z.-F. Han, Hacking measurement-device-independent quantum key distribution, Optica 10, 520 (2023).
  28. A. Baliuka, M. Stöcker, M. Auer, P. Freiwang, H. Weinfurter, and L. Knips, Deep-learning-based radio-frequency side-channel attack on quantum key distribution, Phys. Rev. Appl. 20, 054040 (2023).
  29. A. Acín, N. Gisin, and L. Masanes, From Bell's theorem to secure quantum key distribution, Phys. Rev. Lett. 97, 120405 (2006).
  30. H.-J. Briegel, W. Dür, J. I. Cirac, and P. Zoller, Quantum repeaters: The role of imperfect local operations in quantum communication, Phys. Rev. Lett. 81, 5932 (1998).
  31. H.-K. Lo, M. Curty, and B. Qi, Measurement-device-independent quantum key distribution, Phys. Rev. Lett. 108, 130503 (2012).
  32. Z. Tang, Z. Liao, F. Xu, B. Qi, L. Qian, and H.-K. Lo, Experimental demonstration of polarization encoding measurement-device-independent quantum key distribution, Phys. Rev. Lett. 112, 190503 (2014).
  33. X. Ma, C.-H. F. Fung, and H.-K. Lo, Quantum key distribution with entangled photon sources, Phys. Rev. A 76, 012307 (2007).
  34. Z. Cao, H. Zhou, X. Yuan, and X. Ma, Source-independent quantum random number generation, Phys. Rev. X 6, 011020 (2016).
  35. D. Gottesman and I. Chuang, Demonstrating the viability of universal quantum computation using teleportation and single-qubit operations, Nature (London) 402, 390 (1999).
  36. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, Experimental quantum teleportation, Nature (London) 390, 575 (1997).
  37. V. Makarov, A. Abrikosov, P. Chaiwongkhot, A. K. Fedorov, A. Huang, E. Kiktenko, M. Petrov, A. Ponosova, D. Ruzhitskaya, A. Tayduganov, D. Trefilov, and K. Zaitsev, Preparing a commercial quantum key distribution system for certification against implementation loopholes, Phys. Rev. Appl. 22, 044076 (2024).
  38. 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).
  39. 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).
  40. L. Lydersen, M. K. Akhlaghi, A. H. Majedi, J. Skaar, and V. Makarov, Controlling a superconducting nanowire single-photon detector using tailored bright illumination, New J. Phys. 13, 113042 (2011).
  41. P. Chaiwongkhot, J. Zhong, A. Huang, H. Qin, S. Shi, and V. Makarov, Faking photon number on a transition-edge sensor, EPJ Quantum Technol. 9, 23 (2022).
  42. T. Tsurumaru and K. Tamaki, Security proof for quantum-key-distribution systems with threshold detectors, Phys. Rev. A 78, 032302 (2008).
  43. F. Xu, X. Ma, Q. Zhang, H.-K. Lo, and J.-W. Pan, Secure quantum key distribution with realistic devices, Rev. Mod. Phys. 92, 025002 (2020).
  44. ISO/IEC 23837-2:2023(en). Information security—Security requirements, test and evaluation methods for quantum key distribution—Part 2: Evaluation and testing methods, https://www.iso.org/obp/ui/en/#iso:std:iso-iec:23837:-2:ed-1:v1:en.
  45. C. Marquardt, U. Seyfarth, S. Bettendorf, M. Bohmann, A. Buchner, M. Curty, D. Elser, S. Eul, T. Gehring, N. Jain, T. Klocke, M. Reinecke, N. Sieber, R. Ursin, M. Wehling, and H. Weier, Implementation attacks against QKD systems, BSI Technical Report, https://www.bsi.bund.de/EN/Service-Navi/Publikationen/Studien/QKD-Systems/Implementation_Attacks_QKD_Systems_node.html.
  46. P. Acheva, K. Zaitsev, V. Zavodilenko, A. Losev, A. Huang, and V. Makarov, Automated verification of countermeasure against detector-control attack in quantum key distribution, EPJ Quantum Technol. 10, 22 (2023).
  47. A. Losev, V. Zavodilenko, A. Koziy, Y. Kurochkin, and A. Gorbatsevich, Dependence of functional parameters of sine-gated InGaAs/InP single-photon avalanche diodes on the gating parameters, IEEE Photon. J. 14, 6817109 (2022).
  48. M. K. Bochkov and A. S. Trushechkin, Security of quantum key distribution with detection-efficiency mismatch in the single-photon case: Tight bounds, Phys. Rev. A 99, 032308 (2019).
  49. A. Trushechkin, Security of quantum key distribution with detection-efficiency mismatch in the multiphoton case, Quantum 6, 771 (2022).
  50. A. Koehler-Sidki, J. F. Dynes, A. Martinez, M. Lucamarini, G. L. Roberts, A. W. Sharpe, Z. L. Yuan, and A. J. Shields, Intrinsic mitigation of the after-gate attack in quantum key distribution through fast-gated delayed detection, Phys. Rev. Appl. 12, 024050 (2019).
  51. M. Ware, A. Migdall, J. C. Bienfang, and S. V. Polyakov, Calibrating photon-counting detectors to high accuracy: Background and deadtime issues, J. Mod. Opt. 54, 361 (2007).
  52. S. Sauge, L. Lydersen, A. Anisimov, J. Skaar, and V. Makarov, Controlling an actively-quenched single photon detector with bright light, Opt. Express 19, 23590 (2011).
  53. Sebastian M. F. Raupach, I. P. Degiovanni, H. Georgieva, A. Meda, H. Hofer, M. Gramegna, M. Genovese, S. Kück, and M. López, Detection rate dependence of the inherent detection efficiency in single-photon detectors based on avalanche diodes, Phys. Rev. A 105, 042615 (2022).
  54. Y. Kurochkin, M. Papadovasilakis, A. Trushechkin, R. Piera, and J. A. Grieve, A practical transmitter device for passive state BB84 quantum key distribution, arXiv:2405.08481.
  55. N. Lütkenhaus, Quantum key distribution with realistic states: Photon-number statistics in the photon-number splitting attack, New J. Phys. 4, 44 (2002).
  56. L. Stasi, T. Taher, G. V. Resta, H. Zbinden, R. Thew, and F. Bussières, Enhanced detection rate and high photon-number efficiencies with a scalable parallel SNSPD, ASC Photon. 12, 320 (2025).
  57. ID Quantique, photon-number-resolving detection, https://www.idquantique.com/quantum-detection-systems/photon-number-resolving-detection/.
  58. Y.-Y. Fei, X.-D. Meng, M. Gao, H. Wang, and Z. Ma, Quantum man-in-the-middle attack on the calibration process of quantum key distribution, Sci. Rep. 8, 4283 (2018).
  59. D. Gottesman, H.-K. Lo, N. Lütkenhaus, and J. Preskill, Security of quantum key distribution with imperfect devices, Quantum Inf. Comput. 5, 325 (2004).
  60. W.-Y. Hwang, Quantum key distribution with high loss: Toward global secure communication, Phys. Rev. Lett. 91, 057901 (2003).
  61. V. Scarani, H. Bechmann-Pasquinucci, N. J. Cerf, M. Dušek, N. Lütkenhaus, and M. Peev, The security of practical quantum key distribution, Rev. Mod. Phys. 81, 1301 (2009).
  62. S. Félix, N. Gisin, A. Stefanov, and H. Zbinden, Faint laser quantum key distribution: Eavesdropping exploiting multiphoton pulses, J. Mod. Opt. 48, 2009 (2001).
  63. A. Huang, Q. Peng, J. Liu, X. Yuan, C. Peng, Z. Yang, H. Wu, Z. Chen, G. Sun, F. Wang, and V. Makarov, Penetration testing of quantum key distribution system as a black box, Natl. Sci. Rev. 13, nwag174 (2026).
  64. P. Wang, Q. Zhang, H. Xie, and B. Guo, Optimized polarization encoder with high extinction ratio for quantum key distribution system, Electronics 12, 1859 (2023).
  65. J.-P. Bourgoin, E. Meyer-Scott, B. L. Higgins, B. Helou, C. Erven, H. Hübel, B. Kumar, D. Hudson, I. D'Souza, R. Girard, R. Laflamme, and T. Jennewein, A comprehensive design and performance analysis of low Earth orbit satellite quantum communication, New J. Phys. 15, 023006 (2013).
  66. S.-K. Liao et al., Satellite-to-ground quantum key distribution, Nature (London) 549, 43 (2017).
  67. Y. Li et al., Microsatellite-based real-time quantum key distribution, Nature (London) 640, 47 (2025).
  68. N. Lütkenhaus, Estimates for practical quantum cryptography, Phys. Rev. A 59, 3301 (1999).
  69. L. Lydersen, C. Wiechers, C. Wittmann, D. Elser, J. Skaar, and V. Makarov, Thermal blinding of gated detectors in quantum cryptography, Opt. Express 18, 27938 (2010).
  70. M. Lucamarini, Z. L. Yuan, J. F. Dynes, and A. J. Shields, Overcoming the rate–distance limit of quantum key distribution without quantum repeaters, Nature (London) 557, 400 (2018).
  71. X.-B. Wang, Z.-W. Yu, and X.-L. Hu, Twin-field quantum key distribution with large misalignment error, Phys. Rev. A 98, 062323 (2018).
  72. G. N. Gol'tsman, O. Okunev, G. Chulkova, A. Lipatov, A. Semenov, K. Smirnov, B. Voronov, A. Dzardanov, C. Williams, and R. Sobolewski, Picosecond superconducting single-photon optical detector, Appl. Phys. Lett. 79, 705 (2001).

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Phys. Rev. A 114, 012601– Published 6 July, 2026
  • Received 13 February 2026
  • Accepted 19 May 2026
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