Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
. 2022 Sep 2;24(9):1232.
doi: 10.3390/e24091232.

Detecting a Photon-Number Splitting Attack in Decoy-State Measurement-Device-Independent Quantum Key Distribution via Statistical Hypothesis Testing

Affiliations

Detecting a Photon-Number Splitting Attack in Decoy-State Measurement-Device-Independent Quantum Key Distribution via Statistical Hypothesis Testing

Xiaoming Chen et al. Entropy (Basel). .

Abstract

Measurement-device-independent quantum key distribution (MDI-QKD) is innately immune to all detection-side attacks. Due to the limitations of technology, most MDI-QKD protocols use weak coherent photon sources (WCPs), which may suffer from a photon-number splitting (PNS) attack from eavesdroppers. Therefore, the existing MDI-QKD protocols also need the decoy-state method, which can resist PNS attacks very well. However, the existing decoy-state methods do not attend to the existence of PNS attacks, and the secure keys are only generated by single-photon components. In fact, multiphoton pulses can also form secure keys if we can confirm that there is no PNS attack. For simplicity, we only analyze the weaker version of a PNS attack in which a legitimate user's pulse count rate changes significantly after the attack. In this paper, under the null hypothesis of no PNS attack, we first determine whether there is an attack or not by retrieving the missing information of the existing decoy-state MDI-QKD protocols via statistical hypothesis testing, extract a normal distribution statistic, and provide a detection method and the corresponding Type I error probability. If the result is judged to be an attack, we use the existing decoy-state method to estimate the secure key rate. Otherwise, all pulses with the same basis leading to successful Bell state measurement (BSM) events including both single-photon pulses and multiphoton pulses can be used to generate secure keys, and we give the formula of the secure key rate in this case. Finally, based on actual experimental data from other literature, the associated experimental results (e.g., the significance level is 5%) show the correctness of our method.

Keywords: decoy state; measurement-device independent; photon number splitting attack; quantum key distribution; statistical hypothesis testing.

PubMed Disclaimer

Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
The schematic diagram of statistical hypothesis testing. The value of the test statistic v is 0.236. Given the significance level of the test α=0.05, the critical values are v[1α/2]=1.96 and v[1α/2]=1.96.

References

    1. Bennett C.H., Brassard G. Quantum cryptography: Public key distribution and coin tossing. Theor. Comput. Sci. 2014;560:7. doi: 10.1016/j.tcs.2014.05.025. - DOI
    1. Shor P.W., Preskill J. Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 2000;85:441. doi: 10.1103/PhysRevLett.85.441. - DOI - PubMed
    1. Gisin N., Ribordy G., Tittel W., Zbinden H. Quantum cryptography. Rev. Mod. Phys. 2002;74:145. doi: 10.1103/RevModPhys.74.145. - DOI
    1. Kraus B., Gisin N., Renner R. Lower and upper bounds on the secret-key rate for quantum key distribution protocols using one-way classical communication. Phys. Rev. Lett. 2005;95:080501. doi: 10.1103/PhysRevLett.95.080501. - DOI - PubMed
    1. Gisin N., Thew R. Quantum communication. Nat. Photon. 2007;1:165. doi: 10.1038/nphoton.2007.22. - DOI

LinkOut - more resources