Detecting practical quantum attacks for continuous-variable quantum key distribution using density-based spatial clustering of applications with noise

Continuous-variable quantum key distribution (CVQKD) has been proven to be secure theoretically. However, the practical CVQKD system may still be subject to various quantum attacks due to the imperfections of devices. In this paper, we suggest a general machine learning-based defense strategy against practical quantum attacks by taking advantage of density-based spatial clustering of applications with noise (DBSCAN), which we called DBSCAN-based attack detection scheme (DADS). Specifically, we first construct a set of features that can well reflect the behaviors of different attacks, then DBSCAN is applied to obtain several clusters. This clustering result can explicitly indicate whether the CVQKD system is being eavesdropped or not. Simulation experiments show that the proposed DADS cannot only detect most of known attacks, but also has ability to identify various unknown attacks, thereby improving practical security of the CVQKD system. We also show that the overestimated secret key rate caused by ignoring practical quantum attacks can be amended by DADS so that a reasonable tighter secure bound of the practical CVQKD system can be obtained.

Figure 1

An example for illustrating DBSCAN algorithm. (a) Scattered points are randomly distributed in feature space. (b) Cluster result of DBSCAN with $P_{\min }=4$ and a suitable $\varepsilon$. The blue dots are boundary points, the red dots are core points, and the green dots are noise.

Figure 2

Process of DADS.

Figure 3

Schematic of DADS's measurement. PBS: Polarization beam splitter. AM: Amplitude modulator. PM: Phase modulator. PIN: PIN photodiode. P meter: Power meter. Clock: Clock circuit used to generate the clock signal. DPC: Data processing center used for analog signal sampling, attack detection, and raw key distillation.

Figure 4

A 50-distance graph. The red solid line shows the range with the fastest slope change.

Figure 5

$M_{\mathrm{JC}}$ and $M_{\mathrm{FMI}}$ of the clusters versus different values of $\varepsilon$. Both $M_{\mathrm{JC}}$ and $M_{\mathrm{FMI}}$ are close to 1 when $\varepsilon \in [0.006,0.007]$.

Figure 6

$M_{\mathrm{SC}}$ of the clusters versus different values of $\varepsilon , M_{\mathrm{SC}}$ is close to 1 when $\varepsilon \in [0.005,0.007]$.

Figure 7

$M_{\mathrm{Prec}}, M_{\mathrm{Rec}}, M_{\mathrm{FPR}}$ and $M_{\mathrm{FNR}}$ of DADS against known attacks as a function of $\varepsilon$.

Figure 8

Three-dimensional spatial distribution of $F_{\mathrm{test}}$ before or after DBSCAN clustering

Figure 9

$M_{\mathrm{Prec}}, M_{\mathrm{Rec}}, M_{\mathrm{FPR}}$ and $M_{\mathrm{FNR}}$ of DADS against unknown attacks as a function of $\varepsilon$.

Figure 10

Asymptotic secret key rate as a function of $M_{\mathrm{Rec}}$. Solid lines denote $K_{\mathrm{asym}}^{\mathrm{rev}}$, and dashed lines denote $K_{\mathrm{asym}}^{\mathrm{real}}$. From top to bottom, different colors represent transmission distances 5 km (black), 10 km (red), 20 km (blue), and 30 km (green), respectively.

Figure 11

Asymptotic secret key rate of DADS as a function of $\varepsilon \in [0.003,0.007]$ and $P_{\min }\in [2,50]$.

Figure 12

Secret key rates as a function of transmission distance. Orange dotted line denotes the Piradola-Laurenza-Ottaviani-Banchi (PLOB) bound [45], dashed lines denote the performance of conventional CVQKD without any attack detection strategy, and solid lines denote the performance of the proposed DADS. From top to bottom, different colors (except for orange) represent data block lengths: asymptotic (black), ${10}^{12}$ (red), ${10}^{10}$ (blue), and ${10}^8$ (green).