Security analysis against the Trojan horse attack on practical polarization-encoding quantum key distribution systems

Quantum key distribution (QKD), which theoretically provides unconditional secure communication, has developed rapidly in the past decades. However, the practical QKD systems still have vulnerabilities due to device imperfections. Polarization-encoding systems are one of the most important branches in the field of QKD. To date, a variety of polarization-encoding schemes have been proposed to meet the requirements of high speed and robust modulation, but the security analysis of these schemes is often ignored. In this paper, we experimentally and theoretically evaluated the security of three typical polarization encoders against the Trojan horse attack (THA), which is recognized as one of the critical quantum attacks. We built a system to implement the THA and collected the reflection from QKD configuration with different encoders. According to the experimental results, we further analyzed the secure key rate and the resistance against THAs of the system while BB84 or measurement-device-independent QKD was applied. Our paper plays an important guiding role in the design of polarization encoders and the construction of secure QKD systems with realistic devices.

Figure 1

Schematic diagram of the time domain reflection setup. Encoder: the encoders under test. The specific composition of the three different encoders studied will be shown in Figs. 2, 3, and 4, respectively. ${\mathrm{LD}}_E$, laser diode at Eve; ${\mathrm{LD}}_A$, laser diode at Alice; ATT, optical attenuator; ${\mathrm{FC}}_1$, FC/APC fiber connector; CIR, circulator; SPAD, InGaAs-based time-gated infrared single-photon avalanche detector; DG, digital time delay generator; SM fiber, single-mode fiber.

Figure 2

Experimental setup and test result of encoder $A$. (a) Schematic diagram of the polarization encoder $A$ setup. ${\mathrm{LD}}_A$, laser diode at Alice; ${\mathrm{FC}}_i$, FC/APC fiber connector; ${\mathrm{PC}}_i$, polarization controller; IM, intensity modulator; ${\mathrm{PBS}}_i$, polarization beam splitter; ${\mathrm{PM}}_i$, phase modulator. SM fiber, single-mode fiber. PM fiber, polarization-maintaining fiber. (b) Reflections of THAs on encoder $A$. The distance is measured from the fiber connector ${\mathrm{FC}}_1$ placed at the end of Alice. The corresponding source is marked above each reflection peak. ${\mathrm{C}}_E$, circulator at Eve's setup; ${\mathrm{FC}}_{3,4}$ indicates that the peak is the superposition of ${\mathrm{FC}}_3$'s and ${\mathrm{FC}}_4$'s reflection peaks, as are ${\mathrm{PM}}_{1,2}$ and ${\mathrm{FC}}_{5,6}$.

Figure 3

Experimental setup and test result of encoder $B$. (a) Schematic diagram of the polarization encoder $B$ setup. ${\mathrm{LD}}_A$, laser at Alice; ${\mathrm{FC}}_i$, FC/APC fiber connector; IM, intensity modulator; CIR, circulator; ${\mathrm{FM}}_i$, Faraday mirror; PM, phase modulator; PBS, polarization beam splitter; SM fiber, single-mode fiber; PM fiber, polarization-maintaining fiber. (b) Reflections of THAs on encoder $B$. The distance is measured from the fiber connector ${\mathrm{FC}}_1$ placed at the end of Alice. ${\mathrm{C}}_E$, circulator at Eve's setup; ${\mathrm{C}}_A$, circulator at Alice's setup; ${\mathrm{FM}}_{1,2}$, superposition of the vertical reflections from ${\mathrm{FM}}_1$ and horizontal reflections from ${\mathrm{FM}}_2$; $P_i$, superposition of undesired reflections from different optical paths. These undesired reflections originate from nonflipped light caused by FM imperfections.

Figure 4

Experimental setup and test result of encoder $C$. (a) Schematic diagram of the polarization encoder $C$ setup. ${\mathrm{LD}}_A$, laser at Alice; ${\mathrm{FC}}_1$, FC/APC fiber connector; IM, intensity modulator; CIR, circulator; PC, polarization controller; PBS, polarization beam splitter; PM, phase modulator; SM fiber, single-mode fiber; PM fiber, polarization-maintaining fiber. (b) Reflections of THAs on encoder $C$. The distance is measured from the fiber connector ${\mathrm{FC}}_1$ placed at the end of Alice. ${\mathrm{C}}_E$, circulator at Eve's setup; ${\mathrm{C}}_A$, circulator at Alice's setup.

Figure 5

The SKRs of BB84-QKD systems with encoder $A, B$, and $C$, corresponding to the magenta dash-dotted line, the blue solid line, and the red dashed line, respectively. The corresponding ${\mu }_{\mathrm{out}}$ of each encoder is ${\mu }_{\mathrm{out}}^A=2.975\times {10}^{-7}, {\mu }_{\mathrm{out}}^B=5.606\times {10}^{-8}$, and ${\mu }_{\mathrm{out}}^C=4.544\times {10}^{-8}$. The curve labeled with ${\mu }_{\mathrm{out}}=0$ indicates the situation without THA and information leakage, corresponding to the black dotted line.

Figure 6

The SKRs of MDI-QKD systems with encoder $A, B$, and $C$, corresponding to the magenta dash-dotted line, the blue solid line, and the red dashed line, respectively. The corresponding ${\mu }_{\mathrm{out}}$ of each encoder is ${\mu }_{\mathrm{out}}^A=1.190\times {10}^{-11}, {\mu }_{\mathrm{out}}^B=2.242\times {10}^{-12}$, and ${\mu }_{\mathrm{out}}^C=1.818\times {10}^{-12}$. The curve labeled with ${\mu }_{\mathrm{out}}=0$ indicates the situation without THA and information leakage, corresponding to the black dotted line.

Figure 7

(a) The SKR for the BB84-QKD protocol under the THA with various values of ${\mu }_{\mathrm{out}}$. The red square marks the corresponding ${\mu }_{\mathrm{out}}$ and SKR of encoder $A$ at 100 km, and the purple star and orange circle represent encoder $B$ and $C$, respectively. (b) The SKR for the MDI-QKD protocol under the THA corresponding to various values of ${\mu }_{\mathrm{out}}$. The red square, purple star, and orange circle mark the corresponding ${\mu }_{\mathrm{out}}$ and SKR at 100 km of encoder $A, B$, and $C$, respectively.