Practical security of local local oscillator continuous-variable quantum key distribution systems with pulse width mismatch

TL;DR

This work analyzes a practical vulnerability in local-local-oscillator CVQKD (LLO-CVQKD): pulse width mismatch between the signal and the locally generated LO. By modeling the signal and LO as Gaussian temporal modes and introducing the overlap factor $\gamma$, the authors show how mismatch biases Bob’s measurements and distorts parameter estimation, yielding $T' = γ^2 T$ and $ε_{tot}' = ε_{tot} - \frac{(1-γ^2) v_{el}}{η T γ^2}$. Consequently, the secret-key rate $K$ calculated from estimated parameters can be overestimated, especially at higher excess noise, creating a security loophole that an eavesdropper could exploit via attacks like intercept-resend. The paper proposes a practical countermeasure: real-time pulse-width monitoring of both the signal and LO at Bob, coupled with a CHIRPed Fiber Bragg Grating (CFBG) to reshape the LO waveform so that $τ_{LO}=τ_s$, thereby removing the mismatch. These contributions offer a concrete path to secure and scalable LLO-CVQKD implementations by tight temporal-mode control and waveform engineering.

Abstract

In continuous-variable quantum key distribution (CVQKD) systems, using a local local oscillator (LLO) scheme removes the local oscillator side channel, enhances Bob's detection performance and reduces the excess noise caused by photon leakage, thereby effectively improves the system's security and performance. However, in this scheme, since the signal and the LO are generated by different lasers and the signal propagates through the untrusted quantum channel, their pulse widths may become mismatched. Such mismatches may reduce the precision of detection at Bob, affecting parameter estimation processes and leading to inaccurate calculations of the secret key rate. Moreover, mismatches may introduce potential security loopholes. Thus, this paper investigates the practical security issues of the LLO-CVQKD system when pulse width mismatch occurs between the local oscillator and the signal. We first model the case of pulse width mismatch and analyze its impact on Bob's detection. Then, we simulate the secret key rate under different mismatch levels. Based on the analysis, we find that under such mismatch, the key parameters involved in secret key rate calculation are incorrectly estimated, leading to an overestimation of the system's secret key rate. Therefore, this imperfect mismatch can open a loophole for Eve to perform attacks in practical systems. To close this loophole, we design a scheme at Bob to monitor the pulse widths of both the signal and the local oscillator, and to reshape the waveform of the local oscillator so that the two lights are matched again. This method eliminates the adverse effects caused by pulse width mismatch and effectively resists Eve's attacks which exploit this loophole.

Figures (11)

• Figure 1: Practical optical path of the GMCS CVQKD system. AM, amplitude modulator; BS, beam splitter; LO, local oscillator; PM, phase modulator; PBS, polarization beam splitter; DL, delay line; FM, Faraday mirror; VOA, variable optical attenuator; Hom, homodyne detector; PD, photodetector;
• Figure 2: Optical schematic of an LLO-CVQKD system. Here, the LO is generated locally by Bob, and Alice does not need to transmit it.
• Figure 3: The structure of the homodyne detection. D1 and D2 are photodetectors.
• Figure 4: Actual situation of pulse width mismatch between the local oscillator and the signal.
• Figure 5: Corresponding changes in the measurement offsets of $x_B'$ ($p_B'$) relative to $x_B$ ($p_B$) with different $\gamma$ values. (a) $\gamma=0.9$, (b) $\gamma=0.7$, (c) $\gamma=0.5$.