Monitoring scheme against local oscillator attacks for practical continuous-variable quantum-key-distribution systems in complex communication environments

In a practical continuous-variable quantum-key-distribution (CVQKD) system, a strong local oscillator (LO) signal in a quantum channel may be manipulated by eavesdropper Eve to steal information about secret keys through general attacks (e.g., entangling cloner attack or intercept-resend attack) without being detected, which is an effective quantum hacking strategy, i.e., LO attacks. To guarantee the practical security of the system, a general monitoring scheme has been previously demonstrated to resist this quantum hacking attack, where the channel transmittance was regarded as a fixed value related to transmission distance. However, practical communication environments are complex, which may result in the time-varying transmittance. This deviation may affect the effectiveness of this monitoring scheme. In this paper, we investigate the monitoring of CVQKD systems running in complex communication environments. We first model the LO attacks on practical CVQKD systems in complex environments, where the channel transmittance is assumed to obey a fixed distribution. Then, the low bound of intensity disturbance of the LO signal for Eve successfully concealing herself is obtained based on this model, where we consider all noise that can be used by Eve in complex communication environments. Simultaneously, we obtain an optimal monitoring condition to resist the LO attacks. Our numerical analysis confirms that the proposed monitoring scheme can effectively resist the LO attacks on practical CVQKD systems in complex environments. Subsequently, the feasibility of this way is again demonstrated by using a quantitative example. It is important that this monitoring scheme can also be extended to resist other quantum hacking attacks.

Figure 1

LO attacks model on a practical CVQKD system running in complex environments. Here, channel transmittance $T$ obeys a certain distribution, which may be controlled by Eve. “ATT” is an attenuator.

Figure 2

The relationship between ${\chi }_{\text{BE}}$ and ${\xi }_{e,ca}$ when the channel transmittance obeys two-point distribution. Here, the parameter $P$ is set as 0.98, 0.99, and 1, respectively.

Figure 3

The relationship between ${\chi }_{\text{BE}}$ and ${\xi }_{e,ca}$ when the channel transmittance obeys uniform distribution. Here, the parameter $\lambda$ is set as 0.2, 0.5, and 0.8, respectively.

Figure 4

The minimum value ${\xi }_{e,ia}$ of the excess noise induced by Eve's individual attacks as a function of the disturbance coefficient $g$ of LO intensity when channel transmittance obeys two-point distribution.

Figure 5

Real-time shot-noise measurement procedures against the LO attacks in a practical CVQKD system. PBS is a polarization beam splitter; BS is a beam splitter; FM is a Faraday mirror; PM is a phase modulator; DL is a delay line; LO is a local oscillator; and Hom is a homodyne detector.

Figure 6

The relationship between the secret key rate and the practical disturbance coefficient $g_m$ of the intensity of LO signal for a CVQKD system with monitoring when channel transmittance obeys the two-point distribution.

Figure 7

The judgment principle of security of the CVQKD systems with monitoring based on the low bound of the disturbance coefficient. Here, $g_b$ is the low bound for a given CVQKD system.