## 3 Trojan Horsse Attacks
### Attacks with Different Wavelengths from the Original Pulses  
The characteristics of most optical components, such as attenuation through an optical fiber or reflection from a connector, vary with wavelength. In order to characterize the CV-QKD system, we must perform OTDR measurements in a larger spectral range to prove that Trojan horse attacks are feasible [38,39]. The optical pulse generated by [PERSON]'s laser is divided into a reference pulse and an attack pulse on the coupler. The attack pulse is transmitted to [PERSON]'s device through the multiplexer, then reflected back, and detected after passing through the original multiplexer and coupler. In this article, it is assumed that the detection scheme adopted is homodyne detection, so a reference pulse is needed. Assuming that the reference pulse is delayed in the transmission path, it can enter the homodyne detection together with the reflected pulse. In order to prevent [PERSON]'s photons from being disturbed, a multiplexer must be used. In this section, we use dense wavelength division multiplexing(DWDM) [40,41] technology to attack the system with Trojan horse pulses that are different from the original pulse wavelength (Figure 4). The pulses travel back and forth, Rayleigh backscattered light can considerably increase the noise. The actual transmission uses the concept of frames, a train of pulses that entirely fit in delay line in order to prevent errors that would otherwise result from Rayleigh backscattered. We will calculate and analyze the influence of WDM on excess noise and CV-QKD system performance. In fact, the number of noise photons generated by Trojan horse attacks when using DWDM technology will affect the assessment of shot noise. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\tau\) & **0** & **0.1** & **0.2** & **0.3** & **0.4** \\ \hline \(\epsilon\) & 0.01 & 0.0147 & 0.0194 & 0.0241 & 0.0288 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The total excess noise \(\epsilon\) of the system under different crosstalk levels \(\tau\). Due to the limited isolation of the demultiplexer (DEMUX), a small part of the Trojan horse attack signals will leak into the quantum channel. In order to analyze the noise, we made the following assumptions and restrictions on the existing system:  
(a) [PERSON] cannot modify the equipment in the [PERSON] and [PERSON] boxes, but can take advantage of the internal defects of both parties, such as the inherent laser phase noise on the [PERSON] side, unbalanced homodyne detection or imperfect modulation. (b) Since the positions of the reflective elements in [PERSON] and [PERSON]'s device are not controlled by [PERSON], she cannot always schedule her measurements in such a situation that the pulse can pass through the modulator during or when it is very close to the bit slot. In this case, the control voltage will cause a certain phase error, but this is acceptable to [PERSON], she does not need high precision to most of the bit information. (c) The phase modulation efficiency of the Trojan horse pulses and the original pulses is the same. (d) When [PERSON] sends a bright pulse to [PERSON], the number of reflected photons is only a few, so the noise caused by the reflected photons passing through the DWDM device is ignored. However, this defense measure still has certain loopholes: Take the wideband tunable filter WTF-200-T03 produced by Almair Labs as an example, as shown in the Figure 5. The pulse can still be transmitted normally when the wavelength is within 1549.7-1550.3 nm. So when the original pulse is 1550 nm, our Trojan horse pulse adopts any wavelength of 1549.7-1550.3 nm to achieve the attack. Figure 4: Scheme of a Trojan horse attacks with different wavelengths from original pulse. Figure 5: Spectral responses of the band-pass output of WTF-T03-1550. In the GMCS CV-QKD system, the signals leaked from the classical channel into the quantum channel will cause the noise photons to be in the \"unmatched mode\" of the LO.