## 2 Preliminaries  
### Principle and System Description of CVQKD  
The security of Quantum Key Distribution (QKD) protocols relies on [PERSON]'s uncertainty principle and the quantum no-cloning theorem, allowing for the exchange of unconditionally secure keys for communication [2]. In QKD, [PERSON] and [PERSON] are the two parties involved in communication, utilizing quantum information such as single photons or photon beams [4]. However, the presence of an eavesdropper, referred to as [PERSON], introduces interference. This interference is detected by both [PERSON] and [PERSON], leading to the cancellation of the communication to ensure information security. While discrete-variable QKD relies on single photons to encode information, continuous-variable QKD (CVQKD) utilizes continuous quantum variables of the electromagnetic field, such as the quadratures of optical field modes, to carry information. Both prepare and measure techniques; the key difference is the variable used to encode the key. CVQKD has the advantage of integrating with existing optical fiber networks and showing significant potential for further development. Figure 1 illustrates the schematic of a typical CVQKD system that employs the Gaussian Modulation Continuous Variable Quantum Key Distribution (GMCS CVQKD) methodology, utilizing homodyne detection. Initially, [PERSON] generates coherent light pulses with a wavelength of 1550 nanometers using a telecom diode [22]. These pulses are split into a weak signal and a strong local oscillator (LO) through a beam splitter. Random modulation, involving phase and amplitude modulators, is applied to the signal pulses to follow a Gaussian distribution characterized by a variance \(V_{0}N_{0}\). Polarization multiplexing is incorporated with the use of a polarizing beam splitter between the signal pulses and the LO. Subsequently, [PERSON] transmits the modulated pulses to [PERSON] through a quantum channel that may be susceptible to eavesdropping attempts by [PERSON]. Importantly, [PERSON] may launch both common CVQKD attacks and adversarial attacks simultaneously during the transmission process. Upon reaching [PERSON]'s end, the signal pulses and the LO are separated by [PERSON], employing a polarizing beam splitter and implementing homodyne detection. Moreover, within [PERSON]'s signal path, a fraction of the signal pulses undergo random attenuation to facilitate the timely measurement of shot noise, while the remaining pulses remain unattenuated. A fraction of the LO pulses is also split for monitoring the LO power and generating the clock. By incorporating a phase modulator in the LO path, [PERSON] can selectively choose the quadrature value to be detected by adjusting the measurement phase randomly. Ultimately, the obtained measurement results are forwarded to the data processing center for sampling and the detection of potential attacks. Thus, two related data strings--\(x=[x_{1},x_{2}\ldots,x_{n}]\) and \(y=[y_{1},y_{2}\ldots,y_{n}]\)--are obtained by [PERSON] and [PERSON]; we found the following [23]:  
\[ \begin{split}\overline{x}=0,\ V_{x}=V_{0}N_{0},\\ \overline{y}=0,\ V_{y}=\kappa TV_{0}N_{0}+N_{0}+\kappa T\xi+v_{ \text{el}}N_{0}\end{split}  \tag{1}\]  
where the quadrature value \(X_{\text{A}}\) and \(P_{\text{A}}\) obey variance \(V_{0}N_{0}\). \(T\) represents quantum channel transmittance, and \(\kappa\) denotes efficiency of the homodyne detector. \(v_{\text{el}}\) represents the electronic noise coefficient of the detector; \(\xi\) is the technical excess noise of the system. We mainly consider four common attack strategies in CVQKD systems, including calibration attack, LO intensity attack, saturation attack, and hybrid attack. We find that the four attacks mentioned above in the actual CVQKD system affect different characteristics, such as the intensity \(I_{LO}\) of LO pulses, shot noise variance \(N_{0}\).