## 3 Research Methodology
### Research Model  
The research model (i.e., [PERSON], [PERSON], [PERSON], communication channels, and their supporting optical components) is described in detail in [6; 7; 9]; thus, this section merely provides an overview of the model and its most important configuration parameters. The research model was developed in a discrete event simulation framework specifically designed to study the impact of security and performance implementation non-idealities in QKD systems, algorithms, and protocols [6]. For example, performance and security limitations with respect to speed, accuracy, and environmental disturbances are captured in [PERSON]'s modeled laser source, decoy state generator, pulse modulator, quantum channel, and Avalanche Photo-Diode (APD) detectors. The decoy state enabled BB84 QKD model was developed in three increments each with increasing capability. The first increment provided a hardware-focused QKD notional architecture built in a modular fashion from a library of optical and electro-optical components with probabilistic weak coherent optical pulses [6]. The second increment added the processes and logic required to execute the decoy state protocol [7; 60]. In the third increment, the behaviors of several modeled components were extended to properly handle the propagation of photon number specific representations of optical pulses (i.e., Fock states) and the PNS attack was fully implemented [9]. Throughout model development, considerable effort was spent thoroughly defining, decomposing, modeling, verifying, and validating the decoy state enabled QKD model with each optical component verified against commercial specifications (see Appendix of [6; 61]). Additionally, the model was validated against eight fielded QKD systems [7] with additional modeling and simulation details presented in Section 4.  
In this study, Alice is configured to generate signal, decoy, and vacuum pulses according to the decoy state protocol and BB84 polarization based prepare and measure modulation scheme as described in Section 2. In particular, Alice is programmed to randomly prepare signal, decoy, and vacuum pulses according to the user's prescribed occurrence percentages at a 5 MHz pulse rate with commercially representative laser fluctuations (see Section 4.2 for details). [PERSON] then transmits the prepared pulses through the appropriate 20 or 50 km quantum channel, which has 4 or 10 dB loss respectively with induced physical disturbances which may cause the pulse's polarization to change over time. In accordance with the polarization based prepare and measure scheme, [PERSON]'s model includes beam splitters, polarizing beam splitters, a bandpass filter for a total of 3.5 dB loss. Most importantly, Bob contains models of commercially available APD detectors each configured with 10% detector efficiency, a \(5\times 10^{-6}\) dark count rate (spontaneous detections when no photons are present), and a 0.01 after pulse rate (erroneous detections following a successful detection).  
The research model allows users and developers to more easily (and collectively) study performance and security considerations of the decoy state protocol configurations as presented in Table 4 than when compared to building hardware implementations. Additionally, the model allows security analysts to uniquely study the security profile of decoy state enabled QKD systems in ways that are difficult or impossible with conventional means. For example, the model enables detailed analysis of the PNS attack using a hardware-focused representation--something that cannot yet be fully realized with current technologies [19; 20]. In this way, the model allows for detailed traceability of each multiphoton pulse generated by [PERSON], split by [PERSON], and detected by [PERSON]. Thus, the security analyst is able to explicitly know which weak optical pulses are compromised yet contribute to the QKD-generated secret key bits.