## 2 Materials and Methods
### Dark Fiber Topology
In our study, we adopted at Bob stations an upconversion-assisted single-photon detection scheme based on an integrated periodically poled lithium niobite (ppLN) waveguide pumped by long wavelengths at 2 \(\upmu\)m [40]. Based on the reported results in [40], a total efficiency of 10% and a dark count rate (DCR) of \(6\times 10^{-8}\) ns\({}^{-1}\) were assumed. Finally, the optical loss of the internal components at Bob station was fixed at 2.65 dB. The calculation of SKR was carried out assuming general incoherent attacks in the presence of multiphoton pulses, via the theoretical treatment in [41], while adopting the approximation that the optimized average photon number per pulse is equal to the fiber link Transmittance: \(\upmu\sim\) T [35; 41]. Following that approach, the sifted key rate can be calculated as follows  
\[R_{sift}=(p_{\mu}+2p_{dc}+p_{ap})f_{rep}\eta_{duty}\eta_{dand}, \tag{1}\]  
from which the secret key rate is derived by  
\[R_{\text{sec}}=R_{sift}(I_{AB}-I_{AE}), \tag{2}\]  
where \(p_{\mu},\ p_{dc},\ p_{ap}\) are the signal detection, the dark count and the afterpulse probabilities per gate duration time (=1 ns), respectively, \(\eta_{duty}\) captures the duty cycle imposed by the plug and play protocol synchronization requirements, \(\eta_{dand}\) accounts for the reduced detection rate due to SPADs dead time and \(I_{AB}\), \(I_{AE}\) are the mutual information per bit between [PERSON] and [PERSON] and between [PERSON] and [PERSON] (a potential eavesdropper), respectively [35; 41]. The secret key established from the DV-QKD protocol was then used to encrypt/decrypt the data transmitted between the BBU and the 5G terminal node via the AES-256, by exploiting a pair of Ethernet encryptors. Through our study, we specified the SKR values required for the data encryption, under three different key refresh times which, in turn, lead to different attack surfaces. As specified in [42], a very low key refresh time equal to 1.4 s can be achieved from the key management layer according to the recently reported standardization document by QKD engines providers [42], thereby guaranteeing lower attack surfaces. To achieve this rotation time which boosts the security level, a SKR of at least approximately 256 bits/1.4 s = 183 bps should be available after the post-processing steps of QKD layer. Since this SKR target significantly limits the QKD transmission range, we also considered a scenario with increased size of attack surface. More specifically, a longer refresh time equal to 1 min, which is a frequently reported order of magnitude value in bibliography [24; 35; 43], was also selected. To satisfy this rotation time, SKR values of at least 256 bits/1 min = 4.3 bps SKR are demanded. Lastly, we considered a longer key refresh time value equal to 5.14 min. This value corresponds to the lower bound of SKR such that Attack Success Probability (ASP) can be kept below 2\({}^{-60}\). More specifically, in [44], the ASP for a confidentiality attack was compared to the maximum amount of data that can be processed. In order to keep the ASP as low as possible, i.e., at 2\({}^{-60}\), the maximum data that can be transmitted is about 0.3887 terabytes [44]. By assuming a 10 Gbps packetized data flow over eCPRI transport layer, a key generation rate of at least  
\[\frac{256\ \text{bits}\ \times\ 10\ \times\ 10^{9}\ \text{bps}}{8\ \times\ 0.3887\ \times\ 10^{12}\ \text{bits}}\cong 0.83\ \text{bps} \tag{3}\]  
is required to feed the AES-256 cryptographic engine to preserve the ASP below 2\({}^{-60}\), which corresponds to 256 bits/0.83 bps = 5.14 min refresh time.