# On Global Quantum Communication Networking
## 3 Extending the Distance between Nodes in QCN  
The DV-QKD can be used to build QKD networks, as discussed in the introduction. Unfortunately, the DV-QKD is affected by the deadtime of SPDs. Moreover, even if [PERSON] cannot get the key because DV-QKD is used, she can prevent parties from creating secure keys, which is similar to the Denial of Service (DoS) attack. Further, since SKRs for DV-QKD are low, the quantum key pool, storing the secure keys, will often be empty, hampering the operation of QKD networks. To solve for this problem we propose to use the hybrid QKD-PQC protocols, in which QKD is used for raw key transmission and PQC in information reconciliation to reduce the leakage during the error reconciliation stage, which is illustrated in Figure 4. As mentioned in the introduction, the PQC is typically referred to in various cryptographic algorithms that are thought to be secure against any quantum computer-based attack. Unfortunately, the PQC is also based on unproven assumptions and some of the QPC algorithms might be broken in the future by developing advanced quantum algorithms. For this reason we propose to use the PQC algorithms only in the information reconciliation phase so as to limit the leakage due to transmission of parity bits over an authenticated classical channel (in conventional QKD). The quantum algorithms to be developed (not yet known), which will be capable of breaking the PQC algorithms, will have certain complexity expressed in terms of the number of operations \(L\). By ensuring that the number of parity bits \(N\)-\(K\) is shorter than the number of secure PQC bits \(\log_{2}L\), the proposed cryptographic scheme will be secure. Evidently, the proposed cryptographic scheme exploits the complexity of corresponding quantum algorithms used to break the PQC protocols. Given that the McEliece cryptosystem based on quasi cyclic (QC)-low-density parity-check (LDPC) coding is straightforward to implement as shown in [24], whereas the corresponding LDPC encoders and decoders have been already implemented in field-programmable gate array (FPGA) [25], it represents an excellent candidate to be used for the transmission of parity bits in the TF-QKD scheme. As an illustration, the secret fraction that can be achieved with the BB84 protocol is lower bounded by [1]:  
\[r=q^{(Z)}\big{[}1-h_{2}\big{(}e^{(X)}\big{)}\big{]}-q^{(Z)}f_{e}h_{2}\big{(}e^ {(Z)}\big{)}, \tag{1}\]  
where \(q^{(Z)}\) denotes the probability of declaring a successful result when [PERSON] sent a single-photon and [PERSON] detected it in the \(Z\)-basis, \(f_{e}\) denotes the error correction inefficiency (\(f_{e}\geq 1\)), \(e^{(X)}\) [\(e^{(Z)}\)] denotes the QBER in the \(X\)-basis (\(Z\)-basis), and \(h_{2}(x)\) is the binary entropy function \(h_{2}(x)=-x\log_{2}(x)-(1-x)\,\log_{2}(1-x)\). The second term \(q^{(Z)}h_{2}[e^{(X)}]\) denotes the amount of information [PERSON] was able to learn during the raw key transmission, and this information can be removed from the final key during the privacy amplification phase. The third term \(q^{(Z)}f_{e}\,h_{2}[e^{(Z)}]\) represents the amount of information revealed during the error correction stage. By sending the parity bits over the PQC channel this term can be effectively eliminated and the SKR can be increased. By using this approach, as illustrated in Figure 5, the transmission distance between two nodes in QCN can be significantly extended. Here we provide comparisons of the joint TF-QKD-McEliece encryption scheme against the phase-matching (PM) TF-QKD protocol introduced in [26], the MDI-QKD protocol [6], and the decoy-state-based BB84 protocol [27]. The system parameters are selected as follows: the detector efficiency \(\eta_{\rm d}=0.25\), reconciliation inefficiency \(f_{\rm e}=1.15\), the dark count rate \(p_{d}=8\times 10^{-8}\), the misalignment error \(e_{\rm d}=1.5\%\), and the number of phase slices for PM TF-QKD is set to \(M=16\).