# Secure Physical Layer Network Coding versus Secure Network Coding +
## 5 Conclusions and Discussion  
We have studied the advantages of a secure PLNC over a secure NC. To investigate this type of advantage, we have focused on two typical network models. Section 3 has discussed the butterfly network model given in Figure 2, and Section 4 has discussed the network model with three source nodes given in Figure 4. We have described concrete protocols that efficiently realize the required secrecy and work over these network models. In these examples, the secure PLNC can realize the secrecy even with untrusted intermediate nodes. In particular, as summarized in Table 1, in the butterfly network, although the protocols using secure network codes require a secure shared randomness for this purpose, the secure PLNC does not need it. Comparing the transfer times of the proposed codes, we have shown that the secure PLNC has a shorter transfer time than the the simple combination of secure NC and physical layer network under a certain range of channel parameters. As one of the main reasons of these advantages, we can list the fact that secure PLNC is a cross-layered network protocol. That is, it can be realized by a joint application of the error correction and the secure NC by using the mechanism of a physical layer while the conventional scenario can be considered as separate application of the error correction and the secure NC. In particular, the noise in the channels is utilized for keeping the secrecy in the secure PLNC. Therefore, we can conclude that the secure PLNC is useful to realize the secrecy against information leakage at intermediate (untrusted) nodes. One might consider that the proposed method does not work for jamming attacks [39] or spoofing [40; 41]. The transmitters and the receivers can detect it by attaching authentication [42; 43; 44; 45], which can be realized by using a universal2 hash function and preshared keys. Furthermore, the number of existing applications of the secure PLNC is quite limited. It is an important future study to find much more fruitful applications of the secure PLNC over untrusted relays. In fact, reference [21] also derived an upper bound for the amount of  
Figure 5: Transmission Time for four schemes when \(GT=1\) and the base of the logarithm is 2. The upper dashed line (blue) expresses the time \(\frac{8 GT}{(YA_{1}A_{2}A_{3})_{\text{logarithmic}(2)}}\) of secure NC protocol given in Section 4.1.2 without the MAC channel. The lower dashed line (red) expresses the time \(\frac{6 GT}{I(YA_{1}A_{2}A_{3})_{\text{logarithmic}(2)}}+\frac{2 GT}{I(YA_{1}A_{2})_{ \text{logarithmic}(2)}}\) of the secure NC protocol given in Section 4.1.2 with the MAC channel. The solid line (green) expresses the time \(\frac{3 GT}{I(YA_{1}A_{2})_{\text{logarithmic}(2)}}+\frac{2 GT}{I(YA_{1}A_{2})_{ \text{logarithmic}(2)}}\) of the secure PLNC protocol given in Section 4.2.2. The solid line (black) expresses the time \(\frac{3 GT}{I(YA_{1}A_{2}A_{3})_{\text{logarithmic}(2)}}+\frac{2 GT}{2I(YA_{1}A_{2})_{ \text{logarithmic}(2)}-I(YA_{1}A_{2})_{\text{logarithmic}(2)}}\) of the secure PLNC protocol given in Section 4.2.1. The solid line (black), the solid line (green), and the lower dashed line (red) intersect around \(h=1.7\). the leaked information of the constructed finite-length code. Therefore, it is an interesting future topic to make finite-length analysis by applying the finite-length analysis in [21]. In addition, the analysis of this paper is based on the BPSK scheme. Since many papers on secure PLNC were based on lattice codes, a similar comparison based on lattice codes is needed. Such a comparison remains an interesting open problem. Finally, we list three future problems. The first one is the application of the proposed method to multi-hop untrusted relaying networks [8; 46]. The second one is the realization of covert communication [47; 48] over the wireless networks discussed in this paper. The third one is the problem related to retransmission. In real communication, there is a possibility that we need to perform retransmission due to various reasons.