# Graph Layer Security: Encrypting Information via Common Networked Physics
## 5 Conclusions  
Graph layer security (GLS) is proposed for the first time here, as a way to secure the wireless communication information via the wireless channel-irrelevant networked domain physical dynamics. Our approach is premised on the exploration of the dependencies of nonlinear physical networked dynamics among the network nodes for encryption and decryption. The advantage of this approach, as described and demonstrated, is to rely solely on the IoT sensors' accuracy in measuring the physical dynamics **X** (e.g., water flow rate, contamination, gas pressure, voltage) of a networked system. Over the past few decades, we have developed cheap and accurate sensors. Therefore, encrypting the wireless information by exploiting this accuracy makes sense compared to continuously and accurately estimating the wireless environment in PLS, which remains challenging for small IoT devices.  
Figure 6: Statistical distribution of all (Tx,Rx) pairs with respect to different levels of BERs with active attackers.  
The challenge with GLS is to develop representative GFT operators that can characterise the dynamic dependency into a feasible graph-bandlimited subspace, so that the (Tx,Rx) communication node pair can use such dependent channel-irrelevant dynamic to encrypt their transmitted information. This is especially hard for those that involve PDEs. Our prior work in sparse sensing of water distribution networks has shown that GSP can be applied successfully to Navier-Stokes PDEs in water distribution networks [4]. The generality of this data-driven approach is strong as it does not require knowledge of the underlying physical dynamic model, and, indeed, many real-world systems do not have one, or involve couplings between ODEs and PDEs (e.g., electricity grid connected to a thermo energy storage).  
Then, leveraging the GFT operator, encryption and decryption schemes were designed by maximising the GLS secrecy rate. The simulation results demonstrate both the robustness and the reliability of the proposed GLS, combating both the passive eavesdroppers and the active attackers, which suggests its widespread applicability in secure wireless communications over IoT systems, especially for the challenging radio environments and computational resource scarcity scenarios where traditional cryptography and PLS are less attractive. Here, one problem lies in the relay mechanism in our GLS method, which may cause delay for information transmission and may increase the rate of interception by more sophisticated eavesdroppers. The reason lies in the exploitation of solely the linear dynamic dependency. In our future work, we will study how to extract and utilise the higher-order dynamic dependency for point-to-point wireless communications over IoT systems.  
Conceptualisation, W.G. and Z.W.; methodology, W.G., Z.W. and B.L.; software, S.C.S. and Z.W.; validation, L.W. and S.C.S.; formal analysis, Z.W. and L.W.; investigation, B.L. and W.G.; data curation, S.C.S. and L.W.; writing--original draft preparation, W.G., Z.W., S.C.S. and L.W.; supervision, B.L. and W.G.; project administration, W.G.; funding acquisition, W.G. All authors have read and agreed to the published version of the manuscript. This work is supported by DAWN4 IoE - Data Aware Wireless Network for Internet-of-Everything (778305). Not applicable. Not applicable. Data Availability Statement: Data used by this study is available on request and also at: [[https://github.com/RookieEdward/GraphSec](https://github.com/[PERSON]/GraphSec)]([https://github.com/[PERSON]/GraphSec](https://github.com/[PERSON]/GraphSec)) (accessed on 26 April 2022). The authors declare no conflict of interest.