# Graph Layer Security: Encrypting Information via Common Networked Physics
## 1 Introduction
### Introducing Graph Layer Security (GLS): Encryption Using Networked Physics  
To overcome the PLS requirement of a high-communication SNR for accurate wireless channel estimation, we identify and exploit a different physical attribute that is common to many IoT sensors. The general idea to exploit common physics has been proposed before, such as common heartbeat in different medical IoT devices across a body. However, those devices typically do not suffer from the aforementioned low-communication SNR challenges. Here, we consider IoT devices placed in underground or embedded networked systems, such as oil/gas/water pipes, electrical networks, optical fibre networks, and other underground connected systems. In networked physical systems, a common continuity equation connects all the dynamics (e.g., Navier-Stokes for flow, nonlinear Schrodinger for optic transmission, power flow for electricity). We propose to exploit the common networked physical signals at different IoT monitoring points to encrypt the IoT device's wireless data. Such networked physics are the time-varying networked signals under each node, and are irrelevant with the wireless communications (e.g., channel phases and RSS). For example, in a smart grid, the networked physics is the electricity flow (what we will use in our simulation part). In a water distribution network, the networked physics can be the time-varying water pressure or the concentrations of some compounds. This has the following advantages: (1) IoT sensors usually have very high precision in measuring the physical signals, and (2) it requires no specific knowledge or requirement of wireless channel or public key distribution. This novel physical driven security is distinctive from both PKC and PLS, and its security independence from the digital environment makes it more resilient against digital attacks. The main contributions of this work are summarised in the following. (1) We propose a novel digital encryption paradigm over a physical network called graph layer security (GLS). The process is data-driven and model-agnostic. We exploit the dependency of underlying networked physical dynamics to enable encryption amongst digital transceivers, without complex computations (for key generation/management in traditional cryptography-based method, or for channel estimating techniques in PLS). In GLS, the encryption and decryption is based on an additive noise generated by the wireless channel-irrelevant physical networked dynamic on one node, and can be compensated by other nodes with dependent networked dynamics. Leveraging this idea, for any pair of network nodes as Tx and Rx, we select the relay nodes with dependent dynamics, and the information then can be encrypted, reconciliated, and finally decrypted by Tx, relay, and Rx nodes. (2) One difficulty of the relay selection lies in the dependency analysis on the random networked dynamics. To overcome this, we draw heavily on sparsifying high-dimensional random nonlinear dynamics by the use of a data-driven graph Fourier transform (GFT) operator, which is able to transform the random dynamics into a compact graph-bandlimited subspace, given the graph smoothness of the evolved networked dynamics (or its time-difference) [29]. By doing so, we pursue the dependency analysis of the random dynamics by finding the dependent rows of the GFT-based surrogate matrix. (3) We analyse and evaluate the performance of our proposed GLS using a IEEE 39-Bus system. Both the passive eavesdroppers and the active attackers are considered, where the former is defined as intercepting the transmitted information (encrypted) as well as hacking parts of the network nodes and their dynamics, and the latter is defined to degrade the dynamic dependency by adding jamming perturbations to the network. The simulations show two results. First, the GLS performance depends mostly on the measuring accuracy of the networked dynamics, other than the complex channel estimation techniques for key generations required by the PLS.