# Graph Layer Security: Encrypting Information via Common Networked Physics
## 4 Simulations and Results
### GLS Performance with Passive Eavesdroppers  
We at first evaluate the GLS performance with passive eavesdroppers mentioned in Section 3.3.1. For this experiment, four passive eavesdroppers are considered. The first one only intercepts the transmitted information without lacking any network node for the physical networked dynamics. The second to the fourth are considered to hack 5%, 10%, and 25% network nodes and their underlying physical networked dynamics to recover the whole dynamic matrix \(\mathbf{X}\), via the graph sampling theory in Equation (24). Here, it is noteworthy that the hacked node set \(\mathcal{S}\) are not randomly selected, but follow Equation (24), i.e., satisfying \(rank(\Gamma_{\mathcal{S},:})=r\). For example, in IEEE 39-Bus system, \(|\mathcal{S}|=10\) (or \(|\mathcal{S}|/39\approx 25\%\)) selected by the graph sampling theory is \(\mathcal{S}=\{1,2,6,10,20,21,23,25,28,33\}\). In Figure 3a, we provide the average BERs of legitimate (Tx,Rx) pairs and of eavesdroppers, versus the measurement noise variance (i.e., \(\sigma^{2}\)) of sensors for physical networked dynamic extraction. We can firstly observe that the BER of the legitimate users becomes lower (e.g., \(10^{-1}\) to \(10^{-5}\)) as \(\sigma^{2}\) decreases (from \(10^{-3}\) to \(10^{-5}\)). This highlights the security's dependency on sensor accuracy (i.e., physical measuring accuracy) rather than the wireless channel estimation quality or diversity (PLS) or public key security. For sensitive noise variance (as one expects of good IoT systems), the encrypted communication channel can achieve a decryption BER of \(\approx\)\(10^{-5}\), five orders of magnitude better than the eavesdroppers (that only intercept the wireless transmitted information). This indicates the encryption reliability of GLS, which can be ensured solely by a cheap but accurate physical sensor (to extract and exploit the physical networked dynamics for communication security), as opposed to the existing wireless-based encryption (PLS) that requires complex and unreliable channel estimation techniques. Figure 3: GLS performance with passive eavesdroppers: (**a**) Average BER with eavesdroppers hacking 0% nodes, 5% nodes, 10% nodes, and 25% nodes; (**b**) recovery RMSEs of physical dynamics by eavesdroppers hacking 0% nodes, 5% nodes, 10% nodes, and 25% nodes. Then, it is seen that with the increase of nodes being hacked by the eavesdroppers, the eavesdropping BERs decrease. To be specific, the BER of eavesdroppers hacking 0% nodes (i.e., only intercept transmitted information) is higher than that hacking 5% nodes, higher than that hacking 10%, and the one with 25% hacked nodes is the lowest. This is analysed with the help of Figure 3b, where the dynamic recovery RMSEs by eavesdroppers versus the ratios of their hacked nodes are given, and that when the number of hacked nodes is larger than 25%, the RMSE converges. This is due to the graph sampling theory in Equation (24), which indicates that the appropriate node selection satisfying \(|\mathcal{S}|=r=10\) can guarantee the complete dynamic recovery (\(r=10\) here is given by the data characteristic of IEEE 39-Bus with 10 generators). As such, Figure 3b gives the reason that eavesdroppers with \(10/39\approx 25\%\) hacked nodes can obtain the whole underlying dynamic for encryption and therefore achieve successful decryption. However, it is noteworthy that hacking such a large number of nodes is difficult for the eavesdroppers, as they have to equip their eavesdropping sensors on every network node they are interested in without being discovered. As such, our GLS method provides a novel perspective and security performance for IoT systems, by the utilisation of underlying physical networked dynamics that are hard to extract by the eavesdroppers. In Figure 4, we provide the statistical distribution of (Tx,Rx) pairs with respect to different BER regions, i.e., <\(10^{-3}\), between \(10^{-3}\) and \(10^{-1}\), and >\(10^{-1}\).