## 5 Performance Analysis
### Simulation Results and Discussions
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Value** \\ \hline Initial energy (J) & Initial energy of a sensor node & 0.5 \\ \(E_{\text{loss}}\) (n/bit) & Transmitting circuit energy loss & 50 \\ \(E_{amp}\) (p/bit/m\({}^{4}\)) & Energy for power amplification in the free-space model & 0.0013 \\ \(E_{\text{\emph{$B$}}}\) (p/bit/m\({}^{2}\)) & Energy for power amplification in the multi-path attenuation model & 10 \\ \(d_{o}\) (m) & Threshold distance for the channel models & 87 \\ \(l\) (bit) & Size of the transmitted packet & 1024 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Energy consumption model parameters. is that, as more packets are sent in the network, the probability that the cautious adversary will capture successive packets within the specified waiting timer is increased. At higher data rates, the cautious adversary is capable of capturing enough number of successive packets to allow it to make a successful back tracing attack and capture the asset. Therefore, the level of SLP protection is reduced. Figure 6 shows the attack success rate (ASR) of the adversary against the analyzed protocols. In the analysis, the source packet generation rate was 1 packet/second, the adversary trace time was 900 source packets, and the source-sink distance was fixed at 50 hops. For the results in Figure 6a, the ASR was observed against varied number of sensor nodes in the network. The number of sensor nodes was varied between 2500 and 4000 nodes. The figure shows that the ASR of all the protocols tend to decrease with the increase in the number of sensor nodes in the network. However, for the proposed protocols, the ASR decreases at a slightly higher rate. This means that, the SLP protection in the proposed protocols increases at a higher rate that in the other protocols. The main reason for the increased SLP protection with the increase in node density is that, when the number of nodes in the network increases, the number of neighboring nodes and candidate phantom nodes also increase. As  
Figure 5: Privacy performance of the protocols. (**a**) Safety period against source–sink distance. (**b**) Safety period against source packet generation rate. Figure 6: Attack success rate (ASR) against the protocols. (**a**) ASR under varied number of nodes in network. (**b**) ASR under varied network size. (**c**) ASR under varied adversary detection range. Figure 6c shows the ASR of the adversary against adversary detection range. The adversary detection range was varied between 30 and 90 m. The sensor node sensing range was fixed at 30 m. The figure shows that the ASR increases with the increase in adversary detection range. This is mainly due to the fact that adversary becomes more powerful when it has a longer detection range. The traffic analysis attacks become less complex when the adversary can detect a packet sent from a sensor node which is more than 1 hop away. The figure shows that, when a source node is 50 hops away from the sink node, at a trace time of 900 source packets, an adversary with 60 m detection range can achieve up to 100% ASR against the Pha protocol. An adversary with 90 m detection range can achieve up to 90% ASR against the ProbR protocol and up to 65% ASR against the PhaP protocol. For PhaT and TreeR protocols, an adversary with 90 m detection range can achieve less than 55% ASR. These results establish that, amongst all the analyzed protocols, the PhaT and TreeR protocols have the strongest SLP protection and when the adversary has 30 m detection range, the protocols are capable of limiting the adversary ASR to less than 25%. Figure 7 shows the energy consumption performance of the protocols. In the energy consumption analysis, 15 experiment scenarios were assumed, each scenario with a different source node location. Each scenario involved a transmission of 1000 packets from a source node to the sink node.