## 4 The Proposed Method: SLP-E
### Protocol Execution Phase
#### 4.2.2 Scenario-2
Precisely, we use and suggest packet escape probability \(P_{esc}\) to measure the percentage of packets that escape the SN visibility space which is given by

\[P_{esc}=1-\frac{\beta}{\alpha\gamma} \tag{1}\]

where \(\beta\) is \(sin^{-1}\left(\frac{r_{s}}{d_{CN}}\right)\), \(\alpha\) is number of hops towards the phantom node, and \(\gamma\) is \(cos^{-1}\left(\frac{2d_{s}^{2}-2r_{s}^{2}}{2d_{n}^{2}}\right)\). The ratio \(\frac{\beta}{\alpha\gamma}\) indicates the probability of packets being intercepted by the attacker if it is in the visibility space. If the term \(\alpha\gamma\) is larger than \(\beta\), then packet

Figure 2: SLP-E routing summary. interception probability is low; otherwise, it is one, when \(\alpha\gamma\) is smaller than or equal to \(\beta\). Since the proposed scheme uses divergent routes to send the packets to the BS, the majority of the packets travel beyond the visibility space and thus provide better privacy. ## 6 Performance Characterization

The proposed SLP-E protocol is evaluated based on the metrics listed below:

1. _Safety period_: it is described as the total number of packets sent to the BS until the adversary finds the actual information source [38]. 2. _Capture percentage_: the capture percentage is calculated as the fraction of trials in which an attacker successfully reaches the source node over all trials in the simulations. 3. _Entropy_: We quantify the randomness of the routing paths using this metric. With higher entropy, the enemy is more confused, hence the prolonged safe period. This measure is provided by \[H(Z)=-\sum P(X)\times log_{2}P(X),\] where \(P(X)\) represents the probability function for the random variable \(X\). Assume that \(Y(n_{i})\) represents the number of packets sent by every sensor node (\(n_{i}\)), whereas \(Y_{t}\) represents the total number of packets sent by the source throughout the simulation. Entropy is then provided by \[H(Z)=-\sum_{i=1}^{i=Z}\bigg{(}\frac{Y(n_{i})}{Y_{t}}\bigg{)}\times log_{2} \bigg{(}\frac{Y(n_{i})}{Y_{t}}\bigg{)}.\] The number of nodes in the network is represented by \(Z\) in this scenario. 4. _Energy consumption_: Based on the energy used to send and receive a message, the energy consumption is calculated. We employ the power consumption methodology recommended in [50] to calculate this measure. The notations that are used to analyze energy consumption are shown in Table 1, and here are the equations: \[E_{T_{X}}(l,d)=E_{elce}*l+e_{fs}*l*d^{2},\qquad d<=d_{0};\] \[E_{T_{X}}(l,d)=E_{elce}*l+e_{amp}*l*d^{4},\qquad d>d_{0}.\] where the energy consumption for receiving a message of the length \(l\)-bits is given by: \[E_{Rx}(l)=l*E_{elce}.\]

Figure 3: Privacy analysis. where the energy loss, \(E_{dec}\), is a function of the transmit circuit's filtering, signal spreading, and digital coding. The energy of the amplifier, \(f_{s}*l*d^{2}\) and \(e_{amp}*l*d^{4}\), depends on the receiver's location and the allowed bit-error rate. 5. _Maximum delay:_ We can count the hops that packets must make from their origin to the base station using the delay metrics. In Section 6.1, we come up with the formula for the maximum delay metric. 6. _Network lifespan or lifetime (NLT)_: it is determined by how many packets are sent in the network before the first node runs out of power. The symbols utilized in this work are displayed in Table 1.

### Delay Estimation Models

The analytical models for the suggested solution's _maximum delay_ or _hop count_ are derived in this section. Plotted in Figure 4 are the delays obtained through the developed model. #### 6.1.1 Scenario-1

If the distance (in hops) between the source location and sink is below the established threshold, SLP-E has five phases, with the following maximum delay for each phase: