## 5 Protocol for Source Location Protection Enhancement Based on Limited Flooding  
To defend against attackers with more powerful monitoring ability than that assumed in defining SLP, we further propose an enhanced protocol for source location protection (SLP-E). We assume that the attacker can observe the sensors within \(r\left(0<r<h\right)\) hops rather than only one hop away from it. As a result, once the attacker traces to the unsafe area, which is within r hops from the source, the source is revealed.  
**Definition 1**.: _The inefficient path is the path going through the unsafe area._  
As can be seen in Figure 1, during the shortest path routing process (see Section 4), if the phantom location lies on \(\ p_{i}p_{i}p_{i}\), the path will go through the unsafe area and thus an inefficient path is generated. [PERSON] _et al._[9] proves that for a large sensor network of evenly distributed sensors, the probability of inefficient path generation is:  
\[\left(\arcsin(r\ /\ H)+\arcsin(r\ /\ h)\right)/\pi \tag{1}\]  
Since the attacker can trace the source quickly through an inefficient path, it is important to avoid generating inefficient paths for source location security enhancement. Based on the above discussion, we propose SLP-E to enhance the source location security by avoiding inefficient path generation. SLP-E is based on SLP, but differs from SLP in the following aspects. First, during the network initialization phase, each sensor is preloaded with a new parameter \(r\), where \(r\) stands for the field of vision of the attacker. Second, during the \(h\)-hops limited flooding phase, the sensors within the unsafe area are marked. Finally, during the shortest path routing phase, a packet is routed to the base station bypassing the sensors in the unsafe area. SLP-E can void generating inefficient path and thus improve the source location security.  
During the limited flooding phase of SLP-E, sensors within the unsafe area are marked, where each sensor is preloaded with a parameter \(v_{visual}\) (initialized to 0). After the limited flooding, \(v_{visual}\) will be updated to 1 if the sensor is within the unsafe area.  
Figure 1: The shortest path bypassing the unsafe area.  
After the limited flooding, the source will route the packet to the phantom location by the \(h\)-directed routing introduced in Section 4. Figure 1 shows the packet will be transmitted \(h\)-hops away from the source before arriving at a phantom location such as \(p_{1}\).  
During the shortest path routing process, the packet will be routed from the phantom location to the base station bypassing the unsafe area. As a result, the packet will always be transmitted to a sensor with \(v_{\mathit{visual}}=0\). Specifically, the current sensor, say \(u\), first classifies its neighbors into two sets: V\({}_{1}\) and V\({}_{0}\), where V\({}_{1}\) includes the sensors with \(v_{\mathit{visual}}=1\) and V\({}_{0}\) the sensors with \(v_{\mathit{visual}}=0\). Then, \(u\) will forward the packet to a neighbor that belongs to V\({}_{0}\)\(\cap\)\(u.\mathit{set\_parent}\). Since all the sensors of V\({}_{0}\) are outside the unsafe area, the packets will be routed to the base station without passing through the unsafe area. Figure 1 shows that once the packet arrives at the phantom location (e.g., \(p_{3}\)), it will take three sub-paths, namely \(\mathit{SP}_{{}_{p_{3},E}}\), \(\mathit{SP}_{{}_{\mathit{EF}}}\), and \(\mathit{SP}_{{}_{F,h}}\), to arrive the base station, where \(\mathit{SP}_{{}_{p_{3},E}}\) denotes the shortest path between \(p_{3}\) and \(E\). \(E\) is the intersection of circle G and the line passing through \(p_{3}\) and \(bs\), where \(G\) is a circle with the center point of \(s\) and the radius of \(r\). Similarly, \(\mathit{SP}_{{}_{F,h}}\) denotes the shortest path between \(F\) and \(bs\), and \(\mathit{SP}_{{}_{\mathit{EF}}}\) denotes the path from \(E\) to \(F\) along the inferior arc \(\mathit{EF}\).