## 4 Proposed Method
### Proposed Method: AAD  
Our proposed AAD scheme consists of five phases: pre-deployment phase, post-deployment phase, sensing phase, receiving/forwarding phase, and verification phase. The pre-deployment phase is executed by the network owner to store necessary materials into the sensors. As its name shows, the post-deployment phase is performed by the sink right after the sensor deployment in order to store the materials required for the authentic data acquisition in the sensors. Sensing phase is executed by each sensor so as to sense data, and distribute the sensed data and the necessary MACs. Once receiving the  
Figure 4: \(R_{0.5}\)’s in different settings. packet, each sensor executes forwarding phase to forward the received message to the destination sensor. Verification phase is performed by the sink to collect the sensed data and verify their authenticity. The notations used in the following discussion are listed in Table 1. The details of these five phases are described as follows. **Pre-Deployment Phase. ** For each sensor \(s_{j}\), the sink randomly selects a unique key \(K_{j}\) and a prime number \(p_{j}\). Note that the prime numbers to be stored in different sensors should be chosen to be distinct. Afterwards, \(K_{j}\) and \(p_{j}\) are stored in the sensor \(s_{j}\). The sensors are then deployed over the sensing region. **Post-Deployment Phase. ** Let \(\lambda\) be a user-selected parameter, which leverages the security and the energy consumption. The post-deployment phase is used to equip each sensor with a proper Bloom filter for the query of its \(\lambda\)-hop proximity relationship. Here, we say that the sensor \(s_{j}\) has \(\lambda\)_-hop proximity relationship_ with the sensor \(s_{i}\) (or, \(s_{j}\) is the \(\lambda\)-hop neighbor of \(s_{i}\)) if the hop distance between \(s_{j}\) and \(s_{i}\) is _within_\(\lambda\). The post-deployment phase is automatically accomplished when sensors are deterministically deployed by the sink. This is because when deploying the sensor \(s_{j}\), the sink can also store the Bloom filter \(\mathfrak{B}_{j}\) containing the \(\lambda\)-hop proximity information of \(s_{j}\) in \(s_{j}\), given that the position of each sensor is pre-determined by the network owner. On the other hand, the post-deployment phase will be accomplished within a period of time right after the sensor deployment if sensors are randomly deployed. More specifically, after the sensor deployment, each sensor acquires its geographic position using well-known positioning techniques [16, 17, 18, 19], and then reports the acquired position to the sink. Such a reporting should be accompanied by the message authentication code (MAC) with the unique key \(K_{j}\) so that the authenticity of the reported position can be guaranteed. Note that, the falsified position information could be injected by the adversary. Nevertheless, the falsified position information will be found by the sink because the sink will move to the position, trying to collect the sensed data. Thus, if falsified positions are injected by the adversary, they will be easily detected. After receiving each sensor's position information, the sink first checks its authenticity by examining whether it has the correct MAC. In particular, when the received message is \(\langle\ell_{j},\hbar\rangle\), if \(\hbar\) is equal to \(h_{K_{j}}(\ell_{j})\), then \(\ell_{j}\) is regarded as the position of \(s_{j}\). With the geographic position of each sensor, the sink can construct the _network graph_, wherein the vertices denote the sensors and the edge between two vertices exists if the corresponding sensors can communicate with each other directly, according to the communication range predefined on each sensor. With the constructed network graph,