## 3 Model and Background
### Network Structure
#### 4.1.3 Formation of MFN-Groups  
In the network of this scheme there are \(T\) MFN-groups formed, each of which consists of a monitoring node of \(A_{c}\), a forwarding node of \(A_{c}\) and a neighboring node of \(A_{n}\). It is assumed that a monitoring node can establish a group key \(K_{group}\) with its members that are multiple hops away using an existing group key establishment scheme such as [22].We assume that a path already exists between any two consecutive aggregators via forwarding nodes, and that each aggregator uses only one outgoing path towards BS at a given time. These two consecutive aggregators form one pair and share a symmetric key for false data detection. If they do not have a shared key, they establish a symmetric key \(K_{pair}\) using an existing pairwise key establishment algorithm such as direct key establishment method [20]. The message transmission process in the formation of MFN-group is showed in Figure 3. The formation process of MFN-groups includes the following steps:  
1. \(A_{n}\) computes the MAC of its neighboring node list, adds this MAC and its neighboring node list into a group discovery message M.
2. Then \(A_{n}\) sends M to \(A_{c}\) via forwarding nodes on the path between \(A_{c}\) and \(A_{n}\).
3. Each forwarding node appends its ID to the message it forwards.
4. Assuming that \(A_{n}\) has \(s\) neighboring nodes and there are \(h\) forwarding nodes between \(A_{c}\) and \(A_{n}\) (\(s\), \(h\geq T\)), then the message \(A_{c}\) received contains the IDs of its forwarding nodes and neighboring nodes of \(A_{n}\).  
Figure 3: The message transmission process in the formation of MFN-group.  
5. After receiving this message, \(A_{c}\) concatenates the IDs of the forwarding nodes in a random order and indexes them 1 to \(h\), and also concatenates the IDs of the neighboring nodes in a random order and indexes them 1 to \(s\).
6. Then, \(A_{c}\) computes the MAC of the concatenated IDs list using \(K_{group}\).
7. \(A_{c}\) broadcasts the MAC, \(h\) and \(s\) to its \(T\) monitoring nodes.
8. Each monitoring node of \(A_{c}\) selects an index number between 1 to \(h\) and 1 to \(s\), so that \(M_{l}\) of \(A_{c}\) knows its group members from the concatenated IDs list it received.  
In this process, the monitoring nodes of \(A_{c}\) verify the correctness of the broadcasted IDs and their indexed orders using the previously broadcasted MAC of the concatenated IDs list. Therefore, the formation of MFN-groups cannot be affected even if \(A_{c}\) is attacked or damaged, and this process makes sure that each monitoring node corresponds to only one forwarding node and one neighboring node.  
In conclusion, as shown in Algorithm 2, the process of forming the network structure in this scheme can finally form the MFN-groups. After the monitoring node of \(A_{c}\) performs data aggregation and computes subMAC for the aggregated data, the characteristic of such network structure ensures that the corresponding forwarding node of \(A_{c}\) can verify the data integrity during data transmission, and the corresponding neighboring node of \(A_{n}\) can verify the data integrity during data aggregation. Therefore, it can also detect any false data injection during data transmission and data aggregation.