# Grouping Sensors for the Key Distribution of Implicit Certificates in Wireless Sensor Networks
## 3 The Proposed Methods  
The sensing nodes are safe before deployment, and their positions cannot be changed afterward. Moreover, after deployment, the position of the nodes cannot be predicted in advance. We divided the sensor nodes into three roles: the BS, aggregation node (Aggregator), and general sensor node. Therefore, it can store information for each node. It also controls the selection of aggregation nodes. Unless a replacement instruction is issued, the aggregation node that performs the aggregation function is fixed every time a user makes a request. Generally, the sensing node senses parameters in the environment or serves as an intermediate node that transmits data received from its child nodes to the aggregation node. Each node generates a group key, which is shared between a single node and all nodes in the group to which it belongs for secure data communication. The proposed network approach undergoes six stages to ensure data security between nodes, namely, \"network deployment,\" \"key partitioning and distribution,\" \"network grouping,\" \"group key generation,\" \"key and node management,\" and \"data encryption, transmission, and aggregation,\" in that order. The aggregation nodes are generated by random selection. In network deployment, the algorithm proposed in [44] is used to construct the tree topology for the WSN. First, BS broadcasts a request to build up tree topology for all sensor nodes. The request contains a BS ID and a parameter depth indicating how many levels the tree topology should have. When node \(i\) receives this request from node \(j\), it adds one to the parameter depth, sets node \(j\) as a parent node, and broadcasts the request to other nodes. This step constructs a tree topology for \"all\" network nodes in a normal case. Thus, the process continues until all nodes have received the request. This constraint can be refined to ensure the process does not terminate. Figure 1 shows a schematic of the network deployment. After the network accomplishes deployment, keys need to be added to the network to secure the data. The key partition is a critical element in creating a group key in the next stage. When WSN deployment is completed, the BS produces a specific key partition for each  
Figure 1: Architecture of the network. sensor node following the framework in Figure 2[12]. As expressed in Equations (1) and (2), we assume there are \(k\) roots, \(r_{1}\), \(r_{2}\),..., and \(r_{k}\), and \(p\) is a large prime. In this study, we adopt implicit security techniques to handle keys and to construct a tree-based network that dynamically adjusts its topology. With our mechanism, the network is divided into several subtrees, with each subtree being a group of multiple nodes. Each node within a subtree uses key partitioning to generate a group key, which is used for data transmission between group nodes. Additionally, we use symmetric encryption algorithms and hash functions to achieve secure data aggregation with reduced computational overhead. Notably, the leaking of any piece or partition of information will not expose the original data since its reconstruction requires access to each server and the knowledge about the servers that store data partitions. Accordingly, every partition is implicitly secure without the need for encryption. Each root in Equation (2) represents a partition. Based on [12], all partitions must be acquired to perform the calculation in Equation (3) to recover the original data (key). [PERSON] [12] found the roots in polynomials over a finite field (which was a large prime number), as presented in Equation (1), where there are a total of n roots. To utilize it in encryption algorithms, transformation to a finite field is carried out based on Equation (2). Subsequently, the data is substituted in Equation (1), and \(k\) roots (\(r_{1}\)... \(r_{k}\)) are obtained. Each root is referred to as a partition, and the partitions are randomly distributed among various network servers.