# Grouping Sensors for the Key Distribution of Implicit Certificates in Wireless Sensor Networks
## 2 Related Work  
Data security for wireless communication between nodes is a crucial issue in WSNs. Considering data security, data have been protected using keys while they are communicated among different sensor nodes [13; 14; 15; 16; 17; 18; 19; 20]. However, efficient and lightweight security mechanisms are needed because each sensor node has limited power computation and storage capacities. The matrix-based structure and group key set-up protocols are used in key management to secure multicast communications in heterogeneous WSNs, but it has high energy consumption [21]. Key distribution and management approaches are categorized into four types: single master key (SMK), all pair wise key (APWK), random pair wise key (RPWK), and group-based key (GBK) [13; 14; 16]. SMK is the simplest for distributing keys [22; 23; 24], where all sensor nodes use the same encryption key to protect their communications. Despite its simplicity, the entire protection mechanism is broken when a hacker breaks and captures one of the sensor nodes. In APWK, a unique encryption key protects communication between any two nodes [17]. A break in any communication does not proliferate to other communications, but this approach is not energy efficient, especially during calculations [25]. In RPWK, a key pool is created, from which each node randomly chooses some keys to make its key ring [18; 19; 20; 21; 22; 23; 24; 25; 26]. Nodes broadcast their key ring identities (ID) to other nodes. A secure channel is established if either of the two nodes within the wireless communication coverage has the same ID. For GBK [19; 20], an entire WSN is divided into several groups. Sensor nodes' connections are of two types: in group and inter-group. All sensor nodes in the same group use the same key to protect their communications. One node (or some nodes) has the key of its neighboring group to ensure secure communication between the two groups. Hereafter, such a node is called a \"boundary node.\" Among these four approaches, GBK has good security and resilience since cracking one node will not endanger the entire network. Moreover, GBK is scalable since each node needs to store only one or two keys. In addition, the entire network is more difficult to crack because the damage caused by any single attack will only be confined to its group nodes. An algorithm based on the implicit certificate has been proposed to solve the security problem among the access points in a dynamic access point group and between the users' equipment [27]. The hybrid-session key management scheme for WSN was proposed to reduce power consumption by minimizing public key cryptography [28]. The uneven clustering approach improves the energy efficiency load balance in WSN [29]. In summary, group- and matrix-based management approaches have quick reaction times and high connectivity with networks, respectively. However, they have high computation overhead time and memory consumption [30]. To address these challenges, herein, we use the aggregating method to solve the large memory consumption and constrained computation performance of the existing key management methods. In WSNs, secure aggregation methods are widely employed in inference attack protection [31] and smart grids [32]. Secure aggregation has been employed in federated learning systems, and the results show that the method needs fewer training iterations and is flexible [31]. Regarding data aggregation, Secure Information Aggregation (SIA) [33; 34] targets a flatter WSN hierarchy with only one data aggregator to which all sensor nodes send data. In addition to aggregating the received data, the aggregator uses the hash tree [35; 36; 37] to convert individual data to an authentication code. As SIA considers only one data aggregator, it is unsuitable for large-scale network deployment. Some studies have been conducted to improve the computation efficiency of aggregation methods [12; 37; 38; 39; 40; 41].