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].

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]. The turbo-aggregate method achieves O(nLogn) for a secure aggregation in a network with n users, and it can speed up the network’s dispatching efficiency [37].

Energy consumption is another issue in data aggregation. The facility derived from data aggregation is not fully utilized, and much power is consumed during communication. For energy efficiency in WSN, a fuzzy-based node arrangement is used to select the parent node and format the tree topology. Secure Reference-based Data Aggregation (SRDA), in which each sensor node compares its sensed data with the averaged value of previous sensed data (“reference value”), has been proposed [39]. Each node transmits and encrypts only the differential value between the sensed data and the reference value to reduce bandwidth and power consumption. The main disadvantage of this scheme is that only the cluster root can aggregate sensed data; thus, the aggregation effectiveness is reduced. In [40], the authors proposed “Concealed Data Aggregation” to build upon privacy homomorphism, which can directly perform calculations on encrypted data. Thus, all encrypted data are directly fed into the aggregation function, and the aggregated result is delivered to the BS. However, this scheme cannot render high-level security. The logical key hierarchy is used to speed up the encryption and decryption for implementing an effective key-numbering approach [41,42]. In Ref. [43], the logic operations are used to develop the lightweight authenticated group-key distribution scheme to speed up the encryption and decryption operation. In Ref. [12], a promising scheme called implicit security was proposed. The term “implicit security” implies that data protection comes from the partitioning of data d into pieces using mathematical polynomial operations (instead of relying on cryptography). The time complexity for this implicit security scheme is only O(n) for data partitioning or recovery.