Data aggregation algorithm for wireless sensor networks with different initial energy of nodes

Tree topology

The SMART algorithm, proposed by He et al. (2007) serves as a data privacy-enhancing solution for data aggregation operations in tree topology. SMART utilizes a tree-topology-based data slice-and-mix transmission algorithm, which involves three steps: slicing, mixing, and data transfer. During the slicing stage, each node divides its data into J segments, retains one segment, and randomly transmits the remaining J-1 segments to its J-1 neighboring nodes. In the mixing phase, each node combines the received data fragments with its own data to generate its transmission data. Finally, during the data transfer phase, all nodes transmit their mixed data to the parent node and eventually to the receiver. Another algorithm, PECDA, was proposed by Wang et al. (2018) as a means of achieving privacy-preserving and energy-efficient continuous data aggregation in wireless sensor networks. PECDA is based on the SMART algorithm (Wang et al., 2018). PECDA employs the slice-and-mix technique proposed in SMART on leaf nodes in the network topology, while non-leaf nodes establish secure channels with neighboring nodes to ensure data privacy. Additionally, PECDA takes into account the temporal correlation of data sensed by leaf nodes during continuous data aggregation to reduce the communication overhead in the network and extend the network lifetime. However, it is important to note that this approach may increase the probability of data leakage in some nodes. Hajian & Erfani (2021) proposed a continuous data aggregation algorithm for wireless sensor networks that considers the spatial correlation of nodes. This algorithm takes into account data similarity resulting from the spatial correlation of node locations. Multiple nodes with high correlation alternate between active and sleep states, reducing communication overhead and energy consumption in the network. Additionally, the algorithm employs data slicing and mixing between nodes in sensor networks to enhance privacy protection.

The EPDA chain-based data aggregation algorithm for wireless sensor networks was proposed by Zhou et al. (2019). EPDA elongates sub-trees in the network to form a chain structure, reducing the number of leaf nodes and data slices, thereby achieving a reduction in communication overhead. However, the chained structure increases the number of hops for nodes to reach the receiver, resulting in increased communication overhead for data transmission from trailing nodes to the receiver. Consequently, the chained structure leads to an unbalanced energy load in the network, and some intermediate nodes close to the receiver may experience premature death. Dao et al. (2023) proposed a heuristic algorithm called RRPT to reduce redundant data packets in wireless sensor networks, aiming to maximize their lifespan by minimizing the total transmission and reception energy consumption of sensor nodes. The algorithm constructs an aggregation tree with as few redundant data packets as possible. When a new node joins the aggregation tree, the selection of its parent node is based on the minimum number of redundant data packets along the path from the parent node to the receiver. However, the algorithm does not consider the hierarchical structure of the tree, which can result in excessive levels of the tree structure and higher energy consumption during data transmission. In another study, Tai et al. (2023) consider the known topology of the sensor network and propose a power control strategy for each node based on fairness and end-to-end Quality of Service (QoS) constraints. The objective is to reduce node energy consumption and prolong the overall network lifespan. The optimal strategy computation employs the Lagrange relaxation method as a solution approach. By decomposing the problem into directly solvable subproblems based on different decision variables, each iteration yields an approximately optimal feasible solution until the optimal solution is obtained. This method takes into account the optimal strategy of sensor nodes under practical constraints. However, it does not consider the limitations imposed by the tree topology structure on sensor nodes and its impact on data collection.

Cluster topology

A cluster-based data aggregation algorithm for wireless sensor networks was proposed by He et al. (2007). In this algorithm, WSN nodes are organized into clusters of varying sizes, and cluster heads are selected within each cluster to perform intra-cluster data aggregation. The aggregation results are then transmitted to the receiver. Heinzelman, Chandrakasan & Balakrishnan (2000) proposed the LEACH aggregation algorithm for wireless sensor networkss. This algorithm dynamically selects cluster heads to achieve energy-balanced loads during cluster data aggregation. LEACH enables nodes to form clusters of different sizes and selects cluster heads for intra-cluster data aggregation. In another work (Sekar, Suganthi & Dheepa, 2023), a routing protocol called JSARP is proposed to optimize the selection of cluster head nodes and reduce network energy consumption to improve the network lifespan. JSARP selects cluster heads based on relevant fitness attributes. Once the cluster heads are determined, the jellyfish swarm algorithm is used to choose the optimal path for data transmission, aiming to minimize energy consumption in data collection and prolong the network’s lifespan. However, this method solely focuses on the optimal path for data transmission and does not consider the imbalance in energy consumption across the network. Consequently, the overall energy consumption of the network may not be evenly distributed.

In this study, we propose the DADIE algorithm for data aggregation in wireless sensor networks, specifically designed to handle scenarios where network nodes have different initial energy levels. By leveraging the aforementioned data aggregation algorithm, DADIE aims to decrease network communication overhead and energy consumption, while enhancing network privacy protection and extending the network’s lifetime. In comparison to existing data aggregation algorithms, DADIE specifically addresses the case of data aggregation with WSN nodes having varying initial energy levels. It offers improvements over existing algorithms by effectively dealing with the challenges posed by an unbalanced energy load.

Network model

In this article, the wireless sensor network (WSN) comprises a receiver, also known as the base station (BS), and N sensor nodes. All nodes are deployed within an area of size M*M and form a connected network denoted as G (V, E), where V represents the number of nodes in the sensor network structure and E represents the set of links present in the sensor network G. In this network, all nodes have an identical data transmission radius, denoted as R. We assume the following conditions:

• In the wireless sensor network, all nodes are uniformly and randomly distributed throughout the network area, with fixed positions. Each node is assigned a unique identifier (ID) and possesses a distinct initial energy value. These nodes have the capability to sense data from the environment, receive data from neighboring nodes, and transmit data to other nodes within their transmission radius, denoted as R.

• The network G is composed of three types of nodes: the data receiver BS, intermediate nodes, and leaf nodes. The data receiver BS is equipped with unlimited energy, computing power, and storage space. Therefore, we do not consider its energy consumption and communication overhead in our analysis. The intermediate nodes in the network receive data from their child nodes, aggregate the received data with their own data, and generate a packet that is transmitted to their respective parent node. On the other hand, the leaf nodes in the network sense data from the environment, perform slice-and-mix operations on the sensed data, and then transmit the processed data to their parent node.

• Neighboring nodes in the network establish secure data transmission channels to ensure the confidentiality and integrity of the transmitted data. These secure channels are used for all data transmissions within the network, ensuring that all data is transmitted securely.

• In this study, the data aggregation performed by each node is referred to as complete aggregation. This means that the node retains all the data it receives and encapsulates it into a single packet for transmission. Specifically, we adopt a summation aggregation approach in this article, where the received data at a node is aggregated by performing an additive summation operation.

• Before each cycle of data transmission, the nodes in the network complete the data sensing process. This ensures that the nodes have gathered the required data before initiating the transmission. It is important to note that the data sending and receiving operations of a node cannot be performed simultaneously. In other words, a node cannot send and receive data at the same time. These operations occur sequentially to ensure proper data transmission and reception within the network.

Attack model

Due to the specific characteristics of node distribution and data transmission in sensor networks, attackers primarily launch attacks from two directions (Yousefpoor et al., 2021; Salmi & Oughdir, 2023; Cao et al., 2022):

• Eavesdropping attacks are a prevalent form of attack in wireless sensor networks. In WSNs, where data transmission occurs wirelessly between nodes, attackers can intercept and eavesdrop on the communication channel. By doing so, they can capture the link information exchanged between the transmitting node and the receiving node.

• Cracking attacks represent another type of attack in wireless sensor networks. In this form of attack, the attacker gains unauthorized access to a sensor node and obtains various sensitive information, such as data, keys, location details, and other pertinent data related to the compromised node. Furthermore, through the compromise of one or multiple sensor nodes, the attacker may extract information about neighboring nodes, resulting in a significant breach of the entire network’s security.

Basic idea of DADIE

The DADIE algorithm is specifically designed for data aggregation in scenarios where the initial energy levels of nodes in a sensor network vary. The algorithm consists of four key components:

• Initialization phase: In the initialization phase of the DADIE algorithm, pre-allocated keys are stored in the memory of the sensor nodes before their deployment. Once the nodes are deployed, they begin sensing and collecting information regarding their location, initial energy levels, and other relevant data.

• Topology formation phase: During the topology formation phase of the DADIE algorithm, the goal is to create an aggregation tree that establishes a tree-like structure for the wireless sensor network. The BS serves as the root node, and other nodes are added to the tree starting from the BS. The DADIE algorithm considers both distance and energy factors to optimize the construction process. To account for the higher energy consumption of intermediate nodes closer to the BS, which occurs due to increased data collection, processing, and transmission responsibilities, the DADIE algorithm employs a cyclic approach. It selects nodes that have not yet joined the aggregation tree but possess the minimum distance and maximum initial energy. These selected nodes are given priority to become intermediate nodes in the tree. However, to prevent excessive energy consumption and premature failure of intermediate nodes, the DADIE algorithm sets a constraint on the maximum number of child nodes allowed for each intermediate node. This constraint ensures a balanced energy consumption among the nodes in the aggregation tree. Furthermore, the aggregation tree is reconstructed before each round of data transmission to adapt to potential changes in node energy levels and network conditions. This dynamic reconstruction ensures the efficiency and adaptability of the tree structure, enabling better utilization of network resources and prolonging the network lifetime.

• During the slicing and mixing phase of the DADIE algorithm, leaf nodes in the aggregation tree divide their sensory data into segments. One segment is retained as the node’s own data, while the remaining data slices are randomly transmitted to neighboring nodes. This process allows for data distribution and collaboration among the nodes. Each node receives data segments from its neighboring nodes. It then combines its own sensory data with the received data segments through a mixing process. This mixing operation allows the node to form the transmitted data that will be further propagated through the aggregation tree.

• The data aggregation and transmission phase of the DADIE algorithm initiates with the leaf nodes in the aggregation tree. These leaf nodes transmit their data to their parent node, which is closer to BS. Upon receiving data from their child nodes, each parent node performs data aggregation by combining the received data with its own collected data. This aggregation process typically involves applying specific aggregation functions, such as averaging or summing, to the data. After the aggregation, the parent node transmits the aggregated data to its own parent node in the tree. This process of data aggregation and transmission continues recursively as the data moves up the aggregation tree towards the BS. Each intermediate node receives and aggregates data from its child nodes, forming a consolidated dataset. This aggregated data is then transmitted to the next higher-level node until it reaches the BS.

Description of DADIE

Energy loss model

In this article, we utilize a first-order radio energy consumption model to analyze the energy consumption of the sensor nodes specifically during data transmission and reception. We focus solely on these aspects and do not consider the energy loss that may occur during computation and storage processes. The process is illustrated in Fig. 1, which is divided into two halves. The left half of the figure illustrates the energy consumption of the sensor node during the transmission of data, while the right half depicts the energy consumption during data reception (Gupta, Gupta & Verma, 2022). In Fig. 1, the energy consumption of a sensor node during data transmission is depicted. When a sensor node transmits N bits of data to another node, the energy consumed by the sending node can be calculated as $N\ast E_{en}$. Here, $E_{en}$ represents the energy consumed by the sensor node to transmit or receive 1 bit of data. After the data is transmitted, it passes through the power expansion circuit, which results in additional energy consumption. This additional energy consumption can be calculated as $N\ast \beta (L)$, where $\beta (L)$ represents the amplification factor of the power expansion circuit for data transmission at different distances. Equations (3) and (4) are the calculations of $\beta ()$:

(3) $$\beta (L)=\{\begin{array}{c}{\epsilon }_{FS}\ast L^2,L<L_0\hfill \\ {\epsilon }_{AMP}\ast L^4,L\ge L_0\hfill \end{array}$$

(4) $$L=\sqrt{{(X_1-X_2)}^2+{(Y_1-Y_2)}^2}\text{.}$$

${\epsilon }_{FS}$ and ${\epsilon }_{AMP}$ denote the energy expended in the receiver amplifier in the free space model and in the receiver amplifier in multipath fading model respectively (Eidaks et al., 2022; Tirmizi et al., 2022). Moreover, $L_0$ denotes a distance threshold, L denotes the node communication distance and $(X,Y)$ are the coordinates of the node. When the L is less than $L_0$, the energy consumption is proportional to the square of the distance. On the other hand, when the L is greater than or equal to $L_0$, the energy consumption is proportional to the fourth power of the distance (Hamad, Dag & Gucluoglu, 2023). The distance threshold is defined as:

(5) $$L_0=\sqrt{\frac{{\epsilon }_{FS}}{{\epsilon }_{AMP}}}\text{.}$$

Thus the total energy consumed when a node sends N bit of data is:

(6) $$E{N}_S=N\ast E_{en}+N\ast \beta (L)\text{.}$$

The energy consumed by a node to receive N bit of data is:

(7) $$E{N}_R=N\ast E_{en}\text{.}$$

Form topology

In the DADIE algorithm, BS is designated as the root node of the aggregation tree, and the topology construction starts from the BS. Here is a description of the process: (1) BS broadcasting: The process begins with the BS broadcasting an “invite” message to nodes within its communication range. This message serves as an invitation to nearby nodes, encouraging them to establish a secure channel and become child nodes of the BS. (2) Node response: Upon receiving the invitation message, eligible nodes respond with an “agree” message to indicate their willingness to establish a secure transmission channel and become a child node. These nodes meet certain criteria or conditions specified by the algorithm to be considered eligible. (3) Information exchange: After agreeing to become child nodes, the responding nodes transmit their location, initial energy, and other relevant information to the BS. This data exchange allows the BS to gather necessary information about the nodes. (4) Parent-child relationship: Once the BS receives the “agree” message from a node and receives its transmitted information, it stores the node’s information and designates the corresponding node as a child node. The BS becomes the parent node of these child nodes in the constructed aggregation tree.

By following these steps, the DADIE algorithm constructs the topology of the wireless sensor network, with the BS as the root node and other nodes as child nodes. This hierarchical structure facilitates efficient data aggregation and communication throughout the network. The algorithm flow is shown in Algorithm 1 and Part 1 of Fig. 2A.

Algorithm 1:

Child nodes of the BS join the topology tree.

Data: Sensor Nodes Set N, Data Transmission Radius R

1  set sizeof(Flag)=sizeof(N) and Flag= $\left\{0\right\}$ as a flag to join the tree or not;

2  set set of child nodes of BS, $B{S}_{child}\left\{\right\}$;

3  for $each{N}_i\in N$ do

4   BS sends “invite” message to Ni;

5   if distance of BS and $N_i<R$ and $Fla{g}_i=0$ then

6    Ni reply “aggre” message to BS, set BS as parent node;

7    BS set Ni as one of its child node;

8    Establising a secure transmission channel between BS and Ni;

9    Add node Ni to $B{S}_{child}\left\{\right\}$;

10    $Fla{g}_i=1$;

11   end

12  end

DOI: 10.7717/peerj-cs.1932/table-4

The distribution of nodes in a WSNs is depicted in Fig. 3A, along with the corresponding initial energy and position coordinates provided in Table 1. The BS, acting as the root node, is considered as the origin of the coordinate system (0,0). It initiates an “invite” message to the network, targeting nodes 1, 2, 3, and 4 located within its communication range. Upon receiving the “invite” message, these nodes respond with an “agree” message, providing their initial energy and coordinate position information to the BS. Additionally, they designate the BS as their parent node in the aggregation tree. Upon receiving this information, the BS stores the data and identifies these nodes as its child nodes. This process leads to the formation of the topology depicted in Fig. 3B, where the BS serves as the root node, and nodes 1, 2, 3, and 4 become its child nodes in the aggregation tree.

Table 1:

Initial energy and position coordinate of nodes in the example.

Sensor nodes	Initial energy [J]	Position coordinate
BS	$\mathrm{\infty }$	(0,0)
1	1.42 J	(−4,2)
2	0.92 J	(−2,3)
3	1.52 J	(0.5,5)
4	1.98 J	(4,3)
5	1.62 J	(−6,5)
6	1.51 J	(−3.5,6)
7	1.68 J	(2.5,6)
8	1.64 J	(5,6)
9	1.70 J	(6,4)

DOI: 10.7717/peerj-cs.1932/table-1

In the DADIE algorithm, intermediate nodes play a crucial role in sensing data, receiving data from leaf and child nodes, and aggregating the received data with their own data. They then transmit the aggregated result to their parent node. However, due to their increased responsibilities and data processing tasks, intermediate nodes, especially those closer to the BS, experience higher energy consumption, which can lead to premature node death. In order to achieve a balanced load of network energy and reduce node death rate as much as possible, make the initial energy value of intermediate nodes is as large as possible, also to make the data transmission distance of these nodes smaller. In addition, DADIE limits the number of children of each intermediate node and reassembles the aggregation tree before each round of data transfer. The algorithm is described as follows:

In DADIE, we introduce the parameter CHO, such that it serves as a measure of the node’s choice of child nodes; the parameter $MA{X}_{child}$ is introduced such that it acts as the maximum number of child nodes of the intermediate node.

(8) $$CHO=EN/L$$

EN is the initial energy of the node to be added to the aggregation tree, L denotes the distance between the node to be added to the aggregation tree and this selection node. L uses Euclidean distance calculations, X and Y denote the coordinates of the node.

(9) $$MA{X}_{child}=random(1,Num)$$

$Num$ indicates the number of nodes within communication range of this intermediate node that have not joined the aggregation tree. $random(a,b)$ denotes a randomly generated integer between a and b (include a and b).

To achieve the aforementioned goals, the DADIE algorithm follows a specific procedure. Initially, the BS establishes a secure channel with the child nodes. Starting from the child node with the highest CHO of the BS, it is designated as the selection node. The selection node then broadcasts “pre_invite” messages throughout the network. Nodes that receive the “pre_invite” message and have not yet joined the aggregation tree respond by providing information about their location and initial energy level with the message “agree” to the selection node. Upon receiving these messages, the selection node counts the number of nodes that sent responses, denoted as $P_{num}$. If $P_{num}$ is greater than or equal to 1, the selection node generates a random integer $MA{X}_{child}$ within the range from 1 to $P_{num}$, representing the maximum number of child nodes for a given node. The selection node then chooses the first $MA{X}_{child}$ nodes with the highest CHO values as its children and sends an “invite” message to these nodes. Nodes that receive the “invite” message acknowledge the selection node as their parent and establish a secure communication channel with it. In the case where $P_{num}$ is equal to 0, indicating no responses were received, the selection node becomes a leaf node directly.

Once the selection node completes its selection operation, the node with the highest CHO value among its sibling nodes, who has not yet performed the selection operation, becomes the new selection node. If all sibling nodes have completed the selection operation, the process is repeated with the child node with the highest CHO value among the sibling nodes who performed the selection operation first. This process continues until all child nodes have completed the selection operation. If there are still nodes that have not been included in the aggregation tree, the node with the highest CHO value in the aggregation tree is selected as the parent node by these nodes. The algorithm flow is shown in Algorithm 2. Part 2 of Fig. 2A is the process by which nodes in the network other than the children of BS join the aggregation tree and Fig. 2B is the selection operation, and selection operation is the operation that every leaf node performs when it is looking for a child node.

Algorithm 2:

Child nodes of remaining nodes join the topology tree.

1 ht

Data: Sensor Nodes Set N, Set of Child Nodes of BS $B{S}_{child}\left\{\right\}$, $Flag=\left\{\right\}$, Node Communication Radius R, Maximum Number of Child Nodes, $MA{X}_{child}$, Initial Energy EN, Position Coordinate, X, Y, L, CHO

2 set a queue $Queue\left\{0\right\}$ as the nodes order for finding child nodes;

3 set a set $Flag\mathrm{\_}Queue$= $\left\{0\right\}$ as flag of a child node of BS is added to $Queue\left\{\right\}$ or not;

4 while each $Flag\mathrm{\_}Queue$= $\left\{\right\}$ of $B{S}_{child}\left\{\right\}$ !=1 do

5  select the node in $B{S}_{child}\left\{\right\}$ with the most CHO and $Flag\mathrm{\_}Queue\left\{\right\}$ is 0 to join $Queue\left\{\right\}$;

6  set this node $Flag\mathrm{\_}Queue\left\{\right\}$ to 1;

7 end

8 set the queue’s head pointer is head;

9 set the queue’s tail pointer is tail;

10   set $P_{num}=0$;

11   head and tail point to the head and tail of $Queue\left\{\right\}$ respectively;

12   while $head\le tail$ do

13   $P_{num}=0$;

14   $Queue\left\{head\right\}$ sends “pre_invite” message to N;

15  for $each{N}_i\in N$ do

16   if distance of $Queue\left\{head\right\}$ and $N_i\le$ R and $Fla{g}_i=0$ then

17    Ni reply “aggre” message with location and energy information to $Queue\left\{head\right\}$;

18    Pnum=Pnum+1;

19   end

20  end

21  if Pnum>0 then

22    $MA{X}_{child}$=random(1,Pnum);

23   for $each{N}_i\in N_{P_{num}}$ do

24     $L_{N_i}=\sqrt{{(X_{N_i}-X_{Queue\left\{head\right\}})}^2+{(Y_{N_i}-Y_{Queue\left\{head\right\}})}^2}$;

25     $CH{O}_{N_i}=E{N}_{N_i}/L_{N_i}$;

26    end

27    $Queue\left\{head\right\}$ sends “invite” message to top $MA{X}_{child}$ of CHO in Ni;

28   set these nodes $Fla{g}_i=1$;

29   set these nodes into $Queue\left\{\right\}$ by CHO;

30   set these nodes $Flag\mathrm{\_}Queue=\left\{\right\}$ to 1;

31   tail point to $tail+1$;

32  end

33  else

34   head point to $head+1$;

35  end

36 end

DOI: 10.7717/peerj-cs.1932/table-5

As shown in Figs. 3C and 3D, the BS computes the CHO for all its child nodes. Among the child nodes of the BS, node 4 has the largest CHO value. Node 4 then broadcasts a “pre_invite” message to the network. Nodes 7, 8, and 9, which are within the communication range of node 4, respond to the “pre_invite” message by sending an “agree” message that includes their position and initial energy information. Node 4 receives these “agree” messages and counts the number of received responses, denoted as $P_{num}$. Since $P_{num}$ is greater than 1, node 4 generates a random integer $MA{X}_{child}$ between 1 and $P_{num}$. This value determines the maximum number of child nodes for node 4, which in this case is $MA{X}_{child}=3$. Subsequently, node 4 sends an “invite” message to nodes 7, 8, and 9, designating them as its child nodes and establishing a secure transmission channel with them. Nodes 7, 8, and 9 acknowledge node 4 as their parent and join the topology tree upon receiving the “invite” message. Once this operation is completed, the child node of the BS with the largest CHO value, which has not yet initiated the invitation operation, is node 1. Node 1 then starts the invitation operation by sending a “pre_invite” message to nodes 5 and 6 within its communication range. Nodes 5 and 6, which have not joined the aggregation tree, respond to node 1 with their location and initial energy information in an “agree” message. Node 1 counts the number of received “agree” messages, denoted as $P_{num}$. Since $P_{num}$ is greater than 1, node 1 generates a random integer $MA{X}_{child}$ between 1 and $P_{num}$. In this case, $MA{X}_{child}=1$, indicating that node 1 can have at most one child node. Node 1 calculates the CHO values of nodes 5 and 6, and selects the node with the highest CHO value to send an “invite” message. It establishes a secure transmission channel with the selected node and designates it as its child node. Node 5, upon receiving the “invite” message from node 1, acknowledges node 1 as its parent and joins the topology tree. The above operations are repeated by node 2 and node 3 in sequence.

After all the child nodes of the BS have completed the above operation, among the child nodes of the node that first started the above operation among the child nodes of the BS, the node with the largest CHO is selected to repeat the above operation until all the nodes in the network have completed the above operation. The final topology is shown in Fig. 3E.

Slicing and mixing

To improve the privacy protection of the network and minimize the risk of data being intercepted by malicious attackers, it is recommended to slice-and-mix the data of leaf nodes before transmission. During this phase, all leaf nodes in the aggregation tree slice their sensory data into J (J $\ge$ 2) fragments. The leaf nodes retain one fragment as their transmission data and randomly transmit the remaining J-1 fragments to J-1 neighboring nodes (except for the parent node). The receiving node aggregates the received data fragments with its own data and employs the resulting aggregation as its transmission data. The value of J can either be pre-set in the node or broadcasted to each node in a flooded manner by the BS. The pre-set method reduces unnecessary communication consumption in the network but is less flexible, while the flooded method enhances flexibility but increases the network communication load. In DADIE, we opt for the pre-set method to establish the value of J. The execution process is as Part 3 of Fig. 2A.

As depicted in Fig. 4A, the number of fragments J is set to 3, and the leaf nodes in the network are node 5, 6, 3, 7, 8, and 9, $f(j,i)$ denotes the size of the data fragment received by node $i$ from node $j$. During this phase, each leaf node slices its data into three fragments, retaining one fragment as its transmission data and transmitting the other two fragments to neighboring nodes. For instance, node 5 transmits fragment f(5,6) to neighboring node 6 and fragment f(5,2) to node 2, and the remaining leaf nodes follow a similar protocol. It should be noted that if a leaf node receives a data fragment from another leaf node before its fragment transmission, the received data fragment will be directly incorporated into the leaf node’s data fragments, and the sensor data will be sliced into the residual number of fragments. For example, in Fig. 4B, node 6 has received fragment f(5,6) from node 5 before its fragment transmission, thus requiring node 6 to slice its data into two fragments, mix them with the received data fragment from node 5, and transmit two fragments to neighboring nodes 5 and 3. However, it is crucial to ensure that the fragment received by a node is not transmitted to the neighboring node that sent the fragment, to avoid data redundancy.

Following the completion of fragment transmission, the nodes in the aggregation tree aggregate the received data fragments with their own data, as demonstrated in Eq. (10) (where $D_{N_i}$ denotes the transmission data of node $i$, $k$ denotes the number of data fragments received by node $i$, and $f(j,i)$ denotes the size of the data fragment received by node $i$ from node $j$, ‘+’ denotes stitching data together), to generate the transmission data for that particular node, as illustrated in Fig. 4B.

(10) $$D_{N_i}=D_{N_i}+{\displaystyle \sum _{j=1}^k{f}_{(j,i)}}$$

Data transmission

During this phase, DADIE implements the transmission of data from the sensor network nodes to the BS. The leaf node of the aggregation tree transmits its aggregation result to the parent node through a secure transmission channel, and the intermediate node receives data from the child node, aggregates the received data with its own data to generate a new aggregation result, and subsequently transmits it to the parent node. The parent node repeats this operation until the data reaches the BS. As depicted in Fig. 5 and part 4 of Fig. 2A, nodes 7, 8, and 9 transmit the result of data mixing to their common parent node, node 4. Upon receiving data from child nodes, node 4 aggregates its data with data from child nodes and transmits the aggregation result to the parent node of node 4, i.e., the root node BS. The data volume of each node is calculated using Eq. (11) (where $D_{N_i}$ denotes the transmission data of node $i$, $m$ denotes the number of child nodes of node $i$, and $D_{N_j}$ represents the volume of transmission data from node $j$ to $i$.).

(11) $$D_{N_i}=D_{N_i}+{\displaystyle \sum _{j=1}^m{D}_{N_j}}.$$

Security analysis

The data aggregation approach employed in this study utilizes the slice-and-mix technique and establishes secure transmission channels at nodes. It also reconstructs the aggregation tree before each round of data transfer, making it exceedingly difficult for an attacker to obtain all the data of a node in the network.

In one round of data aggregation in the DADIE algorithm, a leaf node partitions its data into J fragments. One fragment is retained by the leaf node, while the remaining fragments are transmitted to randomly selected neighboring nodes. Thus, the links of leaf nodes include both links for transmitting leaf node fragments and links between leaf nodes and their parents. To compromise the security of a leaf node, an attacker must crack all the links associated with that node. The probability of data leakage of leaf nodes $P_{lea{f}_i}$ is:

(12) $$P_{lea{f}_i}=P_{lost}^{J-1}\times P_{lost}^{J_i^{rec}}\times P_{lost}^{nu{m}_{father}}=P_{lost}^{J+J_i^{rec}}$$where $i$ denotes any leaf node, $P_{lost}$ denotes the probability of one link that belongs to this node is broken, $J_i^{rec}$ denotes the number of data fragments received by this node, $nu{m}_{father}$ denotes the number of parent nodes of this node and always equal to 1.

The link of the intermediate node of DADIE includes its links to the child nodes and the links that receive data fragments from other leaf nodes, so the probability of data leakage of the intermediate node $P_{inte{r}_i}$ is:

(13) $$\begin{array}{l}{P}_{inte{r}_i}=P_{lost}^{nu{m}_{child}}\times P_{lost}^{J_i^{rec}}\times P_{lost}^{nu{m}_{father}}\\ =P_{lost}^{nu{m}_{child}+J_i^{rec}+1}\end{array}.$$where $nu{m}_{child}$ denotes the number of child nodes of this intermediate node.

The above description analyzes the security of DADIE in one round of data transmission, however, the data transmission topology tree is reconstructed before each round of data transmission, so even if all the data of a node is captured, it does not affect the privacy protection of the whole network.

Communication and energy analysis

In the DADIE algorithm, we mainly consider the communication overhead and energy consumption in three phases: formation of topology, slicing and mixing, and data transmission.

Simulation environment configuration

In real-world production scenarios, wireless sensor networks often consist of a large number of nodes deployed over a wide geographical area. To simulate such network structures, we conducted simulation experiments using MATLAB 2017a. We utilized the WNSs scenario and sensor node parameters provided by the Intel Berkeley Research Lab, as referenced in Samuel (2004). In our simulation, we deployed N = 300 sensor nodes within a 100 m × 100 m area denoted as G. Each sensor node, including the BS, had a sensing radius R of 10 m. The initial energy EN of the sensor nodes varied between 0.5 J and 2 J. Based on the specifications outlined in Kavitha et al. (2023), we assumed that the Mica2Dot sensors collected network information and sensory data (e.g., temperature, humidity, voltage, light) every 31 s. The sensory packet size for each node was set to 8,000 bits, while the information packet size was 40 bits. The energy consumption per bit for sending or receiving data was 50 nJ, and the energy consumption for processing data was 5 nJ/bit. During the experiments, we investigated the impact of varying the value of J, representing the number of fragments, using the values 3, 4, 5, and 6. After analyzing the results, we determined that the network achieved the lowest energy consumption while maintaining security when J = 3. To ensure the reliability of our findings, we conducted 20 independent experiments, each with a unique distribution of nodes within the network. The reported experimental data represents the average results obtained from these 20 experimental runs.

To provide a comprehensive overview of the simulation settings, we present the complete parameter configurations in Table 3. This table includes information such as the number of nodes, the geographical area, the sensing radius, the initial energy levels, the sizes of sensory and information packets, the energy consumption values, and the chosen value of J.

Privacy-preserving

A comparison of the simulation results for the proportion of node data leakage is presented in Fig. 6, depicting the performance of the EPDA, PECDA, and DADIE algorithms. The horizontal axis represents the probability of communication links between nodes being compromised, while the vertical axis represents the average proportion of cracked links in the wireless sensor network across 20 independent experiments. This measurement reflects the increase in the proportion of cracked links as the probability of link loss for a node rises.

The EPDA algorithm aims to reduce the number of leaf nodes in the network, which in turn reduces the number of data fragments. However, this algorithm organizes the network topology in a chain structure, resulting in a higher number of intermediate nodes and fewer child nodes for each intermediate node. As intermediate nodes lack data slicing operations, there is an increased likelihood of data leakage at these nodes compared to leaf nodes. This higher probability of data leakage at intermediate nodes can potentially compromise the privacy of the entire network. On the other hand, both the PECDA and DADIE algorithms have a higher number of leaf nodes and a lower number of intermediate nodes. This results in more child nodes participating in data slice-and-mix operations, reducing the probability of data leakage. The PECDA algorithm, however, considers the temporal correlation of sensory data during continuous transmission. This means that some leaf nodes may transmit data fragments to the same destination node in different transmission rounds, increasing the probability of data leakage from these nodes. In contrast, the DADIE algorithm dynamically rebuilds the aggregation tree before each round of data transmission. This ensures that leaf nodes randomly select sliced transmission object nodes from neighboring nodes in each transmission round. This random selection process enhances privacy preservation by reducing the predictability of data transmission paths. As a result, the DADIE algorithm demonstrates slightly better privacy preservation compared to PECDA. The percentage curve of links cracked for the DADIE algorithm shows a flat upward trend and is lower than that of PECDA and EPDA. This indicates that DADIE provides improved privacy preservation performance compared to the other two algorithms.

Overall, experimental results demonstrate that the DADIE algorithm is more efficient and robust in preserving privacy in wireless sensor networks. Its dynamic tree rebuilding and random selection of transmission object nodes contribute to enhanced privacy protection compared to PECDA and EPDA.

Communication overhead and energy consumption

In wireless sensor networks, the communication overhead and energy consumption are influenced by several factors, including the number of nodes, the number of slices, and the network topology. To compare the communication overhead and energy consumption of the three algorithms (PECDA, EPDA, and DADIE), we conducted experiments while controlling the number of sensor nodes and the number of leaf node slices.

In our experiments, we varied the number of nodes in the network from 300 to 1,000, with increments of 100 for each experimental run. This allowed us to observe the impact of network size on communication overhead and energy consumption. Additionally, we varied the number of leaf node fragments from 2 to 6 while keeping the network size fixed at 300 nodes. This enabled us to analyze the effect of the number of slices on the performance of the algorithms.

Figure 6 shows the results of the experimental comparison. The EPDA involves organizing the subtrees of intermediate nodes in the sensor network’s tree topology into a chain structure. This approach reduces the number of leaf nodes in the network, thereby minimizing the number of fragment transmissions and achieving the goal of reducing communication overhead and conserving energy. However, while reducing the number of leaf nodes, EPDA increases the number of intermediate nodes, leading to more data transmission between them and increasing the number of layers in the topology tree. As a result, data transmission to the BS requires more hops, resulting in a greater communication overhead and energy consumption in the network compared to the PECDA and DADIE algorithms.

PECDA algorithm considers the temporal correlation of data during continuous data sensing transmission in WSNs. Specifically, when a leaf node transmits sensory data, PECDA checks whether the difference between the sensed data of two consecutive rounds of data transmission is less than a threshold. If the difference is below the threshold, the node broadcasts a marker signal (1 bit) instead of transmitting the sensed data in the current round. This signal instructs the receiving node to use the base data (typically the data transmitted in the previous round) as the data transmitted in the current round. This approach reduces communication overhead and energy consumption in the network. As a result, when the number of sensor nodes in the network is small, DADIE’s performance is comparable to PECDA. However, as the number of nodes in the network increases, DADIE’s communication overhead and energy consumption gradually become slightly higher than that of PECDA. This can be attributed to the fact that intermediate nodes consume more energy in wireless sensor networks. To address this issue, the DADIE algorithm selects intermediate nodes based on both the transmission distance and the initial energy level, aiming to extend the network’s lifetime. By maximizing the utilization efficiency of intermediate nodes and extending their lifetime, DADIE reduces the number of layers in the tree topology. Consequently, the number of data transmissions from intermediate nodes to other intermediate nodes is significantly reduced, resulting in a notable decrease in communication overhead and energy consumption in the network.

As illustrated in Figs. 7A and 7C, When the number of node slices is constant, DADIE exhibits lower communication overhead, less energy consumption and better network performance as the number of nodes in the network increases. Furthermore, as depicted in Figs. 7B and 7D, when the number of nodes in the network is fixed, the communication overhead and energy consumption of DADIE are always lower than PECDA and EPDA, regardless of the number of slices used.

Network lifetime

To compare the network lifetime of the DADIE, PECDA, and EPDA algorithms, the simulation system conducts 100 rounds of data aggregation operations for each algorithm under the same conditions. The node extinction rate is recorded for each aggregation algorithm in different rounds.

Figure 8 depicts a wireless sensor network comprising 300 randomly distributed nodes within a 100 m × 100 m area, with initial energy values ranging between [0.5, 2] J. The EPDA, PECDA, and DADIE algorithms are compared based on the number of node deaths in the network during varying cycles of data aggregation. As the number of data transmission cycles increases, both the EPDA and PECDA algorithms exhibit a rapid increase in node deaths. However, due to PECDA’s consideration of the temporal correlation of sensed data during continuous data sensing, it achieves a lower node death rate compared to EPDA, effectively conserving network energy. EPDA forms subtrees of intermediate nodes in the network topology, resulting in a chain-like structure that increases the number of hops required for node data transmission to reach the BS. Consequently, this places a heavier load on intermediate nodes near the BS, leading to a rapid increase in the number of node deaths. Conversely, in the DADIE algorithm, the integration of distance and energy allows for the involvement of intermediate nodes with higher initial energy levels and smaller distances from the BS in a greater number of data aggregation and transmission operations, while leaf nodes with lower energy levels participate in fewer operations. As a result, the number of node deaths in the DADIE algorithm exhibits a smoother and slower growth pattern.

As shown in Fig. 8, the node death rate of the DADIE algorithm is approximately 10–30% lower than that of EPDA and PECDA. This indicates that DADIE effectively achieves a balanced network energy load in WSNs, prolonging their lifetime and exhibiting excellent stability.