## 3 Network Model and Acoustic Propagation Model  
### Network Model  
A three-dimensional heterogeneous UWSN is considered. In other words, underwater sensor nodes have different initial energy and different computing, communication, and storage capabilities. The closer the sensor nodes are to the base station, the more energy and storage space is available, so as to balance the energy consumption ratio of the whole network. As shown in Figure 1, the sensor nodes are randomly deployed underwater, and the base stations (or sink nodes) are deployed on the water surface. The packets are transmitted to the surface base station via OR. Only if the distance between two sensor nodes is within the communication radius, can they communicate, and can the sender monitor the nodes in its candidate forwarding set. We adopt a local monitoring mechanism where each node except the neighbor nodes of the sink node is embedded with DOIDS to supervise and detect nodes in its candidate forwarding set. The type of nodes is decided based on the sliding time window to avoid the attacker from being the node with the highest priority.  
* Assume that there are no malicious attacks in the initial stage of network deployment. This assumption is reasonable because the routing attack node is an internal attack. In order to successfully attack UWSNs, it takes a period of time for the internal attack to obtain identity authentication and become a legitimate member of the network.
* Assume that the number of routing attack nodes in the marine application scenario is small. In this paper, the number of malicious nodes is considered to be no more than 20% of the total number of nodes. The node set of UWSNs can be defined as: \[N=\left\{n_{1},n_{2},\cdots n_{i},\cdots n_{m}\right\}\] (1) where \(n\) and \(m\) represent sensor nodes and the number of nodes, respectively. The candidate node set monitored by node \(n_{i}\) in a monitoring slot is defined as: \[C_{i}=\left\{c_{1},c_{2},\cdots c_{j},\cdots c_{k}\right\}_{i}\] (2) where \(c_{j}\) represents the node monitored by supervisory node \(n_{i}\), and \(k\) is the number of candidate nodes. As shown in Figure 1, during data transmission, node \(n_{1}\), \(n_{3}\), and \(n_{6}\) have next-hop nodes other than the sink, so they are supervisory nodes. Taking node \(n_{3}\) as an example, within its communication range, each node that can be used as its next hop under certain conditions is a candidate node of \(n_{3}\). That is, the node set \(\left\{n_{5},n_{6}\right\}\) that will be defined as \(\left\{c_{1},c_{2}\right\}_{3}\) is candidate node set of supervisory node \(n_{3}\).  
This paper mainly considers the following common attacks in the process of data routing, which pose a certain threat to the security of opportunistic routing:  
* Sinkhole attack. It can attract the traffic of the surrounding nodes by forging the distance from the surface base station, which leads to network congestion. It may forward the tampered packet information by disguising its high priority, which affects data correctness.
* Sybil attack. It can use multiple false identities to control or influence a large number of normal nodes in the network. For example, different identities are used to forward the same packet many times, so that the packet falls into a routing loop, increasing end-to-end delay and even causing packet loss.
* Hybrid attack. Malicious nodes embedded in different routing attacks can switch attack modes over a period of time. Sinkhole attack and Blackhole attack alternately, for example.
* On-off attack. Malicious nodes periodically launch attacks to evade detection.