## 1 Introduction  
In recent years, underwater acoustic networks (UANs) have been widely used in marine pollution monitoring, aided navigation, resource exploration, and military fields [1]. UANs are deployed underwater and composed of numerous sensor nodes, autonomous underwater vehicles, and unmanned underwater vehicles [2, 3]. UANs use sensors to collect the physical information of the water, such as temperature, depth, and salinity, and transmit the information to a sink node in a multi-hop manner. Then, the sink node sends the information to the server using the radio signal for data analysis. Usually, research concerning UANs includes topology control, node localization, routing and MAC protocol, reliable transmission, etc. However, compared with terrestrial wireless sensor networks, the following characteristics of UANs bring significant challenges for node deployment, protocol design, and reliable transmission. 1. The propagation speed of the acoustic waves in water is 1500 m/s, which leads to a long propagation delay. 2. The channel error rate is high due to the influence of the Doppler effect, path loss, ship noises, etc. 3. The acoustic signals can decay with increasing transmission distance when transmitted underwater; the exponential decay factor increases with increasing frequency;thus, low-frequency signals are more preferable for long-range communications, which results in a low bit rate. 4. The underwater node is powered by the battery, and it is difficult to recharge or replace the battery in harsh underwater environments, which results in the energy of the node being limited. However, underwater acoustic modems consume more energy in packet transmission than terrestrial radio frequency modems. 5. The nodes move autonomously or with the water flow or other activities, which leads to a dynamically changing network topology [4; 5; 6]. These characteristics have a significant effect on the protocol design as well as the performance of the designed protocol. In addition, the opening and sharing of underwater acoustic channels also bring about great challenges to the reliable transmission of UANs. Nodes of UANs are deployed underwater and are unguarded, and they are easily captured as malicious nodes (MNs), which expose the network to threats and attacks. For example, an MN may flood HELLO packets (HELLO packets are also called beacon messages, which are usually used for neighbor discovery and routing maintenance. In our proposed protocol, HELLO packets are also used for configuring the layer of nodes. The details are provided in Section 3) in the network. The malicious HELLO packets have the following negative impacts. (1) Many collisions occur in the network, which decreases the packet delivery rate. (2) Other nodes are subject to forward malicious HELLO packets, which results in low energy efficiency. (3) Data packets from sensor nodes are transmitted probably to the MNs instead of the sink node. The above-mentioned is a typical HELLO packet flooding attack. Beyond that, there are black hole attacks, selective forwarding attacks, etc. All of these can lead to severe network bandwidth consumption, energy consumption, and channel utilization reduction. Therefore, it is necessary to design trust-aware routing protocols to defend against MN attacks and threats to UANs. In this view, some defensive mechanisms and secure routing protocols, such as an energy-efficient key agreement mechanism [7], a secure and reliable multi-path transmission scheme [8], a secure routing scheme [9], and a secure routing protocol based on depth [10] have been investigated and developed. The existing defensive and security mechanisms can be divided roughly into intrusion protection, intrusion detection, and intrusion tolerance mechanisms. In intrusion tolerance mechanisms, trust evaluation is not only a powerful means to ensure the reliability of routing but also an effective supplement to encryption algorithms and authentication mechanisms in the view of security. [PERSON] et al.