# On Modeling Eavesdropping Attacks in Underwater Acoustic Sensor Networks +
## 1 Introduction
### Related Works  
There are a number of studies on UASNs. In particular, a review of the early history of the acoustic underwater communication was presented in [2]. Research advances and challenges in underwater sensor networks with acoustic communications were summarized in [3]. Generally, the studies on UASNs can be mainly divided into three categories. The first category focused on analyzing the performance of UASNs [4; 5; 6; 7]; the second category focused on improving the network performance in Medium Access Control (MAC) layer [8; 9; 10]; the third category focused on designing routingschemes [11; 12; 13]. Underwater cognitive acoustic networks were proposed in [14] to improve the spectrum reuse of acoustic communications. However, there are few studies investigating the network security of UASNs. In particular, a novel secure scheme was proposed to secure the underwater acoustic sensor networks in [15]. The wormhole attack was investigated in [16]. One of vulnerabilities of UASNs was found in [17] that UASNs are suffering from denial-of-service jamming attacks.  
On the other hand, as one of the typical security threats in _terrestrial_ wireless sensor networks, eavesdropping attacks have received extensive attention recently. It is difficult to detect the eavesdroppers since they just passively wiretap the transmissions without disclosing their existence. Many malicious attacks often follow the eavesdropping activities [18]. Encryption is one of the most commonly used techniques to protect the confidential communications in cellular networks (e.g., Cellular Message Encryption Algorithm [19]), wireless local area networks (e.g., WEP [20], WPA and WPA2 [21]) and wireless personal area networks (WPAN) [22]. However, encryption algorithms may not be feasible to wireless sensor networks since sensor nodes have the energy constraints and computational constraints [23].  
In addition to message encryption, there are a number of anti-eavesdropping countermeasures [24; 25; 26; 27; 28; 29; 30; 31; 32]. In particular, it is shown [24] that to adjust transmitting power can reduce the eavesdropping risk. Besides, [26; 27; 28; 29] found that using directional antennas in wireless sensor networks can enhance the security. Moreover, to deliberately send spurious messages or (dummy data) [25] can also effectively reduce the eavesdropping success rate. Other anti-eavesdropping schemes include the use of defensive jammers [31; 32] to protect the normal transmissions.  
It is necessary to investigate the eavesdropping behaviors conducted by eavesdroppers since we can offer better protection on the confidential communications if we have a better knowledge on the eavesdroppers [33; 34]. For example, we only need to encrypt the communications in the area or the direction that is vulnerable to eavesdropping attacks so that the security cost can be significantly saved.  
However, to the best of our knowledge, there is no study on investigating the eavesdropping attacks in UASNs. The previous analytical models on investigating the eavesdropping activities in terrestrial wireless sensor networks [30; 35] can not be used to UASNs due to the different features of acoustic signals in underwater environments. For example, the path loss effect of an underwater acoustic channel depends on both the distance and the signal frequency. However, the terrestrial radio channel is independent of the radio signal frequency. Therefore, this is the goal of this paper to establish a novel analytical model and to investigate the eavesdropping activities in UASNs.