# Secure Localization in the Presence of Colluders in WSNs
## 1 Introduction  
In a wireless sensor networks (WSNs), several small devices (hereinafter referred to as sensor nodes) collaboratively exchange information. Most existing WSN applications include environmental monitoring [1] and tracking of goods and people [2]. WSNs usually work in a hostile environment. Therefore, they are vulnerable to various malicious attacks such as cyber attacks [3] and wormhole attacks [4]. In several WSN applications, the ability to localize a sensor plays a critical role [4; 5; 6; 7; 8; 9; 10; 11]. Most of these applications are complemented by geographic routing and location-based authentication which, in turn, require node position determination techniques. If such a process does not include security measures, the WSN will eventually suffer from location-based threats conducted by adversarial scenarios, including both Sybil and sinkholing attacks [12; 13]. Attacks to the localization process may successfully interfere with the objectives of a given WSN application. Consider, for instance, a WSN-based system that monitors forest fires. Localization errors can incorrectly report in which precise geographic area to intervene. Similarly, erroneous positioning in critical infrastructure scenarios can report incorrect information to security and safety operators. It is thus crucial to use a secure localization algorithm, in order to guarantee the accuracy of the reported position of the nodes of a WSN. Localization involves two steps: first, acquiring data, and then conducting position calculation. During either of these two steps, an (internal or external) [14] attack can disrupt the localization process by having a node either sending false information or by simply replaying data previously obtained under normal operations. Either case may disrupt the system, since the network may end upwith nodes advertising geographical positions that have been wrongly computed. Security measures have been created to mitigate the impact of these attacks. However, issues pertaining to collusion remain: (1) How do colluders work together? and (2) To which extent can they interfere with the localization process? Collusion may take many forms in a WSN. Collaborating attackers could announce false information in a coordinated manner and/or position themselves into evasion patterns (for example to disclose collinear positions that fool detection). Both cases may result in calculating an incorrect position for a node. Additionally, such attackers could target other data such as the reputation lists used in several locational algorithms [15; 16; 17; 18]. Such a possibility is downplayed in current approaches to localization. Indeed, it is often assumed that (a) such reputation lists are incorruptible and that (b) coordination of adversarial nodes does not affect the localization process. Some existing studies do consider collusion, that is, they assume that a group of malicious sensor nodes does collaborate to alter the information they exchange with (i.e., receive from and forward to) other nodes. They number few and are limited. Let us elaborate. First consider the situation where the adversaries evade detection by positioning themselves at 'blind' positions of the detection algorithm [16]. For example, an evil ring attacker _era_ (_ibid._) fools location-unknown nodes that rely on trilateration to compute their geographic location using _era_'s position. Such an attack is not detectable by algorithms that detect _simple liars_, where a'simple liar' is taken to be a sensor that sends out randomly generated fake coordinates to its neighbours. We have presented elsewhere [16; 19] an algorithm able to detect and handle a single evil ring attacker. We emphasize that this algorithm cannot handle localization in the presence of multiple evil ring attackers. We also remark that the few techniques that exist in the literature to handle colluders (hereafter also referred to as colluding attackers or colluding sensors) cannot handle the evil ring attack.