# Secure Localization in the Presence of Colluders in WSNs
## 2 Related Work
First, provers must properly compute their distance with regard to honest verifiers, including those situations in which adversaries exist. Second, provers must compute upper bounds on their distance to dishonest verifiers, also including situations where colluders do exist. If the aforementioned premises hold, then provers may mutually authenticate verifiers by using cryptographic solutions (global synchronization of messages is required). Positioning algorithms in [27; 28; 29] enable location-unknown nodes to geolocate their coordinates in a WSN despite the presence of malicious anchor nodes lying about their position in the network. A firstalgorithm, referred to as _majority-three neighbour signals_, uses trilateration to calculate the position of location-unknown nodes [30]. The algorithm relies on the use of majority decision rules to obtain the positions. Triplets determining a location in disagreement with the majority are considered to contain malicious anchor nodes. In [16], an attack referred to as _evil ring_ is presented against the _majority-three neighbour signals_ algorithm. Attackers are assumed to provide wrong positions, while remaining undetectable by the _majority-three neighbour signals_ since the victims of the attack derive consistent positions with the majority. When asked, the malicious nodes report fake positions that sit on a circle centred at the victim's location and with a radius corresponding to the distance separating attackers and victims. The calculation of the distance between attackers and victims remains consistent. Thus, location-unknown sensor nodes correctly determine their location but fail at properly identifying the position of that malicious node. This is because an evil ring attacker is a'smart liar' that does not merely send out randomly generated fake coordinates to its neighbours (which is what a simple liar does). Instead, an evil ring attacker computes a special location that will further interfere with the localization computation of other sensors. Such behaviour is undetectable by any sensor running any of the previous detection algorithms that use trilateration to determine sensor position and detect liars. The algorithm presented in [16] handles the localization issue by _cross-checking_ the information provided by an evil ring attacker. More precisely, the solution relies on requesting the locations of all neighbouring nodes and computing every possible three-neighbour combination using majority decision rules. Then, a list is created to store all those triplets that agree with the majority. The computed position and the cross-check lists are broadcasted to neighbours, which allows for the detection of the evil ring attacker (i.e., the smart liar). Sensor nodes wait until they receive the equivalent lists from two other neighbours and compare the results. Every neighbouring node that is consistently reported with the same position in the three lists is reported as truth-teller--or as a liar otherwise. The proposals presented in [16; 27; 28; 29] assume collusion-free dense networks. The absence of collusion in TMCA and in the _evil ring_ attack is a typical assumption. As previously mentioned, very few studies pertaining to secure localization have investigated attacks perpetrated by colluders. Let us consider models that do address collusion, for example, the solution presented in [31]. This solution assumes location information that can be received and forwarded by collaborating malicious nodes. However, as mentioned in the previous section, this solution fails to detect an evil ring attack and has other limitations.