# Secure Localization in the Presence of Colluders in WSNs
## 6 Experimental Results
### Second Set of Simulations: Random Deployment of Nodes  
In this section, we report numeric simulation in which all sensor nodes, both regular location-known and location-unknown nodes, are positioned at random. As in the uniform deployment case, any regular location-known sensor can be a colluder. Figure 7 depicts a sample random deployment of 44 sensor nodes, consisting of 34 location-known nodes and then nodes of type location-unknown. Of the 34 location-known nodes, 15 are acting as colluder nodes. Black-patterned white dots represent location-unknown nodes executing algorithm CC or SCC. White-patterned black dots represent regular location-known nodes acting as truth-telling sensors. Finally, grey dots represent colluder nodes. Solid black circles represent the communication range of the location-unknown sensor nodes.  
Figure 5(b) contains the simulation results. Each simulation corresponds the deployment of eighty nodes of type non-colluders, and ten nodes of location-unknown type. An incremental number of additional location-known sensors act as colluders. The percentage of colluders is presented in proportion to the number of location-known sensors acting as truth-telling nodes (e.g., 10% of colluders means a WSN with eight location-known sensors acting as colluders in addition to the eighty nodes of type location-known acting as non-colluders; and ten regular nodes of type location-unknown). Results  
Figure 5: Comparative representation of the successful detection rate with regard to the super cross-check (SCC) algorithm and the cross-check (CC) algorithm. _Advantage_ represents the difference between the success rate of the SCC and CC algorithm results. (**a**) Uniform deployment; (**b**) Random deployment. WSN: wireless sensor network.  
Figure 6: Comparison of colluder detection failures in the uniformly deployed WSN simulations. _Failure type_ 1 refers to a final CC list that is empty. _Failure type_ 2 refers to a non-empty final CC list containing, at least, one attacker. _Failure type_ 3 means a non-empty final CC list containing exactly one attacker. (**a**) CC algorithm; (**b**) super cross-check algorithm.  
focus on the worst case, i.e., the case in which colluders are positioned randomly and uniformly within the WSN. Results are measured using 100 runs per percentage-of-attacker case and 95% confidence intervals. The SCC and CC curves in Figure 5b show the success rate of randomly positioned location-unknown nodes at detecting colluders after executing either algorithm. Success means that all neighbouring attackers of a location-unknown sensor node are successfully identified and removed from a final list of truth-telling nodes prior computation of the routing tables. The _advantage_ curve in Figure 5b represents the difference between the success rate of SCC and CC. We can see from this curve that the detection success rate of SCC is superior to the detection success rate of CC under the random sensor deployment scenario. The very narrow 95% confidence intervals of the simulation results reflect the stability of the two algorithms in the random case.