As deployment of wireless ad hoc networks for location-based services increases, accurate localization of mobile nodes is becoming more important. Localization of a mobile node is achieved by estimating its distances from a group of anchor nodes. If some anchors are malicious and colluding, localization accuracy cannot be guaranteed. In this article, we present the security conditions for exact localization in the presence of colluding malicious anchors. We first derive the minimum number of truthful anchors that are required for exact localization in 2-D Euclidean space where some anchors may be collinear. Second, we extend our security condition to 3-D localization where some anchors may be coplanar.