Security against Sybil Attack in Wireless Sensor Network through Location Verification

A new functional for planar triangulation called Inner Core has been proposed in [4] for a location verification based defense against Sybil attack for sensor network, and also has been shown that the legitimacy of a new node inside the Inner Core of a triangle obtained by the triangulation of the set of sensor nodes can be established. In [4] it has been conjectured that Inner Core of a triangulation of a set of planar points achieves its maximum for Delaunay triangulation. In this paper, we present a formal proof of the conjecture. In order for the protocol proposed in [4] to work, what is required is an empty triangle formed out of three existing sensor nodes in whose Inner Core new node claims its presence. We present here an algorithm to find out such an empty triangle, so that it can be used for checking the legitimacy of the new node.