Constructing Disjoint Paths for Secure Communication

We propose a bandwidth-efficient algorithmic solution for perfectly-secure communication in the absence of secure infrastructure. Our solution involves connecting vertex pairs by a set of k edge-disjoint paths (a structure we call a k-system) where k is a parameter determined by the connectivity of the network. This structure is resilient to adversaries with bounded eavesdropping capability. To ensure that bandwidth is efficiently used we consider connection requests as inputs to the kEdge Disjoint Path Coloring Problem (k-EDPCOL), a generalization of the Path Coloring Problem, in which each vertex pair is connected by a k-system, and each k-system is assigned a color such that two overlapping k-systems do not have the same color. The objective is to minimize the number of colors. We give a distributed and competitive online algorithm for k-EDPCOL. Additionally, since security applications are our focus we prove that a malicious adversary which attacks the algorithm during the process of construction of a k-system cannot learn anything more than if it had attacked the k-system once it was built.