On the optimal design of secure network coding against wiretapping attack

In this paper, we study the optimal design of weakly secure linear network coding (WSLNC) against wiretapping attack. Specifically, given a set of wiretapped links, we investigate how to maximize the weakly secure transmission rate of multiple unicast streams between a pair of source and destination nodes, and how to minimize the size of the required finite field, over which the WSLNC can be implemented. In our study, we apply a novel approach that integrates the WSLNC design and the transmission topology construction. We first provide theoretical analysis and prove that the problem of finding the optimal transmission topology is NP-hard. We then develop efficient algorithms to find optimal and sub-optimal topologies in different scenarios. With the transmission topology, we design WSLNC schemes and theoretically analyze the relationships between the transmission topology and two important system factors: (1) the size of the finite field, and (2) the probability that a random linear network coding is weakly secure. Based on the relationships, we further improve our algorithms to address the two system factors, while keeping the same maximal STR. Extensive simulation results show that the proposed heuristic algorithms can achieve good performance in various scenarios.