Weakly Secure Network Coding for Wireless Cooperative Data Exchange

We consider the problem of secure cooperative data exchange in wireless networks. The cooperative data exchange problem includes a set of wireless clients that exchange information over a lossless broadcast channel. The clients are missing some packets but collectively know all packets. Each client can transmit packets it currently has or a combination thereof. The problem asks for a scheme that allows all clients to recover all packets with the minimum number of transmissions. We focus on secure information exchange in the presence of an eavesdropper that can observe all packets transmitted over the broadcast channel. Our goal is to construct a \emph{weakly secure} solution to the cooperative data exchange problem, i.e., a solution that does not reveal information about any single packet. This is in contrast to \emph{strongly secure} solutions that do not reveal any data about the entire set of packets. Weakly secure solutions can be implemented more efficiently in practical settings and do not require sharing secret keys. Our paper makes the following contributions. First, we establish necessary and sufficient conditions for the feasibility of weakly secure data exchange for any given instance of the weakly secure data exchange problem. Second, we show that if it is possible to obtain a weakly secure solution for an instance of the cooperative data exchange problem, then weak security can be achieved with no penalty in terms of the total number of transmissions. Finally, we present an algorithm that finds an optimal weakly secure solution to the cooperative data exchange problem.