Algorithms for weakly secure data exchange

We consider the problem of direct data exchange among a group of wireless clients in the presence of an eavesdropper. An instance of this problem includes a set of packets X and a set of clients, such that each client has an access to a subset of packets and requests the rest of the packets in X. The clients use a lossless broadcast channel to transmit packets to other clients in the group. All transmitted packets can be observed by an eavesdropper that might have prior side information about the packets exchanged by the clients. Our goal is to construct a coding scheme that prevents the eavesdropper from decoding any individual packet in X (beyond those it already knowns). In weakly secure schemes, the more packets the eavesdropper has, the harder it is to construct a scheme that prevents the eavesdropper from obtaining additional packets. Thus, it is natural to measure the degree of secrecy by the maximum number of packets that can be held by the eavesdropper. Accordingly, our goal is to construct a coding scheme that can handle an eavesdropper that has as many packets as possible. We also present randomized and deterministic solutions for this problem and analyze their performance. We also establish a tight upper bound on the maximum degree of secrecy that a weakly secure scheme can provide for each instance of the problem.