Universally Secure Network Coding with Feedback

In the model of Secure Network Coding, a sender is connected to several receivers by a network, i.e. a directed graph with a single source node and several destination nodes, where each node can perform operations on the values received via the incoming edges and sends the results via the outbound edges. An active adversary controls some of the edges; this means that he can read every symbol transmitted over the edges under his control and replace them with symbols of his choice. The goal of Secure Network Coding is to design protocols that allow transmission of a secret message from the sender to all receivers in a private and reliable way. Classically, only one-way communication (from sender to receivers) has been studied; in this setting, security can be guaranteed as long as the number of edges controlled by the adversary is less than one third of the network connectivity. In this paper, we present a procedure where receivers are allowed to send feedback to the sender; with this feature, security is guaranteed against a stronger adversary: namely, the number of corrupted edges only needs to be smaller than one half of the connectivity. Furthermore, like previous state-of-the-art work on the single-round scenario, our scheme is universal, i.e. it does not require knowledge of the network code