Random Linear Network Codes for Secrecy over Wireless Broadcast Channels
This addresses secure communication in wireless networks for scenarios with multiple privileged recipients, though it appears incremental as it generalizes a previous work.
The paper tackles the problem of securely delivering messages to privileged clients over a broadcast erasure channel, using random linear network coding to hide decoding coefficients from unprivileged clients, with an information-theoretic proof showing no meaningful information leakage and low decoding complexity.
We consider a set of $n$ messages and a group of $k$ clients. Each client is privileged for receiving an arbitrary subset of the messages over a broadcast erasure channel, which generalizes scenario of a previous work. We propose a method for secretly delivering each message to its privileged recipients in a way that each receiver can decode its own messages but not the others'. Our method is based on combining the messages using linear network coding and hiding the decoding coefficients from the unprivileged clients. We provide an information theoretic proof for the secrecy of the proposed method. In particular we show that an unprivileged client cannot obtain any meaningful information even if it holds the entire set of coded data packets transmitted over the channel. Moreover, in our method, the decoding complexity is desirably low at the receiver side.