An information-theoretic cryptanalysis of network coding - is protecting the code enough?

We consider the issue of confidentiality in multicast network coding, by assuming that the encoding matrices, based upon variants of random linear network coding, are given only to the source and sinks. Based on this assumption, we provide a characterization of the mutual information between the encoded data and the two elements that can lead to information disclosure: the matrices of random coefficients and, naturally, the original data itself. Our results, some of which hold even with finite block lengths, show that, predicated on optimal source-coding, information-theoretic security is achievable for any field size without loss in terms of decoding probability. It follows that protecting the encoding matrix is generally sufficient to ensure confidentiality of network coded data.