Network codes resilient to jamming and eavesdropping

We consider the problem of communicating information over a network secretly and reliably in the presence of a hidden adversary who can eavesdrop and inject malicious errors. We provide polynomial-time, rate-optimal distributed network codes for this scenario, improving on the rates achievable in [1]. Our main contribution shows that as long as the sum of the adversary's jamming rate ZO and his eavesdropping rate ZI is less than the network capacity C, (i.e., Z_O + Z_I < C), our codes can communicate (with vanishingly small error probability) a single bit correctly and without leaking any information to the adversary. We then use this to design codes that allow communication at the optimal source rate of C -Z_O -Z_I, while keeping the communicated message secret from the adversary. Interior nodes are oblivious to the presence of adversaries and perform random linear network coding; only the source and destination need to be tweaked. In proving our results we correct an error in prior work [2] by a subset of the authors in this work.