Network Codes Resilient to Jamming and Eavesdropping (1001.3714v3)

Abstract: 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 previous work. 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., Zo+Zi<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-Zo-Zi, 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 by a subset of the authors in this work.