Optimal Information Security Against Limited-View Adversaries: Beyond MDS Codes

Maximum distance separable (MDS) codes are often considered to have the optimal error correction capability against malicious adversaries because they achieve the Singleton bound in terms of the rate-distance tradeoff. However, by allowing a vanishing probability of decoding error and considering an adversary with limited knowledge, it is interesting to understand whether a rate higher than the Singleton bound is achievable, and if so, what the optimal rate is. To answer these questions, we instantiate the aforementioned problem as a communication problem where the transmission medium is a wiretap multipath network that consists of multiple parallel links. A malicious adversary is able to eavesdrop on a subset of links, and also jam on a potentially overlapping subset of links. The primary objective is to ensure the communication is robust to adversarial jamming; additionally, another goal is to guarantee that the communication is information-theoretically secure with respect to the adversary. We present a complete characterization of both capacity and secrecy capacity as functions of the number of links that can be eavesdropped and/or jammed. Our achievability schemes are computationally efficient, and rely on a non-trivial combination of MDS codes and a pairwise hashing scheme.