Optimal Information Security Against Limited-View Adversaries: The Benefits of Causality and Feedback

Abstract

The Singleton bound provides a fundamental limit on the maximum possible size of an error-correcting code of a given length and distance. However, recent work by Zhang et. al. [IEEE Trans. Comm., Dec. 2023] showed that in the context of the wiretap multipath network when the adversary has limited knowledge about the codewords and a vanishing probability of decoding error is permitted, a rate higher than the Singleton bound is achievable. Their results, however, are confined to an ideal setting where the adversary is allowed to behave non-causally. Motivated by real-world scenarios, this work considers communication over a wiretap multipath network in the presence of a causal adversary (i.e., the adversary which is only allowed to use the observations up to the current time slot to decide the current jamming strategy) and in the presence of passive feedback from the receiver to the transmitter. We characterize both the capacity and secrecy capacity of the wiretap multipath network, either with or without passive feedback. We observe that in comparison to the non-causal and non-feedback setting, the capacity and secrecy capacity can be strictly higher for a wide variety of parameters, demonstrating the benefits of causality and feedback.