On the capacity of the binary adversarial wiretap channel

TL;DR

This paper establishes new bounds on the maximum secure communication rate over a binary adversarial wiretap channel, considering an adversary that can read and modify parts of the transmitted codeword.

Contribution

It provides the first achievable rate and nearly matching upper bounds for the semantic secrecy capacity under adversarial reading and writing constraints.

Findings

Achievable rate of 1 - h(ρ_w) - ρ_r for the channel.

Upper bounds close to the achievable rate when ρ_r is small.

New theoretical bounds on the secrecy capacity of the adversarial wiretap channel.

Abstract

New bounds on the semantic secrecy capacity of the binary adversarial wiretap channel are established . Against an adversary which reads a $\rho_r$ fraction of the transmitted codeword and modifies a $\rho_w$ fraction of the codeword, we show an achievable rate of $1-h(\rho_w)-\rho_r$, where $h(\cdot)$ is the binary entropy function. We also give an upper bound which is nearly matching when $\rho_r$ is small.