Secure Polar Coding for Adversarial Wiretap Channel
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The adversarial wiretap channel (AWTC) model is a secure communication model that eavesdropper can directly read and write fractions of the transmitted bits in legitimate communication. In this paper we propose a secure polar coding scheme to provide secure and reliable communication over the AWTC model. For the adversarial reading and writing action, we present a ρ equivalent channel block and apply the non-stationary polarization on it. By comparing the polarization result of ρ equivalent channel block with a ρ BEC block (channel block of BEC with erase probability ρ), we find that the polarized subsets of ρ BEC block is fully contained by the polarized subsets of ρ equivalent channel block by choosing the polarization parameter β properly. Based on this observation, we construct a secure polar coding scheme on the ρ BEC blocks for the AWTC model. We theoretically prove that the proposed scheme achieves the secrecy capacity of AWTC model under both reliability and strong security criterions with an infinite block length N. Further, by simulations, we prove that the proposed scheme can provide secure and reliable communication over AWTC model with a finite block length N.
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