Secure Polar Coding for Adversarial Wiretap Channel

The adversarial wiretap channel (AWTC) model is a secure communication model in which adversary can directly read and write the transmitted bits in legitimate communication with fixed fractions. 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 $\rho$ equivalent channel block and study its transformation under the channel polarization operation. We find that the generated channels are polarized in the sense that part of them are full-noise channels with probability almost $1$ and the rest part of them are noiseless channels with probability almost $1$. Based on this result, we polarize both equivalent channel blocks of adversarial reading and writing, and then construct a secure polar coding scheme by applying the multi-block chaining structure on the polarized equivalent blocks. Theoretically we prove that when block length $N$ goes infinity, the proposed scheme achieves the secrecy capacity of the AWTC model under both reliability and strong security criterions. Then by simulations, we prove that the proposed scheme can provide secure and reliable communication over AWTC model.