Polar Coding for Secure Transmission and Key Agreement

Abstract

Achieving information theoretic security with practical coding complexity is of definite interest. This work first focuses on the key agreement problem. For this problem, a new cross-layer secure coding protocol over block fading channels is proposed. The proposed scheme requires only the statistical knowledge about the eavesdropper channel state information (CSI), and, utilizing a privacy amplification technique, reduces the problem of key agreement to a provably secure coding problem per block. Focusing on this secure coding problem, it is shown that polar codes, introduced by Arikan, achieve nonzero perfect secrecy rates for the binary-input degraded wiretap channel while enjoying a remarkably low encoding-decoding complexity. We further show that, in the special case of symmetric main and eavesdropper channels, this coding technique achieves the secrecy capacity. This approach is also extended to the multiple-access channel with a degraded eavesdropper where a nontrivial achievable secrecy region is established. This polar coding method is then utilized in the proposed key agreement protocol, where the secure coding per block is used to create an advantage for the legitimate nodes over the eavesdropper, which is then turned into a private key via the privacy amplification module.