Laura Luzzi – Finite blocklength secrecy analysis of polar and Reed-Muller codes in binary erasure wiretap channels

Physical layer security aims to exploit the randomness of noisy channels in order to enhance security through coding and signal processing techniques. Unlike cryptography, it does not place any limitations on the adversary’s computational power, but relies on an asymmetry in the channel quality between the legitimate users and the adversary. In this talk, we focus on the wiretap channel model, where a legitimate transmitter and receiver communicate in the presence of an eavesdropper who observes a degraded version of the receiver’s outputs. For this model, secrecy can be measured in terms of mutual information leakage, or alternatively in terms of the average variational distance between output distributions corresponding to different confidential messages.

Motivated by IoT applications that require short packets or low latency, we focus on the performance of wiretap codes in finite blocklength. We consider a simple channel model where the main channel is noiseless and the eavesdropper’s channel is a binary erasure channel, and provide lower bounds for the achievable secrecy rates of polar and Reed-Muller codes. We show that under a total variation secrecy metric, Reed-Muller codes can achieve secrecy rates very close to the optimal second order coding rates.