Finite-Length Analysis of Polar Secrecy Codes for Wiretap Channels

TL;DR

This paper analyzes the finite-length performance of polar secrecy codes in wiretap channels, providing bounds on secrecy leakage and insights into their practical security guarantees.

Contribution

It introduces bounds on mutual information security leakage for polar secrecy codes and characterizes their finite-length scaling behavior.

Findings

Bounds on MIS leakage are derived for polar secrecy codes.

Finite-length scaling behavior of secrecy codes is characterized.

Numerical bounds on secrecy guarantees are provided for practical code lengths.

Abstract

In a classical wiretap channel setting, Alice communicates with Bob through a main communication channel, while her transmission also reaches an eavesdropper Eve through a wiretap channel. In this paper, we consider a general class of polar secrecy codes for wiretap channels and study their finite-length performance. In particular, bounds on the normalized mutual information security (MIS) leakage, a fundamental measure of secrecy in information-theoretic security frameworks, are presented for polar secrecy codes. The bounds are utilized to characterize the finite-length scaling behavior of polar secrecy codes, where scaling here refers to the non-asymptotic behavior of both the gap to the secrecy capacity as well as the MIS leakage. Furthermore, the bounds are shown to facilitate characterizing numerical bounds on the secrecy guarantees of polar secrecy codes in finite block lengths of practical relevance, where directly calculating the MIS leakage is in general infeasible.