RankGuardPolar Private Public Finite Length Polar Codes with Rank-Certified Leakage

TL;DR

This paper presents RankGuard-Polar, a framework for securely publishing polar code coordinates with algebraic leakage characterization and efficient certification methods over shared public resources.

Contribution

It introduces a novel algebraic approach to quantify and certify leakage in polar codes, including an explicit linear extractor and efficient algorithms.

Findings

Leakage from published indices admits an exact algebraic characterization.

An explicit linear extractor identifies leaked linear combinations.

Efficient procedures and algorithms for leakage computation and certification are proposed.

Abstract

We introduce \textbf{RankGuard-Polar}, a framework for safely publishing a subset of polar codeword coordinates over shared public resources. We assume a strong eavesdropper who has access to the channel input, i.e., the transmitted codeword coordinates published on a public resource access model. Working over \(\mathbb F_2\) and focusing on time-shared public/private BEC uses, we show that leakage from a published index set \(\mathbf{P}\) admits an exact algebraic characterization comes from an information-theoretic viewpoint, and we construct an explicit linear extractor ($R$) that identifies the leaked linear combinations. Building on this identity, we (i) give efficient procedures to compute and certify leakage for any \(\mathbf{P}\), (ii) propose a practical fast algorithm with provable efficiency.