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

2026-05-11

AI Summary

This work addresses the vulnerability of polar codes to strong eavesdroppers who exploit public channels to acquire sensitive information about specific code coordinates. To mitigate this threat, the authors propose RankGuard-Polar, a novel framework that, for the first time, provides an exact algebraic characterization of information leakage arising from publicly disclosed index sets under binary-field and time-division public-private BEC channel models. Leveraging linear-algebraic extractors, the framework introduces a provably efficient algorithm capable of rapidly computing and certifying the leakage magnitude for any given public index set. Combining theoretical rigor with practical utility, this study establishes a new coding-theoretic foundation for securely deploying polar codes in privacy-sensitive applications.

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.

Problem

• Polar Codes
• Information Leakage
• Privacy
• Eavesdropping
• Finite Length

Innovation

• Polar codes
• information leakage
• linear extractor
• rank-certified security
• public-private communication