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arXiv · 2605.11356

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

Hassan Tavakoli·Thinh Nguyen·Bella Bose
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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.

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Hassan Tavakoli, Thinh Nguyen, Bella Bose. 2026-05-12. RankGuardPolar Private Public Finite Length Polar Codes with Rank-Certified Leakage. https://arxiv.org/abs/2605.11356

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