Coding for Positive Rate in the Source Model Key Agreement Problem

DOI10.1109/TIT.2020.2990750zbMATH Open1452.94043arXiv1709.05174OpenAlexW2796784263MaRDI QIDQ5138811

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Publication date: 4 December 2020

Published in: IEEE Transactions on Information Theory (Search for Journal in Brave)

Abstract: A two-party key agreement problem with public discussion, known as the source model problem, is considered. By relating key agreement to hypothesis testing, a new coding scheme is developed that yields a sufficient condition to achieve a positive secret-key (SK) rate in terms of R'enyi divergence. The merits of this coding scheme are illustrated by applying it to an erasure model for Eve's side information, and by deriving an upper bound on Eve's erasure probabilities for which the SK capacity is zero. This bound strictly improves on the best known single-letter lower bound on the SK capacity. Moreover, the bound is tight when Alice's or Bob's source is binary, which extends a previous result for a doubly symmetric binary source. The results motivate a new measure for the correlation between two random variables, which is of independent interest.

Full work available at URL: https://arxiv.org/abs/1709.05174

zbMATH Keywords

Rényi divergence positive secret-key (SK) rate source model problem two-party key agreement problem with public discussion

Mathematics Subject Classification ID

Parametric hypothesis testing (62F03) Statistical aspects of information-theoretic topics (62B10) Source coding (94A29)