Common information in well-mixing graphs and applications to information-theoretic cryptography
Abstract
We study the connection between mixing properties for bipartite graphs and materialization of the mutual information in one-shot settings. We show that mixing properties of a graph imply impossibility to extract the mutual information shared by the ends of an edge randomly sampled in the graph. We apply these impossibility results to some questions motivated by information-theoretic cryptography. In particular, we show that communication complexity of a secret key agreement in one-shot setting is inherently uneven: for some inputs, almost all communication complexity inevitably falls on only one party.
Keywords
Cite
@article{arxiv.2405.05831,
title = {Common information in well-mixing graphs and applications to information-theoretic cryptography},
author = {Geoffroy Caillat-Grenier and Andrei Romashchenko and Rustam Zyavgarov},
journal= {arXiv preprint arXiv:2405.05831},
year = {2025}
}
Comments
25 pages, 1 figure; version 3: an extended version of the conference paper published in the Proceedings of the IEEE Information Theory Workshop, Shenzhen, 2024. In this version, we provide complete proofs of all results along with more detailed discussions