Information Hiding Using Matroid Theory
Combinatorics
2021-05-20 v2 Information Theory
math.IT
Abstract
Inspired by problems in Private Information Retrieval, we consider the setting where two users need to establish a communication protocol to transmit a secret without revealing it to external observers. This is a question of how large a linear code can be, when it is required to agree with a prescribed code on a collection of coordinate sets. We show how the efficiency of such a protocol is determined by the derived matroid of the underlying linear communication code. Furthermore, we provide several sufficient combinatorial conditions for when no secret transmission is possible.
Cite
@article{arxiv.2009.02991,
title = {Information Hiding Using Matroid Theory},
author = {Ragnar Freij-Hollanti and Olga Kuznetsova},
journal= {arXiv preprint arXiv:2009.02991},
year = {2021}
}