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arXiv · 2009.02991

Information Hiding Using Matroid Theory

Ragnar Freij-Hollanti·Olga Kuznetsova
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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.

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BibTeXRIS

Ragnar Freij-Hollanti, Olga Kuznetsova. 2021-04-05. Information Hiding Using Matroid Theory. https://doi.org/10.1016/j.aam.2021.102205

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