### Lattice-theoretic Characterization of Secret Sharing Representable Connected Matroids

A. N. Alekseychuk

##### Abstract

Necessary and sufficient conditions for a connected matroid to be secret sharing (ss-)representable are obtained. We show that the flat lattices of ss-representable matroids are closely related with well-studied algebraic objects called linear lattices. This fact implies that new powerful methods (from lattice theory and mathematical logic) for investigation of ss-representable matroids can be applied. We also obtain some necessary conditions for a connected matroid to be ss-representable. Namely, we construct an infinite set of sentences (like to Haiman’s “higher Arguesian identities”) which are hold in all ss-representable matroids.

Available format(s)
Category
Cryptographic protocols
Publication info
Published elsewhere. Unknown where it was published
Keywords
secret sharing
Contact author(s)
alex-crypto @ mail ru
History
Short URL
https://ia.cr/2010/348

CC BY

BibTeX

@misc{cryptoeprint:2010/348,
author = {A.  N.  Alekseychuk},
title = {Lattice-theoretic Characterization of Secret Sharing Representable Connected Matroids},
howpublished = {Cryptology ePrint Archive, Paper 2010/348},
year = {2010},
note = {\url{https://eprint.iacr.org/2010/348}},
url = {https://eprint.iacr.org/2010/348}
}

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