Paper 2010/348 Original: eprint.iacr.org/2010/348 ↗
Lattice-theoretic Characterization of Secret Sharing Representable Connected Matroids
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.
Metadata
- Available format(s)
PDF- Category
- Cryptographic protocols
- Publication info
- Preprint.
- History
- 2010-06-18: last updated
- 2010-06-18: published
- Short URL
- https://ia.cr/2010/348
- License
- https://creativecommons.org/licenses/by/4.0/
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},
url = {https://eprint.iacr.org/2010/348}
}