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Lattice-theoretic Characterization of Secret Sharing Representable Connected Matroids
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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 Haimans higher Arguesian identities) which are hold in all ss-representable matroids. |
BibTeX
@misc{eprint-2010-23249, title={Lattice-theoretic Characterization of Secret Sharing Representable Connected Matroids}, booktitle={IACR Eprint archive}, keywords={cryptographic protocols / secret sharing}, url={http://eprint.iacr.org/2010/348}, note={ alex-crypto@mail.ru 14776 received 16 Jun 2010}, author={A. N. Alekseychuk}, year=2010 }