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Lattice-theoretic Characterization of Secret Sharing Representable Connected Matroids

Authors:
A. N. Alekseychuk
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URL: http://eprint.iacr.org/2010/348
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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 Haiman’s “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
}