Lattice-theoretic Characterization of Secret Sharing Representable Connected Matroids

A.  N.  Alekseychuk

Paper 2010/348

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.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Published elsewhere. Unknown where it was published
Keywords: secret sharing
Contact author(s): alex-crypto @ mail ru
History: 2010-06-18: received
Short URL: https://ia.cr/2010/348
License: 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},
      url = {https://eprint.iacr.org/2010/348}
}