You are looking at a specific version 20100618:183714 of this paper. See the latest version.

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
Creative Commons Attribution
CC BY
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.