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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)
- 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