Paper 2012/595
Extending Brickell-Davenport Theorem to Non-Perfect Secret Sharing Schemes
Oriol Farràs and Carles Padró
Abstract
One important result in secret sharing is the Brickell-Davenport Theorem: every ideal perfect secret sharing scheme defines a matroid that is uniquely determined by the access structure. Even though a few attempts have been made, there is no satisfactory definition of ideal secret sharing scheme for the general case, in which non-perfect schemes are considered as well. Without providing another unsatisfactory definition of ideal non-perfect secret sharing scheme, we present a generalization of the Brickell-Davenport Theorem to the general case. After analyzing that result under a new point of view and identifying its combinatorial nature, we present a characterization of the (not necessarily perfect) secret sharing schemes that are associated to matroids. Some optimality properties of such schemes are discussed.
Note: Revised version. A new section with examples added.
Metadata
- Available format(s)
-
PDF
- Category
- Cryptographic protocols
- Publication info
- Published elsewhere. Unknown where it was published
- Keywords
- Secret sharingNon-perfect secret sharing schemeMatroidPolymatroid
- Contact author(s)
- cpadro @ ma4 upc edu
- History
- 2012-12-18: last of 2 revisions
- 2012-10-25: received
- See all versions
- Short URL
- https://ia.cr/2012/595
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2012/595,
author = {Oriol Farràs and Carles Padró},
title = {Extending Brickell-Davenport Theorem to Non-Perfect Secret Sharing Schemes},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/595},
year = {2012},
url = {https://eprint.iacr.org/2012/595}
}
