Cryptology ePrint Archive: Report 2009/141

Ideal Hierarchical Secret Sharing Schemes

Oriol Farras and Carles Padro

Abstract: Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention since the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization is based on the well known connection between ideal secret sharing schemes and matroids and, more specifically, on the connection between ideal multipartite secret sharing schemes and integer polymatroids. In particular, we prove that every hierarchical matroid port admits an ideal linear secret sharing scheme over every large enough finite field. Finally, we use our results to present a new proof for the existing characterization of the ideal weighted threshold access structures.

Category / Keywords: cryptographic protocols / secret sharing, ideal secret sharing schemes, hierarchical secret sharing, weighted secret sharing schemes, multipartite secret sharing

Publication Info: This is the full version of the paper that appeared in TCC 2010.

Date: received 27 Mar 2009, last revised 30 Jun 2011

Contact author: cpadro at ma4 upc edu

Available format(s): PDF | BibTeX Citation

Note: thorough revision

Version: 20110630:082423 (All versions of this report)

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