Paper 2009/141

Ideal Hierarchical Secret Sharing Schemes

Oriol Farras and Carles Padro


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.

Note: thorough revision

Available format(s)
Cryptographic protocols
Publication info
Published elsewhere. This is the full version of the paper that appeared in TCC 2010.
secret sharingideal secret sharing schemeshierarchical secret sharingweighted secret sharing schemesmultipartite secret sharing
Contact author(s)
cpadro @ ma4 upc edu
2011-06-30: last of 3 revisions
2009-03-31: received
See all versions
Short URL
Creative Commons Attribution


      author = {Oriol Farras and Carles Padro},
      title = {Ideal Hierarchical Secret Sharing Schemes},
      howpublished = {Cryptology ePrint Archive, Paper 2009/141},
      year = {2009},
      note = {\url{}},
      url = {}
Note: In order to protect the privacy of readers, does not use cookies or embedded third party content.