Complexity of universal access structures

Laszlo Csirmaz

Paper 2011/375

Complexity of universal access structures

Laszlo Csirmaz

Abstract

An important parameter in a secret sharing scheme is the number of minimal qualified sets. Given this number, the universal access structure is the richest possible structure, namely the one in which there are one or more participants in every possible Boolean combination of the minimal qualified sets. Every access structure is a substructure of the universal structure for the same number of minimal qualified subsets, thus universal access structures have the highest complexity given the number of minimal qualified sets. We show that the complexity of the universal structure with $n$ minimal qualified sets is between $n/\log_2n$ and $n/2.7182\dots$ asymptotically.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. Unknown where it was published
Keywords: secret sharing complexity entropy method
Contact author(s): csirmaz @ degas ceu hu
History: 2011-07-12: received
Short URL: https://ia.cr/2011/375
License: CC BY

BibTeX

@misc{cryptoeprint:2011/375,
      author = {Laszlo Csirmaz},
      title = {Complexity of universal access structures},
      howpublished = {Cryptology {ePrint} Archive, Paper 2011/375},
      year = {2011},
      url = {https://eprint.iacr.org/2011/375}
}