**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.

**Category / Keywords: **foundations / secret sharing; complexity; entropy method;

**Date: **received 11 Jul 2011

**Contact author: **csirmaz at degas ceu hu

**Available format(s): **PDF | BibTeX Citation

**Version: **20110712:020454 (All versions of this report)

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