# Complexity of universal access structures

Csirmaz, László (2012) Complexity of universal access structures. Information Processing Letters, 112 (4). pp. 149-152. ISSN 0020-0190

 Preview
PDF
141Kb

## 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.

Item Type: Article secret sharing; complexity; entropy method; harmonic series 90C25 Convex programming05B35 Matroids, geometric lattices94A62 Authentication and secret sharing Research Groups > Theoretical cryptography 05 Mar 2013 12:49

Repository Staff Only: item control page