Eprints of Rényi Institute

Complexity of universal access structures

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



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
Keywords and phrases:secret sharing; complexity; entropy method; harmonic series
Subjects:90C25 Convex programming
05B35 Matroids, geometric lattices
94A62 Authentication and secret sharing
Divisions:Research Groups > Theoretical cryptography
Last Modified:05 Mar 2013 12:49

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