Tight Bounds on the Information Rate of Secret SharingSchemes
Designs, Codes and Cryptography
Secret sharing schemes with three or four minimal qualified subsets
Designs, Codes and Cryptography
An impossibility result on graph secret sharing
Designs, Codes and Cryptography
Optimal complexity of secret sharing schemes with four minimal qualified subsets
Designs, Codes and Cryptography
Decomposition constructions for secret-sharing schemes
IEEE Transactions on Information Theory
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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... asymptotically.