On the Composition of Matroids and Ideal Secret Sharing Schemes

Authors:
Siaw-Lynn Ng;Michael Walker
Affiliations:
Mathematics Department, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UKs.ng@rhbnc.ac.uk;Information Security Group, Royal Holloway, University of London, Egham, Surrey TW20 0EX, UKmike.walker@vf.vodafone.co.uk
Venue:
Designs, Codes and Cryptography
Year:
2001

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Abstract

In an ideal secret sharing scheme, the access structure is uniquely determined by its minimal sets \Delta_s. The purpose of this paper is to characterise \Delta_s. We introduce the concept of strong connectivity and show that under this equivalence relation, an ideal secret sharing scheme decomposes into threshold schemes. We also give a description of the minimal sets that span the strong connectivity classes. As a result we obtain a necessary condition on the types of subsets that are allowed in an ideal access structure as well as an upper bound on the number of such access structures.