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A Flaw in the Use of Minimal Defining Sets for Secret Sharing Schemes

Authors:	Mike J Grannell Terry S Griggs Anne Penfold Street

Institution:	(1) Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes, MK7 6AA, United Kingdom;(2) Department of Mathematics, University of Queensland, Queensland, 4072, Australia

Abstract:	It is shown that in some cases it is possible to reconstruct a block design $\mathcal{D}$ uniquely from incomplete knowledge of a minimal defining set for $\mathcal{D}$ . This surprising result has implications for the use of minimal defining sets in secret sharing schemes.

Keywords:	Block design Minimal defining set Secret sharing Strongbox
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