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

  • Authors:

  • Mike J. Grannell;Terry S. Griggs;Anne Penfold Street

  • Affiliations:

  • Department of Pure Mathematics, The Open University, Milton Keynes, United Kingdom MK7 6AA;Department of Pure Mathematics, The Open University, Milton Keynes, United Kingdom MK7 6AA;Department of Mathematics, University of Queensland, Queensland, Australia 4072

  • Venue:
  • Designs, Codes and Cryptography
  • Year:
  • 2006

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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.