Nonperfect secret sharing schemes and matroids

  • Authors:
  • Kaoru Kurosawa;Koji Okada;Keiichi Sakano;Wakaha Ogata;Shigeo Tsujii

  • Affiliations:
  • Tokyo Institute of Technology, Japan;Tokyo Institute of Technology, Japan;Tokyo Institute of Technology, Japan;Tokyo Institute of Technology, Japan;Tokyo Institute of Technology, Japan

  • Venue:
  • EUROCRYPT '93 Workshop on the theory and application of cryptographic techniques on Advances in cryptology
  • Year:
  • 1994

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Abstract

This paper shows that nonperfect secret sharing schemes (NSS) have matroid structures and presents a direct link between the secret sharing matroids and entropy for both perfect and nonperfect schemes. We define natural classes of NSS and derive a lower bound of |Vi| for those classes. "Ideal" nonperfect schemes are defined based on this lower bound. We prove that every such ideal secret sharing scheme has a matroid structure. The rank function of the matroid is given by the entropy divided by some constant. It satisfies a simple equation which represents the access level of each subset of participants.