On secret-sharing matroids

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Abstract

A matroid M is secret-sharing if there is a finite set S and a matrix A = (aij: i ∈ I, j ∈ E(M)) with entries in S, such that for all X ⊇ E(M), the submatrix (aij : i ∈ I, j ∈ X) has precisely |S|rk(χ) distinct rows. Such matroids occur naturally in the study of secret-sharing schemes in cryptography. Brickell and Davenport (J. Cryptography, to appear) asked if every matroid is a secret-sharing matroid. We answer this negatively, by showing that the Vamos matroid is not.

Original languageEnglish (US)
Pages (from-to)69-73
Number of pages5
JournalJournal of Combinatorial Theory, Series B
Volume56
Issue number1
DOIs
StatePublished - Sep 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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