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 language | English (US) |
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Pages (from-to) | 69-73 |
Number of pages | 5 |
Journal | Journal of Combinatorial Theory, Series B |
Volume | 56 |
Issue number | 1 |
DOIs | |
State | Published - Sep 1992 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics