| Speaker: Songbao Mo Affiliation: University of Auckland Time: 14:00 Thursday, 23 April, 2020 Location: Zoom ID: 998-8497-5790 |
| A milestone paper in secret sharing by Brickell and Davenport (1991) shows the important connection between ideal secret sharing schemes and matroids which are combinatorial objects that abstract linear independence. More precisely they show that an ideal access structure is always a matroid port (the concept that extensively studied in combinatorics by Seymour). In this talk, I will introduce some basic concepts in secret sharing and matroid theory. In particular, I will introduce a class of well-studied access structures named hierarchical access structures and a special class of matroids named lattice path matroids. I will show that hierarchical access structures can be characterised as matroid ports of lattice path matroids. Moreover, we show that a hierarchical access structure is conjunctive or disjunctive if and only if it is a matroid port of a shifted matroid. |