Information Rates of Minimal Non-Matroid-Related Access Structures

Details Information Rates of Minimal Non-Matroid-Related Access Structures Information Rates of Minimal Non-Matroid-Related Access Structures

2008-01-23

arxiv.org/abs/0801.3642v1

Computer Science

Cryptography and Security

8 pages

Scientific paper

In a secret sharing scheme, shares of a secret are distributed to participants in such a way that only certain predetermined sets of participants are qualified to reconstruct the secret. An access structure on a set of participants specifies which sets are to be qualified. The information rate of an access structure is a bound on how efficient a secret sharing scheme for that access structure can be. Marti-Farre and Padro showed that all access structures with information rate greater than two-thirds are matroid-related, and Stinson showed that four of the minor-minimal, non-matroid-related access structures have information rate exactly two-thirds. By a result of Seymour, there are infinitely many remaining minor-minimal, non-matroid-related access structures. In this paper we find the exact information rates for all such structures.

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