Secret sharing schemes on access structures with intersection number equal to one.
Discrete Applied Mathematics 154 (2006) 552-563.
A previous version of this paper appeared in Third Conference on Security in Communication Networks'02, Lecture Notes in Computer Science 2576 (2003) 354-363. Amalfi, Italy (2002).

The characterization of ideal access structures and the search for bounds on the optimal information rate are two important problems in secret sharing. These problems are studied in this paper for access structures with intersection number equal to one, that is, access structures such that there is at most one participant in the intersection of any two different minimal qualified subsets.
The main result in this work is the complete characterization of the ideal access structures with intersection number equal to one. Besides, bounds on the optimal information rate are provided for the non-ideal case.