A probabilistic concept of accessibility for access structures

In this paper we introduce the concept of weighted accessibility for access structures. In some sense, it represents a measure of how difficult or how easy is to recover the secret. We give also a numerical measure of accessibility for each participant depending on his position in the access structure. Both concepts, the accessibility of the access structure and the accessibility of the participants are closely related. We also provide an axiomatic characterization of the weighted accessibility for access structures based on four simple properties.