Groups of parties that are granted access are called qualified. In set theoretic terms they are referred to as qualified sets; in turn, the set of all such qualified sets is called the access structure of the system. Less formally it is a description of who needs to cooperate with whom in order to access the resource.
Qualified groups, those granted access, are defined as sets within a broader framework. This framework, called the access structure, defines how these groups interact and collaborate to access a shared resource.