Suppose that there are players in two hierarchical groups and acomputationally unlimited eavesdropper. Using arandom deal of cards, aplayer in the higher group wishes to send aone-bit message information-theoretically securely either to all the players in her group or to all the players in the two groups. This can be done by the s0-called 2-level key set protocol. In this paper we give anecessary and sufficient condition for the 2-level key set protocol to succeed.