Necessary and Sufficient Numbers of Cards for Sharing Secret Keys on Hierarchical Groups

Abstract

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.