Unconditionally secure conference key distribution: Security definitions and their relations

A non-interactive conference key distribution scheme (NICKDS) is a system that allows selected sets of users to securely share a common key without interacting with each other. In this paper, we consider unconditionally secure setting where the is no limit on adversary's computation power. Unconditionally secure NICKDS has been considered with security against an adversary who can corrupt up to w users. We strengthen the security model of the system by allowing the adversary to also obtain conference keys of conferences whose members are honest, and use a game bases approach to define security. We give two other ways of defining security, using probability distance and mutual information and show the relationship between the three definitions of security.