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.