Distributed Secret Sharing for Discrete Memoryless Networks

This correspondence studies the distributed secret sharing problem which is a twist of the classical secret sharing problem. In this new problem, each user needs to encode his or her own unique secret message without collaboration with other users and without the use of any common secret materials or cryptographic keys. The goal is to ensure that an adversary without access to all of the encoded messages learns as little as possible about the secret messages, while a legitimate joint decoder with all the encoded messages can decode all of them without cryptographic keys. Furthermore the users do not know the channels that will be compromised ahead of time, and thus must protect all channels. Specifically, we study two related variants of this problem. The first problem deals with source coding and secrecy, while the second problem deals with channel coding and secrecy. From the results of these two problems, we conclude that interference is necessary for unconditional secrecy.