Trade-Offs in Information-Theoretic Multi-party One-Way Key Agreement

We consider the following scenario involving three honest parties, Alice, Bob, and Carol, as well as an adversary, Eve. Each party has access to a single piece of information, jointly distributed according to some distribution P. Additionally, authentic public communication is possible from Alice to Carol and from Bob to Carol. Their goal is to establish two information-theoretically secret keys, one known to Alice and Carol, and one known to Bob and Carol. We derive joint bounds on the lengths of these keys. Our protocols combine distributed variants of Slepian-Wolf coding and the leftover hash lemma. The obtained bounds are expressed in terms of smooth Renyi entropies and show that these quantities are useful in this--single-serving--context as well.

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