Secret key generation with one communicator and a one-shot converse via hypercontractivity

A new model of multi-party secret key agreement is proposed, in which one terminal called the communicator can transmit public messages to other terminals before all terminals agree on a secret key. A single-letter characterization of the achievable region is derived in the stationary memoryless case. The new model generalizes some other (old and new) models of key agreement. In particular, key generation with an omniscient helper is the special case where the communicator knows all sources, for which we derive a zero-rate one-shot converse for the secret key per bit of communication.