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Secret Key Agreement: General Capacity and Second-Order Asymptotics
We revisit the problem of secret key agreement using interactive public
communication for two parties and propose a new secret key agreement protocol.
The protocol attains the secret key capacity for general observations and
attains the second-order asymptotic term in the maximum length of a secret key
for independent and identically distributed observations. In contrast to the
previously suggested secret key agreement protocols, the proposed protocol uses
interactive communication. In fact, the standard one-way communication protocol
used prior to this work fails to attain the asymptotic results above. Our
converse proofs rely on a recently established upper bound for secret key
lengths. Both our lower and upper bounds are derived in a single-shot setup and
the asymptotic results are obtained as corollaries