Secret Key Agreement: General Capacity and Second-Order Asymptotics
This addresses secure communication for parties needing shared secret keys, offering a non-incremental advance by enabling interactive protocols to reach theoretical limits.
The paper tackles the problem of secret key agreement via interactive public communication, proposing a new protocol that achieves the general secret key capacity and second-order asymptotic term for i.i.d. observations, unlike prior one-way methods.
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.