The Sender-Excited Secret Key Agreement Model: Capacity, Reliability and Secrecy Exponents

TL;DR

This paper introduces a new secret key agreement model where the sender excites sources to generate keys, deriving capacity and exponents, and proposing a coding scheme that combines wiretap coding and key extraction for improved performance.

Contribution

It presents a novel secret key agreement model with sender excitation, deriving capacity and exponents, and introduces a combined coding scheme for enhanced key rates under constraints.

Findings

Derived single-letter expressions for secret key capacity.

Established lower bounds on reliability and secrecy exponents.

Proposed a coding scheme combining wiretap coding and key extraction.

Abstract

We consider the secret key generation problem when sources are randomly excited by the sender and there is a noiseless public discussion channel. Our setting is thus similar to recent works on channels with action-dependent states where the channel state may be influenced by some of the parties involved. We derive single-letter expressions for the secret key capacity through a type of source emulation analysis. We also derive lower bounds on the achievable reliability and secrecy exponents, i.e., the exponential rates of decay of the probability of decoding error and of the information leakage. These exponents allow us to determine a set of strongly-achievable secret key rates. For degraded eavesdroppers the maximum strongly-achievable rate equals the secret key capacity; our exponents can also be specialized to previously known results. In deriving our strong achievability results we introduce a coding scheme that combines wiretap coding (to excite the channel) and key extraction (to distill keys from residual randomness). The secret key capacity is naturally seen to be a combination of both source- and channel-type randomness. Through examples we illustrate a fundamental interplay between the portion of the secret key rate due to each type of randomness. We also illustrate inherent tradeoffs between the achievable reliability and secrecy exponents. Our new scheme also naturally accommodates rate limits on the public discussion. We show that under rate constraints we are able to achieve larger rates than those that can be attained through a pure source emulation strategy.