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

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.

💡 Research Summary

This paper studies secret‑key generation in a setting where the legitimate transmitter (Alice) can actively influence the state of a discrete memoryless broadcast channel (DMBC) by sending a sounding sequence that is generated from a private random source. After the channel use, Alice observes her own channel output, forms a one‑way public message, and transmits it over a noiseless public discussion link that is also observed by the legitimate receiver (Bob) and the eavesdropper (Eve). Bob, using his channel output together with the public message, must recover a key that matches Alice’s key, while Eve should learn essentially nothing about the key.

The authors first derive a single‑letter expression for the secret‑key capacity under an average cost constraint on the excitation sequence. The capacity is
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