The Sender-Excited Secret Key Agreement Model: Capacity and Error Exponents

Details The Sender-Excited Secret Key Agreement Model: Capacity and Error Exponents The Sender-Excited Secret Key Agreement Model: Capacity and Error Exponents

2011-07-21

arxiv.org/abs/1107.4148v2

Computer Science

Information Theory

Submitted to the IEEE Transactions on Information Theory; Minor changes to proof of Lemma 9

Scientific paper

We consider fundamental limits of the secret key generation problem when the sources are randomly excited by the sender and there is a noiseless public discussion channel. In many practical communication settings, the sources or channels may be influenced by some parties involved. Similar to recent works on probing capacity and channels with action-dependent states, our system model captures such a scenario. We derive single-letter expressions for the secret key capacity. Our coding strategy involves wiretap channel coding and a key generation scheme. We show that the secret key capacity is composed of both source- and channel-type randomness. By assuming that the eavesdropper receives a degraded version of the legitimate receiver's observation, we also obtain a capacity result that does not involve any auxiliary random variables, and thus it is amenable to numerical evaluation. By evaluating the capacity for several degraded channels, we show that there is a fundamental interplay between the portion of the secret key rate that can be derived from common randomness and that from wiretap secrecy. In addition, we derive lower bounds on the achievable reliable and secrecy exponents. These exponents allow us to determine the set of strongly-achievable secret key rates. Our exponents explicitly capture the twin effects of the channel and the source in the model. The exponents can be specialized to previously known results. We also demonstrate that there is an inherent tradeoff between the achievable reliability and secrecy exponents.

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