'Secret-key Agreement with Channel State Information at the Transmitter'
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Introduction
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Secret keys are a fundamental requirement for any application involving secure communication or computation. An information theoretic approach to secret key generation between two or more terminals was pioneered in [@maurer:93; @ahlswedeCsiszar:93] and subsequently extended in [@CsiszarNarayan:04; @CsiszarNarayan:10; @Gohari:1; @Gohari:2]. In the setup considered in these works, the transmitter communicates to a legitimate receiver and the eavesdropper over a memoryless broadcast channel and is interested in generating a secret key shared with the legitimate receiver. The legitimate terminals can also exchange an unlimited number of messages over a public channel. There has been a significant interest in developing practical approaches for generating shared secret keys between two or more terminals based on such techniques, see e.g., [@wilsonTseScholtz:07; @pap1; @pap2; @pap3; @pap4; @pap5; @pap6; @mathur] and references therein.

In the present work, we study the secret key agreement capacity over a broadcast channel controlled by a random state variable. The importance of studying channels with state parameters [@shannon:58; @gelfandPinsker:80; @wolfowitz:coding] has become increasingly evident in recent times due a variety of applications including fading channels [@caireShamai99], broadcast channels [@caireShamai:01] and digital watermaking [@chenWornell:01]. For example in fading channels, the 