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We study the signal sets for information theoretically secure key agreement with public discussion over the Gaussian and flat fading channels. Alice transmits signals to Bob over a noisy channel while Eve receives signals through an independent noisy channel. By utilizing this noisy resource, Alice and Bob wish to share a secret key on which Eve has a negligible amount of information. We present a protocol that allows Alice and Bob to share a common secret information, and encompass the signal sets for an efficient protocol in information theoretic sense.