Information-Theoretic Secret-Key Agreement: The Asymptotically Tight Relation Between the Secret-Key Rate and the Channel Quality Ratio

Information-theoretic secret-key agreement between two parties Alice and Bob is a well-studied problem that is provably impossible in a plain model with public (authenticated) communication, but is known to be possible in a model where the parties also have access to some correlated randomness. One particular type of such correlated randomness is the so-called satellite setting, where uniform random bits (e.g., sent by a satellite) are received by the parties and the adversary Eve over inherently noisy channels. The antenna size determines the error probability, and the antenna is the adversary’s limiting resource much as computing power is the limiting resource in traditional complexity-based security. The natural assumption about the adversary is that her antenna is at most Q times larger than both Alice’s and Bob’s antenna, where, to be realistic, Q can be very large.