On the Secret-Key Rate of Binary Random Variables

Consider a scenario in which two parties Alice and Bob as well as an opponent Eve receive the output of a binary symmetric source (e.g. installed in a satellite) over individual, not necessarily independent binary symmetric channels. Alice and Bob share no secret key initially and can only communicate over a public channel completely accessible to Eve. We derive a lower bound on the rate at which Alice and Bob can generate secret-key bits about which Eve has arbitrarily little information. This lower bound is strictly positive as long as Eve's binary symmetric channel is not perfect, even if Alice's and Bob's channels are by orders of magnitude less reliable than Eve's channel.