On the Secret-Key Rate of Binary Random Variables

Martin Gander and Ueli Maurer


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.