  In this paper we propose a two-way protocol of physical layer security using
the method of privacy amplification against eavesdroppers. First we justify our
proposed protocol by analyzing the physical layer security provided by the
classic wiretap channel model (i.e. one-way protocol). In the Gaussian
channels, the classic one-way protocol requires Eve's channel to be degraded
w.r.t. Bob's channel. However, this channel degradation condition depends on
Eve's location and whether Eve's receiving antenna is more powerful than Bob's.
To overcome this limitation, we introduce a two-way protocol inspired in IEEE
TIT (1993) that eliminates the channel degradation condition.
  In the proposed two-way protocol, on a first phase, via Gaussian channel, Bob
sends randomness to Alice, which is partially leaked to Eve. Then, on a second
phase, Alice transmits information to Bob over a public noiseless channel. We
derive the secrecy capacity of the two-way protocol when the channel to Eve is
also Gaussian. We show that the capacity of the two-way protocol is always
positive. We present numerical values of the capacities illustrating the gains
obtained by our proposed protocol. We apply our result to simple yet realistic
models of satellite communication channels.
