  Efficiency is a key issue in any real implementation of a cryptographic
protocol since the physical resources are not unlimited. We will first show
that Quantum Key Distribution is possible with an "Entanglement based" scheme
with NPPT symmetric Gaussian states in spite of the fact that these systems
cannot be distilled with Gaussian operations (they are all bound entangled). In
this work we analyze the secrecy properties of Gaussian states under Gaussian
operations. Although such operations are useless for quantum distillation, we
prove that it is possible to distill efficiently a secret key secure against
finite coherent attacks from sufficiently entangled Gaussian states with
non-positive partial transposition. Moreover, all such states allow for
efficient key distillation, when the eavesdropper is assumed to perform
individual attacks before in an efficient way.
