  Recent results have shown that structured codes can be used to construct good
channel codes, source codes and physical layer network codes for Gaussian
channels. For Gaussian channels with secrecy constraints, however, efforts to
date rely on random codes. In this work, we advocate that structured codes are
useful for providing secrecy, and show how to compute the secrecy rate when
structured codes are used. In particular, we solve the problem of bounding
equivocation rates with one important class of structured codes, i.e., nested
lattice codes. Having established this result, we next demonstrate the use of
structured codes for secrecy in two-user Gaussian channels. In particular, with
structured codes, we prove that a positive secure degree of freedom is
achievable for a large class of fully connected Gaussian channels as long as
the channel is not degraded. By way of this, for these channels, we establish
that structured codes outperform Gaussian random codes at high SNR. This class
of channels include the two-user multiple access wiretap channel, the two-user
interference channel with confidential messages and the two-user interference
wiretap channel. A notable consequence of this result is that, unlike the case
with Gaussian random codes, using structured codes for both transmission and
cooperative jamming, it is possible to achieve an arbitrary large secrecy rate
given enough power.
