  Recent results have shown that lattice codes can be used to construct good
channel codes, source codes and physical layer network codes for Gaussian
channels. On the other hand, for Gaussian channels with secrecy constraints,
efforts to date rely on random codes. In this work, we provide a tool to bridge
these two areas so that the secrecy rate can be computed when lattice codes are
used. In particular, we address the problem of bounding equivocation rates
under nonlinear modulus operation that is present in lattice encoders/decoders.
The technique is then demonstrated in two Gaussian channel examples: (1) a
Gaussian wiretap channel with a cooperative jammer, and (2) a multi-hop line
network from a source to a destination with untrusted intermediate relay nodes
from whom the information needs to be kept secret. In both cases, lattice codes
are used to facilitate cooperative jamming. In the second case, interestingly,
we demonstrate that a non-vanishing positive secrecy rate is achievable
regardless of the number of hops.
