  Polar lattices, which are constructed from polar codes, are provably good for
the additive white Gaussian noise (AWGN) channel. In this work, we propose a
new polar lattice construction that achieves the secrecy capacity under the
strong secrecy criterion over the mod-$\Lambda$ Gaussian wiretap channel. This
construction leads to an AWGN-good lattice and a secrecy-good lattice
simultaneously. The design methodology is mainly based on the equivalence in
terms of polarization between the $\Lambda/\Lambda'$ channel in lattice coding
and the equivalent channel derived from the chain rule of mutual information in
multilevel coding.
