  We propose a new scheme of wiretap lattice coding that achieves semantic
security and strong secrecy over the Gaussian wiretap channel. The key tool in
our security proof is the flatness factor which characterizes the convergence
of the conditional output distributions corresponding to different messages and
leads to an upper bound on the information leakage. We not only introduce the
notion of secrecy-good lattices, but also propose the {flatness factor} as a
design criterion of such lattices. Both the modulo-lattice Gaussian channel and
the genuine Gaussian channel are considered. In the latter case, we propose a
novel secrecy coding scheme based on the discrete Gaussian distribution over a
lattice, which achieves the secrecy capacity to within a half nat under mild
conditions. No \textit{a priori} distribution of the message is assumed, and no
dither is used in our proposed schemes.
