  We consider the Gaussian wiretap channel, where two legitimate players Alice
and Bob communicate over an additive white Gaussian noise (AWGN) channel, while
Eve is eavesdropping, also through an AWGN channel. We propose a coding
strategy based on lattice coset encoding. We analyze Eve's probability of
decoding, from which we define the secrecy gain as a design criterion for
wiretap lattice codes, expressed in terms of the lattice theta series, which
characterizes Eve's confusion as a function of the channel parameters. The
secrecy gain is studied for even unimodular lattices, and an asymptotic
analysis shows that it grows exponentially in the dimension of the lattice.
Examples of wiretap lattice codes are given. Interestingly, minimizing Eve's
probability of error involves the same optimization of the theta series as does
the flatness factor, another newly defined code design that characterizes
lattice codes that achieve strong secrecy.
