Secrecy gain, flatness factor, and secrecy-goodness of even unimodular lattices

Nested lattices Ae ⊂ Ab have previously been studied for coding in the Gaussian wiretap channel and two design criteria, namely, the secrecy gain and flatness factor, have been proposed to study how the coarse lattice Ae should be chosen so as to maximally conceal the message against the eavesdropper. In this paper, we study the connection between these two criteria and show the secrecy-goodness of even unimodular lattices, which means exponentially vanishing flatness factor as the dimension grows.