Lattice codes achieving strong secrecy over the mod-Λ Gaussian Channel

We consider a wiretap scenario where the main channel and eavesdropper's channel are modulo lattice Gaussian channels. We prove that nested lattice codes can achieve strong secrecy for this model, which gives considerable insights to tackle the genuine Gaussian wiretap channel. The key tool in our proof is an L
¹
convergence result for the conditional output distributions corresponding to different messages, which follows from the properties of the lattice Gaussian measure. No constraint on the a priori distribution of the message is imposed, which means that the proposed scheme is actually semantically secure. We not only show the existence of lattice codes that are good for secrecy, but also propose the flatness factor as a design criterion.