Semantically Secure Lattice Codes for the Gaussian Wiretap Channel
Cong Ling, Laura Luzzi, Jean-Claude Belfiore and Damien
Stehlé
Abstract: We prove that nested lattice codes can achieve semantic
security and strong secrecy over the Gaussian wiretap channel. The key
tool in our 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 show the existence of lattice codes that are good
for secrecy, but also propose the flatness factor as a new design
criterion. Both the modulo-lattice Gaussian channel and the genuine
Gaussian channel are considered. In the latter case, we propose a new
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 a priori distribution of the
message is assumed, and no dither is used in our proposed
schemes.
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