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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