Journal
IEEE TRANSACTIONS ON INFORMATION THEORY
Volume 60, Issue 10, Pages 6399-6416Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2014.2343226
Keywords
Lattice coding; information theoretic security; strong secrecy; semantic security; wiretap channel
Funding
- FP7 Project Phylaws [EU FP7-ICT-317562]
- Royal Society International Joint Project
- Marie Curie Fellowship [PIEF-GA-2010-274765]
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We propose a new scheme of wiretap lattice coding that achieves semantic security and strong secrecy over the Gaussian wiretap channel. The key tool in our security 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 introduce the notion of secrecy-good lattices, but also propose the flatness factor as a design criterion of such lattices. Both the modulo-lattice Gaussian channel and genuine Gaussian channel are considered. In the latter case, we propose a novel 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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