Unimodular Lattices for the Gaussian Wiretap Channel

Abstract

In a recent paper, the authors introduced a lattice invariant called "Secrecy Gain" which measures the confusion experienced by a passive eavesdropper on the Gaussian Wiretap Channel. We study, here, the behavior of this invariant for unimodular lattices by using tools from Modular Forms and show that, for some families of unimodular lattices, indexed by the dimension, the secrecy gain exponentially goes to infinity with the dimension.

6 pages, 9 figures, 2010 Information Theory Workshop, Dublin

References in corpus (2)

• Providing Secrecy With Structured Codes: Tools and Applications to Two-User Gaussian Channels
• Reduction mod $\ell$ of Theta Series of Level ${\ell }^n$

Cited by in corpus (9)

• A Classification of Unimodular Lattice Wiretap Codes in Small Dimensions
• On a conjecture by Belfiore and Solé on some lattices
• Nonasymptotic Probability Bounds for Fading Channels Exploiting Dedekind Zeta Functions
• On the Eavesdropper's Correct Decision in Gaussian and Fading Wiretap Channels Using Lattice Codes
• On the secrecy gain of $\ell$-modular lattices
• Lattice Code Design for the Rayleigh Fading Wiretap Channel
• Some results related to the conjecture by Belfiore and Solé
• Probability Estimates for Fading and Wiretap Channels from Ideal Class Zeta Functions
• 2- and 3-modular Lattice Wiretap Codes in Small Dimensions