A New Secrecy Function for Modular Lattices

Abstract

A recent line of work to improve the secrecy capacity within wiretap gaussian channel has introduced a new lattice invariant called secrecy gain. Belfiore and Sol´e made a conjecture about the point at which the the secrecy gain is maximum. Verified by most unimodular lattices, this conjecture does not hold in general for l-modular lattices (l ≥ 2). Ernvall-Hytönen modified the secrecy function and proved that it satisfies the conjecture for 2-odd modular lattices. In this paper, the authors introduce a new secrecy function for 2-modular lattices. They show that, by using the lattice D4 instead of Dl = Z⊕√lZ , the conjecture holds for both 2-even and odd modular lattices in dimension n ≥ 4. Using that result, they further prove that the modified secrecy function of A.-M. Ernvall-Hytönen holds for both 2-even and odd modular lattices.