Secrecy gain of Gaussian wiretap codes from unimodular lattices

Abstract

We consider lattice coding over a Gaussian wiretap

channel, where an eavesdropper listens to the transmissions

between a transmitter and a legitimate receiver. In [1], a new

lattice invariant called the secrecy gain was introduced as a code

design criterion for wiretap lattice codes, shown to characterize

the confusion that a chosen lattice code can cause at the

eavesdropper: the higher the secrecy gain of the lattice, the

more confusion. In this paper, a formula for the secrecy gain

of unimodular lattices is derived. Secrecy gains of extremal odd

unimodular lattices as well as unimodular lattices in dimension

16 are computed and compared. Finally, best wiretap lattice codes

coming from unimodular lattices in dimension n, 8 ≤ n ≤ 16

are classified.