On the eavesdropper´s correct decision in Gaussian and fading wiretap channels using lattice codes

In this paper, the probability of Eve the Eavesdropper´s correct decision is considered both in the Gaussian and Rayleigh fading wiretap channels when using lattice codes for the transmission. First, it is proved that the secrecy function determining Eve´s performance attains its maximum at y = 1 on all known extremal even unimodular lattices. This is a special case of a conjecture by Belfiore and Solé. Further, a very simple method to verify or disprove the conjecture on any given unimodular lattice is given. Second, preliminary analysis on the behavior of Eve´s probability of correct decision in the fast fading wiretap channel is provided. More specifically, we compute the truncated inverse norm power sum factors in Eve´s probability expression. The analysis reveals a performance-secrecy-complexity tradeoff: relaxing on the legitimate user´s performance can significantly increase the security of transmission. The confusion experienced by the eavesdropper may be further increased by using skewed lattices, but at the cost of increased complexity.