  This paper studies an untrusted relay channel, in which the destination sends
artificial noise simultaneously with the source sending a message to the relay,
in order to protect the source's confidential message. The traditional
amplify-and-forward (AF) scheme shows poor performance in this situation
because of the interference power dilemma: providing better security by using
stronger artificial noise will decrease the confidential message power from the
relay to the destination. To solve this problem, a modulo-and-forward (MF)
operation at the relay with nested lattice encoding at the source is proposed.
For this system with full channel state information at the transmitter (CSIT),
theoretical analysis shows that the proposed MF scheme approaches the secrecy
capacity within 1/2 bit for any channel realization, and hence achieves full
generalized security degrees of freedom (G-SDoF). In contrast, the AF scheme
can only achieve a small fraction of the G-SDoF. For this system without any
CSIT, the total outage event, defined as either connection outage or secrecy
outage, is introduced. Based on this total outage definition, analysis shows
that the proposed MF scheme achieves the full generalized secure diversity gain
(G-SDG) of order one. On the other hand, the AF scheme can only achieve a G-SDG
of 1/2 at most.
