  In this paper, we consider the Gaussian diamond-wiretap channel that consists
of an orthogonal broadcast channel from a source to two relays and a Gaussian
fast-fading multiple access-wiretap channel from the two relays to a legitimate
destination and an eavesdropper. For the multiple access part, we consider both
the case with full channel state information (CSI) and the case with no
eavesdropper's CSI, at the relays and the legitimate destination. For both the
cases, we establish the exact secure degrees of freedom and generalize the
results for multiple relays.
  For the converse part, we introduce a new technique of capturing the
trade-off between the message rate and the amount of individual randomness
injected at each relay. In the achievability part, we show (i) how to strike a
balance between sending message symbols and common noise symbols from the
source to the relays in the broadcast component and (ii) how to combine
artificial noise-beamforming and noise-alignment techniques at the relays in
the multiple access component. In the case with full CSI, we propose a scheme
where the relays simultaneously beamform common noise signals in the null space
of the legitimate destination's channel, and align them with the message
signals at the eavesdropper. In the case with no eavesdropper's CSI, we present
a scheme that efficiently utilizes the broadcast links by incorporating
computation between the message and common noise symbols at the source.
Finally, most of our achievability and converse techniques can also be adapted
to the Gaussian (non-fading) channel model.
