I've got no idea what "ATA Enhanced Erase" is, but if I'm not mistaken, I
know of 2 ways of deleting a drive.
One is the overwriting with zeroes thing. It takes a long time, but basically
removes all data.
The other method I know of (which I think is more commonly used) is that it
simply makes a computer think there's blank space where there isn't which, if
that "blank" space is used, it will only take place by the data that was
already present being overwritten (with no dramas whatsoever). The data
that's not yet overwritten can still be recovered using file recovery
software.
http://www.dedoimedo.com/computers/low-level-formatting.html
"But I cannot securely erase my whole HDD using Trsiquel"
I assume you mean from the live session. If so, does installing GParted and
erasing using that help?