Security considerations for Galois non-dual RLWE families

We explore further the hardness of the non-dual discrete variant
of the Ring-LWE problem for various number rings, give improved
attacks for certain rings satisfying some additional assumptions, construct
a new family of vulnerable Galois number fields, and apply some
number theoretic results on Gauss sums to deduce the likely failure of
these attacks for 2-power cyclotomic rings and unramified moduli.