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The paper The Relationship between Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms contains some results of interest, although they are somewhat technical.
Specifically, it needs:
Smoothness Assumption: For $n\in\mathbb{N}$, define
$\nu(n)$ to be the minimum, over $d\in [n-2\sqrt{n}+1, n+2\sqrt{n}+1]$ of the largest prime factor of $d$...
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Section 4 of [P16] is perhaps the key section to read. I quote it below:
We stress that all these insecure instantiations—excepting [EHL14], for which the following conclusions still apply—are for the “non-dual” version of Ring-LWE with spherical Gaussian errors relative to $R$ (in the canonical embedding). By contrast, the definition of Ring-LWE from [...
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