Any ring isomorphism between fully-split (or same-factorization-structure) PLWE rings reduces evaluation-based root attacks to the original roots and always distorts samples enough to prevent new distinguishability.
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Extensions of root-based attacks against PLWE via isomorphisms of rings
Any ring isomorphism between fully-split (or same-factorization-structure) PLWE rings reduces evaluation-based root attacks to the original roots and always distorts samples enough to prevent new distinguishability.