We describe a decisional attack against a version of the PLWE problem in which the samples are taken from a certain proper subring of large dimension of the cyclotomic ring $\mathbb{F}_q[x]/(\Phi_{p^k}(x))$ with $k>1$ in the case where $q\equiv 1\pmod{p}$ but $\Phi_{p^k}(x)$ is not totally split over $\mathbb{F}_q$. Our attack uses the fact that the roots of $\Phi_{p^k}(x)$ over suitable extensions of $\mathbb{F}_q$ have zero-trace and has overwhelming success probability as a function of the number of input samples. An implementation in Maple and some examples of our attack are also provided.

翻译：我们描述了一种针对PLWE问题特定版本的决定性攻击，其中样本取自循环域$\mathbb{F}_q[x]/(\Phi_{p^k}(x))$（$k>1$）中某一大维数真子环，且满足条件$q\equiv 1\pmod{p}$但$\Phi_{p^k}(x)$在$\mathbb{F}_q$上非完全分裂。该攻击利用$\Phi_{p^k}(x)$在$\mathbb{F}_q$的适当扩域上的根具有零迹这一性质，其成功概率随输入样本数量增加而趋于完全。文中还给出了Maple实现及若干攻击实例。