分圆域上的RLWE与PLWE不等价
RLWE and PLWE over cyclotomic fields are not equivalent
摘要：
证明了分圆域$\mathbb{Q}(ζ_n)$上的带误差环学习（RLWE）和带误差多项式学习（PLWE）问题是不等价的.准确地说，我们表明，减少一个问题，以其他增加了噪音的一个因素，是超过多项式在$n$。我们这样做是通过提供一个下界，持有无穷多个正整数$n$，为条件数的范德蒙矩阵的$n$ th分圆多项式。
英文摘要：
We prove that the Ring Learning With Errors (RLWE) and the Polynomial Learning With Errors (PLWE) problems over the cyclotomic field $\mathbb{Q}(ζ_n)$ are not equivalent. Precisely, we show that reducing one problem to the other increases the noise by a factor that is more than polynomial in $n$. We do so by providing a lower bound, holding for infinitely many positive integers $n$, for the condition number of the Vandermonde matrix of the $n$th cyclotomic polynomial.
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