论文标题
RLWE和PLWE在循环组磁场上不相同
RLWE and PLWE over cyclotomic fields are not equivalent
论文作者
论文摘要
我们证明，通过错误（rlwe）和多项式学习的环学习（PLWE）问题（PLWE）问题在环形磁场上$ \ mathbb {q}（ζ_N）$不是等效的。确切地说，我们表明将一个问题减少到另一个问题会使噪声增加的因素不仅仅是$ n $中的多项式。我们这样做是通过为无限的许多正整数$ n $提供的下限，为$ n $ th Cyclotomic多项式的Vandermonde矩阵的状况编号。
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.
