论文标题
在rlwe/plwe上的环数字字段
On the RLWE/PLWE equivalence for cyclotomic number fields
论文作者
论文摘要
我们研究环学习与误差和多项式学习之间的等效性，以及对于环形数字字段的错误问题：我们证明，只要划分导体的不同数量的数量保持恒定，我们就会证明，通过多项式噪声增加了这两个问题。我们在最多三个素数可排除的情况下完善我们的界限，并且我们给出了一个渐近的次指定公式，以适用于所附的vandermonde矩阵的条件数，对任意程度有效。
We study the equivalence between the Ring Learning With Errors and Polynomial Learning With Errors problems for cyclotomic number fields,namely: we prove that both problems are equivalent via a polynomial noise increase as long as the number of distinct primes dividing the conductor is kept constant. We refine our bound in the case where the conductor is divisible by at most three primes and we give an asymptotic subexponential formula for the condition number of the attached Vandermonde matrix valid for arbitrary degree.
