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.

中文翻译：

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关于分圆数场的 RLWE/PLWE 等价

我们研究了分圆数域的带错误环学习和带错误多项式学习问题之间的等价性，即：我们证明，只要分割导体的不同素数的数量保持不变，通过多项式噪声增加，这两个问题是等价的。在导体最多可被三个素数整除的情况下，我们改进了我们的界限，并且我们给出了对任意次数有效的附加 Vandermonde 矩阵的条件数的渐近次指数公式。