有限域上通过低阶单位根的稀疏插值
Sparse interpolation over finite fields via low-order roots of unity
摘要：
我们提出了一个新的Monte Carlo算法插值的直线程序作为一个稀疏多项式$f$在任意有限域的大小$q$。我们假设先验界$D$和$T$的程度和数量的$f$。本文提出的方法是一个混合的多样性和递归插值算法，这两个以前最快的已知概率方法，这个问题。通过有效地利用系数本身所包含的信息，该新算法通过$T$、$\log D$或$\log q$的“软Oh”因子改进了先前方法的比特复杂度。
英文摘要：
We present a new Monte Carlo algorithm for the interpolation of a straight-line program as a sparse polynomial $f$ over an arbitrary finite field of size $q$. We assume a priori bounds $D$ and $T$ are given on the degree and number of terms of $f$. The approach presented in this paper is a hybrid of the diversified and recursive interpolation algorithms, the two previous fastest known probabilistic methods for this problem. By making effective use of the information contained in the coefficients themselves, this new algorithm improves on the bit complexity of previous methods by a "soft-Oh" factor of $T$, $\log D$, or $\log q$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
