In 2008, Kedlaya and Umans designed the first multivariate multi-point evaluation algorithm over finite fields with an asymptotic complexity that can be made arbitrarily close to linear. However, it remains a major challenge to make their algorithm efficient for practical input sizes. In this paper, we revisit and improve their algorithm, while keeping this ultimate goal in mind. In addition we sharpen the known complexity bounds for modular composition of univariate polynomials over finite fields.

中文翻译：

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快速多变量多点评估

在2008年，Kedlaya和Umans在有限域上设计了第一个多元渐近评估算法，其渐近复杂度可以任意逼近线性。然而，使它们的算法对于实际输入大小有效仍然是一个重大挑战。在本文中，我们在牢记这一最终目标的同时重新审视和改进了它们的算法。此外，我们对有限域上单变量多项式的模数合成的已知复杂性界限进行了改进。