We describe new fast algorithms for evaluation and interpolation on the “novel” polynomial basis over finite fields of characteristic two introduced by Lin et al. (2014). Fast algorithms are also described for converting between their basis and the monomial basis, as well as for converting to and from the Newton basis associated with the evaluation points of the evaluation and interpolation algorithms. Combining algorithms yields a new truncated additive fast Fourier transform (FFT) and inverse truncated additive FFT which improve upon some previous algorithms when the field possesses an appropriate tower of subfields.

中文翻译：

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快速转换特征二的有限域

我们描述了由Lin等人介绍的特征2的有限域上基于“新颖”多项式的评估和插值新的快速算法。（2014）。还描述了快速算法，用于在其基础和单项基础之间进行转换，以及与评估和内插算法的评估点关联的牛顿基础之间的转换。组合算法产生了新的截断加性快速傅里叶变换（FFT）和逆截断加性FFT，当该场具有适当的子场塔时，它们会改进一些以前的算法。