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Journal Articles Journal of Symbolic Computation Year : 2021

Fast transforms over finite fields of characteristic two

Transformées rapides sur les corps finis de caractéristique deux

Abstract

We describe new fast algorithms for evaluation and interpolation on the "novel" polynomial basis over finite fields of characteristic two introduced by Lin, Chung and Han (FOCS 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.
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Dates and versions

hal-01845238 , version 1 (20-07-2018)
hal-01845238 , version 2 (05-09-2019)
hal-01845238 , version 3 (22-01-2021)

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Nicholas Coxon. Fast transforms over finite fields of characteristic two. Journal of Symbolic Computation, 2021, 104, pp.824-854. ⟨10.1016/j.jsc.2020.10.002⟩. ⟨hal-01845238v3⟩
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