Frobenius Additive Fast Fourier Transform

Li, Wen-Ding; Chen, Ming-Syan; Kuo, Po-Chun; Cheng, Chen-Mou; Yang, Bo‐Yin

doi:10.48550/arxiv.1802.03932

Cited by 1 publication

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References 14 publications

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“…To avoid confusion, we refer to such algorithms as multiplicative FFTs hereafter. Additive FFTs have been investigated as an alternative to multiplicative FFTs for use in fast multiplication algorithms for binary polynomials [28,6,23,8,9,18], and have also found applications in coding theory and cryptography [4,3,10,1].…”

Section: Introductionmentioning

confidence: 99%

Fast Hermite interpolation and evaluation over finite fields of characteristic two

Coxon

2020

Journal of Symbolic Computation

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An additive fast Fourier transform over a finite field of characteristic two efficiently evaluates polynomials at every element of an F 2 -linear subspace of the field. We view these transforms as performing a change of basis from the monomial basis to the associated Lagrange basis, and consider the problem of performing the various conversions between these two bases, the associated Newton basis, and the "novel" basis of Lin, Chung and Han (FOCS 2014). Existing algorithms are divided between two families, those designed for arbitrary subspaces and more efficient algorithms designed for specially constructed subspaces of fields with degree equal to a power of two. We generalise techniques from both families to provide new conversion algorithms that may be applied to arbitrary subspaces, but which benefit equally from the specially constructed subspaces. We then construct subspaces of fields with smooth degree for which our algorithms provide better performance than existing algorithms.

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Section: Introductionmentioning

confidence: 99%

Fast Hermite interpolation and evaluation over finite fields of characteristic two

Coxon

2020

Journal of Symbolic Computation

View full text Add to dashboard Cite

show abstract

Frobenius Additive Fast Fourier Transform

Cited by 1 publication

References 14 publications

Fast Hermite interpolation and evaluation over finite fields of characteristic two

Fast Hermite interpolation and evaluation over finite fields of characteristic two

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