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Pré-Publication, Document De Travail Année : 2015

Randomized root finding over finite fields using tangent Graeffe transforms

Résumé

Consider a finite field Fq whose multiplicative group has smooth cardinality. We study the problem of computing all roots of a polynomial that splits over Fq, which was one of the bottlenecks for fast sparse interpolation in practice. We revisit and slightly improve existing algorithms and then present new randomized ones based on the Graeffe transform. We report on our implementation in the Mathemagix computer algebra system, confirming that our ideas gain by an order of magnitude in practice.
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Dates et versions

hal-01104279 , version 1 (16-01-2015)

Identifiants

  • HAL Id : hal-01104279 , version 1

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Bruno Grenet, Joris van der Hoeven, Grégoire Lecerf. Randomized root finding over finite fields using tangent Graeffe transforms. 2015. ⟨hal-01104279⟩
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