Fast Polynomial Multiplication over F_(2^60)

David Harvey (1) , Joris van der Hoeven (2) , Grégoire Lecerf (2)

1 UNSW - School of Mathematics and Statistics [Sydney]
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

Can post-Schönhage–Strassen multiplication algorithms be competitive in practice for large input sizes? So far, the GMP library still outperforms all implementations of the recent, asymptotically more efficient algorithms for integer multiplication by Fürer, De–Kurur–Saha–Saptharishi, and ourselves. In this paper, we show how central ideas of our recent asymptotically fast algorithms turn out to be of practical interest for multiplication of polynomials over finite fields of characteristic two. Our Mathemagix implementation is based on the automatic generation of assembly codelets. It outperforms existing implementations in large degree, especially for polynomial matrix multiplication over finite fields.

Mots clés: Finite fields; Polynomial multiplication; Mathemagix

Domaines: Calcul formel [cs.SC]

David Harvey, Joris van der Hoeven, Grégoire Lecerf. Fast Polynomial Multiplication over F_(2^60). 2016. ⟨hal-01265278⟩