Faster polynomial multiplication over finite fields

David Harvey (1) , Joris van der Hoeven (2) , Grégoire Lecerf (3)

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

Let p be a prime, and let M_p(n) denote the bit complexity of multiplying two polynomials in F_p[X] of degree less than n. For n large compared to p, we establish the bound M_p(n)=O(n log n 8^(log^∗ n) log p), where log^∗ is the iterated logarithm. This is the first known Fürer-type complexity bound for F_p[X], and improves on the previously best known bound M_p(n)=O(n log n log log n log p).

Mots clés: Polynomial multiplication; finite field; algorithm; complexity bound; FFT

Domaines: Logiciel mathématique [cs.MS]

David Harvey, Joris van der Hoeven, Grégoire Lecerf. Faster polynomial multiplication over finite fields. 2014. ⟨hal-01022757v2⟩