Fast integer multiplication using generalized Fermat primes - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Mathematics of Computation Année : 2019

Fast integer multiplication using generalized Fermat primes

Résumé

For almost 35 years, Schönhage-Strassen's algorithm has been the fastest algorithm known for multiplying integers, with a time complexity O(n · log n · log log n) for multiplying n-bit inputs. In 2007, Fürer proved that there exists K > 1 and an algorithm performing this operation in O(n · log n · K log n). Recent work by Harvey, van der Hoeven, and Lecerf showed that this complexity estimate can be improved in order to get K = 8, and conjecturally K = 4. Using an alternative algorithm, which relies on arithmetic modulo generalized Fermat primes, we obtain conjecturally the same result K = 4 via a careful complexity analysis in the deterministic multitape Turing model.
Fichier principal
Vignette du fichier
furer.pdf (425.93 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01108166 , version 1 (22-01-2015)
hal-01108166 , version 2 (28-01-2016)
hal-01108166 , version 3 (10-08-2017)
hal-01108166 , version 4 (13-04-2018)

Identifiants

Citer

Svyatoslav Covanov, Emmanuel Thomé. Fast integer multiplication using generalized Fermat primes. Mathematics of Computation, 2019, 88 (317), pp.1449-1477. ⟨10.1090/mcom/3367⟩. ⟨hal-01108166v4⟩
1129 Consultations
1397 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More