Modular composition via factorization

Abstract : Modular composition is the problem to compute the composition of two univariate polynomials modulo a third one. For polynomials with coefficients in a finite field, Kedlaya and Umans proved in 2008 that the theoretical bit complexity for performing this task could be made arbitrarily close to linear. Unfortunately, beyond its major theoretical impact, this result has not led to practically faster implementations yet. In this article, we explore particular cases of moduli over finite fields for which modular composition turns out to be cheaper than in the general case. In the most favourable cases, our algorithms achieve quasi-linear costs.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01457074
Contributeur : Joris Van Der Hoeven <>
Soumis le : lundi 27 mars 2017 - 11:11:30
Dernière modification le : mercredi 29 mars 2017 - 01:09:19
Document(s) archivé(s) le : mercredi 28 juin 2017 - 13:16:49

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  • HAL Id : hal-01457074, version 2

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Joris Van Der Hoeven, Grégoire Lecerf. Modular composition via factorization. 2017. 〈hal-01457074v2〉

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