Composition modulo powers of polynomials

Abstract : Modular composition is the problem to compose 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 paper, we study the more specific case of composition modulo the power of a polynomial. First we extend previously known algorithms for power series composition to this context. We next present a fast direct reduction of our problem to power series composition.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01455722
Contributeur : Joris Van Der Hoeven <>
Soumis le : jeudi 27 avril 2017 - 22:04:10
Dernière modification le : mardi 2 mai 2017 - 14:40:48

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  • HAL Id : hal-01455722, version 2

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Joris Van Der Hoeven, Grégoire Lecerf. Composition modulo powers of polynomials. 2017. <hal-01455722v2>

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