Composition modulo powers of polynomials

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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.

Original languageEnglish
Title of host publicationISSAC 2017 - Proceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation
EditorsMichael Burr
PublisherAssociation for Computing Machinery
Pages445-452
Number of pages8
ISBN (Electronic)9781450350648
DOIs
Publication statusPublished - 23 Jul 2017
Event42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017 - Kaiserslautern, Germany
Duration: 25 Jul 201728 Jul 2017

Publication series

NameProceedings of the International Symposium on Symbolic and Algebraic Computation, ISSAC
VolumePart F129312

Conference

Conference42nd ACM International Symposium on Symbolic and Algebraic Computation, ISSAC 2017
Country/TerritoryGermany
CityKaiserslautern
Period25/07/1728/07/17

Keywords

  • Algorithm
  • Complexity
  • Modular composition
  • Series composition

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