Classification of all the minimal bilinear algorithms for computing the coefficients of the product of two polynomials modulo a polynomial

Amir Averbuch, Shmuel Winograd, Zvi Galil

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

In view of the results of Theorems III.1 and Theorem III.2, all the minimal bilinear algorithms for computing the coefficients of R(u)S(u) mod Q(u)l have multiplications of the form R(αj)S(αj) hence the algorithm requires large coefficients (as in l=1). Therefore using the identity R(u)S(u)=R(u)S(u) mod P(u) where degP(u)=2n − 1 with distinct irreducible, but not necessarily only linear, factors, does not reduce the large coefficients generated by the algorithm. In order to achieve better "practical" algorithms, non-minimal algorithms should be studied. In addition, classification of all the minimal algorithms for computing the coefficients of R(u)S(u) mod Q(u)l remains open.

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 13th International Colloquium, Proceedings
EditorsLaurent Kott
PublisherSpringer Verlag
Pages31-39
Number of pages9
ISBN (Print)9783540167617
DOIs
StatePublished - 1986
Externally publishedYes
Event13th International Colloquium on Automata, Languages and Programming, ICALP 1986 - Rennes, France
Duration: 15 Jul 198619 Jul 1986

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume226 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference13th International Colloquium on Automata, Languages and Programming, ICALP 1986
Country/TerritoryFrance
CityRennes
Period15/07/8619/07/86

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