Subquadratic Polynomial Multiplication over GF(2m) Using Trinomial Bases and Chinese Remaindering

  • Éric Schost
  • Arash Hariri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5381)

Abstract

Following the previous work by Bajard-Didier-Kornerup, McLaughlin, Mihailescu and Bajard-Imbert-Jullien, we present an algorithm for modular polynomial multiplication that implements the Montgomery algorithm in a residue basis; here, as in Bajard et al.’s work, the moduli are trinomials over \({\mathbb{F}}_2\). Previous work used a second residue basis to perform the final division. In this paper, we show how to keep the same residue basis, inspired by l’Hospital rule. Additionally, applying a divide-and-conquer approach to the Chinese remaindering, we obtain improved estimates on the number of additions for some useful degree ranges.

Keywords

Montgomery multiplication Chinese remainder theorem finite fields subquadratic area complexity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Éric Schost
    • 1
  • Arash Hariri
    • 2
  1. 1.ORCCA, Computer Science DepartmentThe University of Western OntarioLondon, OntarioCanada
  2. 2.Department of Electrical and Computer EngineeringThe University of Western OntarioLondon, OntarioCanada

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