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)


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.


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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