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On the Efficiency of Scalar Multiplication on the Elliptic Curves

  • Siham Ezzouak
  • Abdelmalek Azizi
Conference paper
Part of the Smart Innovation, Systems and Technologies book series (SIST, volume 111)

Abstract

The scalar multiplication or point multiplication is the main computationnal operation in the most known cryptosystems based on elliptic curves. Therefore, relevant methods have been studied over centuries. This paper give a detailed study of the efficiency issues in scalar multiplication on the elliptic curves. First, we describe significant speedups in point multiplication. Second, we show that more optimizations can be achieved when better combination of multiplication methods for elliptic curves are performed.

Keywords

Elliptic curves Jacobian coordinate Chudnovasky coordinate Binary method NAF method Scalar multiplication 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Laboratory LAGA, Faculty of SciencesDhar El Mahraz Sidi Mohamed Ben Abdellah UniversityFesMorocco
  2. 2.Laboratory ACSA, Faculty of ScienceUniversity Mohammed First Oujda MoroccoOujdaMorocco

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