Efficient scalar multiplications on elliptic curves with direct computations of several doublings

Yasuyuki Sakai, Kouichi Sakurai

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We introduce efficient algorithms for scalar multiplication on elliptic curves defined over IFp. The algorithms compute 2kP directly from P, where P is a random point on an elliptic curve, without computing the intermediate points, which is faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves, and analyze their computational complexity. As a result of their implementation with respect to affine (resp. weighted projective) coordinates, we achieved an increased performance factor of 1.45 (45%) (resp. 1.15 (15%)) in the scalar multiplication of the elliptic curve of size 160-bit.

Original languageEnglish
Pages (from-to)120-129
Number of pages10
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
VolumeE84-A
Issue number1
Publication statusPublished - Jan 1 2001
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Electrical and Electronic Engineering
  • Applied Mathematics

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