On the power of multidoubling in speeding up elliptic scalar multiplication

Yasuyuki Sakai, Kouichi Sakurai

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We discuss multidoubling methods for efficient elliptic scalar multiplication. The methods allows computation of 2kP directly from P without computing the intermediate points, where P denotes a randomly selected point on an elliptic curve. We introduce algorithms for elliptic curves with Montgomery form and Weierstrass form defined over finite fields with characteristic greater than 3 in terms of affine coordinates. These algorithms are faster than k repeated doublings. Moreover, we apply the algorithms to scalar multiplication on elliptic curves and analyze computational complexity. As a result of our implementation with respect to the Montgomery and Weierstrass forms in terms of affine coordinates, we achieved running time reduced by 28% and 31%, respectively, in the scalar multiplication of an elliptic curve of size 160-bit over finite fields with characteristic greater than 3.

Original languageEnglish
Title of host publicationSelected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers
EditorsSerge Vaudenay, Amr M. Youssef
PublisherSpringer Verlag
Pages268-283
Number of pages16
ISBN (Print)9783540430667
Publication statusPublished - Jan 1 2001
Event8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001 - Toronto, Canada
Duration: Aug 16 2001Aug 17 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2259
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other8th Annual International Workshop on Selected Areas in Cryptography, SAC 2001
CountryCanada
CityToronto
Period8/16/018/17/01

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Sakai, Y., & Sakurai, K. (2001). On the power of multidoubling in speeding up elliptic scalar multiplication. In S. Vaudenay, & A. M. Youssef (Eds.), Selected Areas in Cryptography - 8th Annual International Workshop, SAC 2001, Revised Papers (pp. 268-283). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2259). Springer Verlag.